key: cord- -t f kv authors: flores, marco v.; cohen, mark title: preventing airborne disease transmission: implications for patients during mechanical ventilation date: - - journal: noninvasive ventilation in high-risk infections and mass casualty events doi: . / - - - - _ sha: doc_id: cord_uid: t f kv the organisms causing respiratory infections such as influenza are spread in droplets or aerosols or by direct or indirect contact with contaminated surfaces. certain medical procedures have been termed aerosol generating because they are associated with high or augmented inspiratory and expiratory flows, which can increase microbial dissemination. invasive ventilation maneuvers and noninvasive ventilation (niv) fall into that category. we discuss the risk of transmitting these procedures and the strategies for mechanical ventilation in future airborne epidemics with special consideration given to the issue of protecting health care workers (hcws). the organisms causing respiratory infections such as infl uenza are spread in droplets or aerosols or by direct or indirect contact with contaminated surfaces. certain medical procedures have been termed aerosol generating because they are associated with high or augmented inspiratory and expiratory fl ows, which can increase microbial dissemination. invasive ventilation maneuvers and noninvasive ventilation (niv) fall into that category. we discuss the risk of transmitting these procedures and the strategies for mechanical ventilation in future airborne epidemics with special consideration given to the issue of protecting health care workers (hcws). pathogens in the air are spread on particles or droplets. the solid matter may come from skin, and the droplets may be generated from the upper or lower respiratory tract, mouth, or nose and under such circumstances as vomiting, dripping water taps, and diarrhea. respiratory droplets, which can carry microorganisms such as bacteria and viruses, constitute a medium for the transmission of infectious diseases. droplets from the nose and mouth contain bacteria but do not travel > m. the concept of airborne transmission and large droplet transmission is based on droplet size. the classic study of airborne transmission by wells revealed the relation between droplet size, evaporation, and falling rate. it was determined by studying the evaporation of falling droplets and is referred to as the wells evaporation-falling curve of droplets. wells postulated what is now a widely accepted hypothesis of the distinction between droplet size and airborne transmission routes. small droplets start to evaporate after release, and thus change their size resulting in droplet nuclei that are suffi ciently small to remain suspended in air for a long time and still be infectious. large droplets (> μm) can settle on the ground before they become droplet nuclei [ , ] . most respiratory droplets are < μm in diameter and evaporate rapidly in the surrounding environment. they become droplet nuclei, which are suspended in the air or are transported away by airfl ow. the size distribution of droplets is a matter of great debate, but in general various particle sizes are generated: large droplets (> μm) that fall directly to the ground or surface; medium-sized particles ( - μm), fall at a slower rate or remain temporarily suspended by air currents and evaporate; to become droplet nuclei (aerosol) particles < μm in diameter, which remain suspended for longer periods of time [ , ] . studies have demonstrated that particles < μm in diameter are more likely to cause infection in the lower respiratory tract [ , ] . the suspension of these droplet nuclei may cause infection over greater distances and increase the duration of infection risk following generation of the initial respiratory aerosol. in addition, the concentration of particles in the secretion and the infectious dose of the pathogen affect the risk of infection. droplets in the respirable range (~ μm) may play a signifi cant part in transmission. a few studies have quantifi ed the viral load in droplets or aerosols [ ] . an observational study [ ] of infl uenza a and infl uenza b in exhaled breath showed viral rna in one-third of infected patients. also, % of the particles had a diameter < μm when sampled during tidal breathing. although some individuals recover from seasonal or h n infl uenza after having experienced minimal symptoms, a subgroup of high-risk patients develop complications, including respiratory failure. with the appearance of more pathogenic strains, such as h n , respiratory insuffi ciency may occur in > % of those affected. these patients are managed with antiviral therapy and antibiotics for secondary bacterial pneumonia. however, but the mainstay of management is supportive respiratory care, which includes titrated oxygen therapy for hypoxemic patients and ventilatory support for those with respiratory insuffi ciency [ , ] . in contrast to the situation regarding severe acute respiratory syndrome (sars) or tuberculosis prevention in hcws, little attention has been given to the importance of hcws personal protective equipment (ppe) (gowns, gloves, masks) for prevention and management of infl uenza. this situation has arisen because vaccination of hcws has been shown to reduce or prevent nosocomial transmission. it seems prudent for nonvaccinated workers to wear n- masks, particularly during high-risk procedures or with very ill patients. there is limited evidence that upperair ultraviolet light is effective in reducing infl uenza transmission rates. some medical procedures have been termed aerosol-generating procedures (agps) as their most common feature is that they are associated with high or augmented inspiratory and expiratory tidal fl ows, which may increase viral aerosol dissemination. the list of agps [ ] include bronchoscopy, airway intubation, and invasive ventilation maneuvers such as open suctioning, cardiopulmonary resuscitation, niv, and continuous positive airway pressure (cpap) therapy, high-frequency oscillation ventilation, and induction of sputum. certain other procedures, such as delivery of nebulized medication therapy and high-fl ow o , are considered possible aerosol generators but of lesser infective risk. there is an association between some of these agps and an increased incidence of sars in hcws with super-spreading events on the wards [ ] . much of the evidence for the link between agps and increased transmission of respiratory viral infection was generated during the sars epidemic. in toronto, china, and singapore, hcws constituted approximately % of the critical care cases. infection rates were higher in doctors and nurses carrying out endotracheal intubation [relative risk (rr) . , % confi dence interval (ci) . - . , p = . ], and nurses caring for sars patients receiving niv may have been at increased risk (rr . ), but these fi ndings did not reach signifi cance [ % confidence interval (ci) . - . , p = . ] [ ] . in a case-control study of the dissemination of sars from an index case to other patients on the same ward, yu et al. [ ] showed an increased risk associated with the index patient requiring oxygen or bilevel niv. case reports [ , ] have also linked transmission of infection to nebulizer use in the index patient. however, patient variables are also important factors to consider: sicker patients have a higher viral load and are more likely to require oxygen and ventilator support, and those with underlying asthma require nebulizer therapy and cough more because of airway hyperreactivity. both settings increase the risk of aerosol transmission. there is additional evidence concerning agps and the risk they present to hcws. experimental studies that have investigated airfl ows around oxygen masks and during niv [ - ] . these studies used human simulator models or normal subjects mimicking respiratory distress. hui et al. [ ] examined smoke particle dispersion from the lungs of a human simulation model receiving oxygen therapy, frequently used in the treatment of patients with respiratory failure. the authors found that a jet plume of smoke could be generated from exhaust holes up to . m from the mask. although this model provides a visual image of smoke aerosol behavior, and the possible zone of transmission risk, it is not necessarily representative of the behavior of a respiratory aerosol and infectious particles contained therein. two similar studies were carried out on oxygen masks. one indicates that oxygen mask usage might contribute to droplet-respiratory transmission of sars [ ] . the other observed a visible range of the smoke plume of . - . m depending on the type and fl ow rate of the mask used [ ] . simonds et al. [ ] evaluated the characteristics of droplet/aerosol dispersion around delivery systems during niv, o , nebulizer treatment, and chest physiotherapy by measuring the droplet size, geographical distribution of droplets, decay in droplets over the time after the intervention was discontinued, and the impact of modifying the niv circuit in clinical practice. three groups of patients were studied: normal control subjects; subjects with coryzal symptoms; adults with chronic lung disease who were admitted with an infective exacerbation. each group received o , niv using a vented mask system, and a modifi ed circuit with a nonvented mask and an exhalation fi lter. all received nebulized saline and a period of standardized chest physiotherapy. droplet counts in mean diameter sizes ranging from . to > . μm were measured with a counter placed adjacent to the face and at m distance from the patient at the height of the nose/mouth of an average hcw. niv using a vented mask produce large droplets (> μm) in patients ( p = . ) and coryzal subjects ( p = . ) compared with baseline values but not in normal controls ( p = . ). this increase in large droplets was not seen using the niv circuit modifi cation. chest physiotherapy produced droplets predominantly > μm ( p = . ), with the droplet count (as in the niv patients) falling signifi cantly by m. o did not increase the droplet count in any size range. nebulized saline delivered droplets in the small and medium size aerosol/droplet range, in keeping with the specifi ed performance characteristics of the device, but did not increase the large-droplet count. preliminary analyses suggest that droplet counts fall to within a baseline range within - min of discontinuing the niv and chest physiotherapy. in conclusion, niv and chest physiotherapy are droplet-(not aerosol-) generating procedures, producing droplets > μm. because of their large mass, most fall on local surfaces within m. the only device producing an aerosol was the nebulizer. the output profi le is consistent with nebulizer characteristics rather than dissemination of large droplets from patients. these fi ndings suggest that hcws who are providing niv and chest physiotherapy and are working within m of an infected patient should have a high level of respiratory protection. infection control measures designed to limit aerosol spread (e.g., negative-pressure rooms) may have less relevance. tran et al. [ ] systematically reviewed the literature regarding the risk of transmitting acute respiratory infections to hcws exposed to patients undergoing an agp compared with the risk of transmission to hcws caring for patients not undergoing an agp. the outcome of interest was the risk of acute respiratory infection. they identifi ed fi ve case-control and fi ve retrospective cohort studies that evaluated transmission of sars to hcws. the procedures reported to present an increased risk of transmission included tracheal intubation [ n = , cohort: odds ratio (or) . ( . - . ); n = , case-control study: or . ( . - . )] and niv [ n = , cohort: or . ( . - . )]; tracheotomy [ n = , case-control: or . ( . - . )]; and manual ventilation before intubation [ n = , cohort: or . ( . - . )]. other intubation-associated procedures, endotracheal aspiration, suction of body fl uids, bronchoscopy, nebulizer treatment, administration of o , high-fl ow o , manipulation of o masks or bilevel positive airway pressure (bi-pap) masks, defi brillation, chest compression, insertion of a nasogastric tube, and collection of sputum were not signifi cant. these fi ndings suggest that some procedures potentially capable of generating aerosols have been associated with increased risk of sars transmission to hcws or were a risk factor for transmission. the most consistent association across multiple studies was tracheal intubation. the results of this report should not be generalized to all acute respiratory infections because the evidence available is strictly limited to sars. noninvasive ventilation and continuous positive airway pressure are likely to play a minor role in the management of moderate to severe acute lung injury caused by infl uenza or secondary bacterial pneumonia, or in patients with multisystem failure. however, niv was used successfully in some sars cases [ ] . there is also potential for niv to reduce the need for intubation in patients with infl uenza pneumonia or chronic respiratory disease, facilitate extubation, and widen the provision of ventilator support outside the intensive care unit (icu). it may also be used as ventilator care in patients with chronic obstructive pulmonary disease, congestive cardiac failure, and other serious co-morbidities. niv is sometimes used to palliate symptoms in those with end-stage disease in whom icu admission is not indicated [ ] . these indications should be set against the risk of droplet dissemination during the delivery of niv. despite the study of simonds et al. [ ] , which indicated that niv generates large droplets adjacent to the patient that fall significantly at m from the patient, and that adding a circuit using a nonvented mask plus a fi ltered exhalate reduces the number of large droplets produced, there is still concern about dispersion of infectious particles. nevertheless, in a hong kong hospital where more than patients were placed on noninvasive positive ventilation, all hcws on the ward performed meticulous infection-control procedures and used ppe. despite the intense exposure, none became infected with sars [ ] . patient selection is important for niv as it has not been shown to improve the mortality rate among patients with acute respiratory distress syndrome (ards) and may be not suitable for patients in whom short-term improvement is not expected [ , ] . protection of the hcw during mechanical ventilation includes isolation of infected patients, use of ppe, and strict hand hygiene by all. the world health organization and the centers for disease control and prevention have issued guidelines that recommend the use of standard, contact, and airborne protection, including respirators of n- standard or higher, which fi lter at least % of particles that are ≥ mm with < % face seal air leak. these fi lters not only protect against virus-transmitted diseases but also against tuberculosis (tb), fi ltering at least % of the -to -mm tb bacilli out of the air inhaled by hcws. the need for n- masks depends on the mode of transmission. if transmission is solely by droplet, face shields, eye protection, and surgical masks are adequate. however, if transmission is airborne, n- masks should be used. as reviewed earlier, there is evidence that airborne transmission of sars occurred, at least from the super-spreaders or during aerosol-generating activities such as intubation or suctioning. knowing that super-spreaders are identifi ed only in retrospect, it may be prudent for workers to wear n- masks at all times. standard personal protective equipment includes n- masks, gloves, gowns, caps, and face shields or goggles [ , ] . all staff should be mask fi t-tested to ensure adequate seal. when performing high-risk procedures such as intubation, bag-mask ventilation, or bronchoscopy, protection should be enhanced with powered air-purifying respirators. also, the hcw should be aware that these procedures have been associated with increased risk of infection transmission and should upgrade to airborne infection control precautions [ ] (table . ). in view of the high risk of disease transmission during endotracheal intubation, airway management protocols have been proposed: early intubation should be performed, preferably in the icu, rather than performing a crash intubation on the ward. adequate sedation and neuromuscular blockade is recommended during intubation to minimize cough and dispersion of respiratory secretions. finally, the procedure should be performed by the most experienced person available to minimize the dispersal of infectious particles and reduce the number of individuals exposed during intubation [ ] . measures to minimize respiratory droplet transmission include using in-line suctioning to maintain the ventilator circuit as a closed system. humidifi cation should be done via heat-moisture exchangers with viral-bacterial fi lter properties rather than heated humidifi ers. each ventilator should have two fi lters-one between the inspiratory port and ventilator circuit and the other between the expiratory port and ventilator circuit-to provide additional protection from exhaust gases and minimize ventilator contamination [ ] . other general recommendations include using a unidirectional/displacement ventilation system for a single patient room. it should not be used in a multi-bed ward where the potentially aerosol-transmitted infection patient source is unknown as this ventilation system may unintentionally disseminate the infection throughout the ward to other patients. hence, the situation where such a ventilation system is used needs to be considered carefully. even though an ideal isolation unit is fi tted with a negative-pressure system and sliding glass doors (to reduce airfl ow generated by traditional hinged doors), it is possibly the movement of people in and out of the room that produces the most signifi cant airfl ow. of course, it is impossible to prevent such movement in a health care facility, but reducing the number of times the room is entered or exited can reduce the volume of potentially infected air exchanged across the doorway. an essential component of an infection-control strategy is staff training. clear management protocols must implemented, including the use of ppe, monitoring staff health, quarantining staff, transport of patients, transfer to the icu, airway management, aerosol generating procedures, environment and equipment disinfection, and visitation policies. the health care environment could be an important reservoir for viruses, bacteria, and fungi during outbreaks, given their proven ability to survive on surfaces and to become airborne. changes in temperature and humidity in hospitals could have relevance for the viability of microorganisms and their spread to other patients. adequate ventilation is necessary to dilute the airborne microbial load. heat and humidity need to be controlled. it is recommended that upper and lower limits for temperature and humidity be specifi ed according to the outbreak facial respirator (eu ffp or us niosh certifi ed as n- ) eye protection (goggles or a face shield) clean nonsterile, long-sleeved gown gloves (some procedures required sterile gloves) procedures performed in an adequately ventilated room (> air changes per hour) avoidance of unnecessary individuals into the room attention to hand hygiene before and after patient contact and after removing personal protective equipment pathogen and that air changes at the patient level be tested regularly, especially after any restriction to airfl ow. it is important for intensive care providers to be prepared to meet the challenge of large-scale airborne epidemics causing mass casualty respiratory failure. previous outbreaks have exposed the vulnerability of hcws and highlighted the importance of establishing stringent infection control and crisis management protocols. there should be an established lung-protective, low tidal volume strategy for treating patients with acute lung injury or ards who require mechanical ventilation. the use of niv remains controversial. current infection-control policies that limit or prohibit the use of niv as a high-risk intervention are based largely on supposition [ ] . standard contact and airborne precautions should be instituted in the icu, with special care taken when aerosol-generating procedures are performed (table . ). airbone transmission of disease in hospitals preventing airbone disease transmission: review of methods for ventilation design in health care facilities transmission of infl uenza: implications for control in health care settings the airbone transmission of infection in hospital buildings: fact or fi ction? a review of the risks and disease transmission associated with aerosol generating medical procedures infl uenza virus in human exhaled breath: an observational study critical care services and h n infl uenza in australia and new zealand hospitalised patients with h n infl uenza in the united states why did outbreaks of severe acute respiratory syndrome occur in some hospitals wards an not others? transmission of severe acute respiratory syndrome during intubation and mechanical ventilation a major outbreak of severe acute respiratory syndrome in hong kong index patient and sars outbreak in hong kong dispersal of respiratory droplets with open vs closed oxygen delivery masks. implications for the transmission of severe acute respiratory syndrome noninvasive positive-pressure ventilation. an experimental model to assess air and particle dispersion airfl ows around oxygen mask. a potential source of infection? exhaled air dispersion during oxygen delivery via a simple oxygen mask key major recommendations • the evidence regarding the risk of transmission during niv is confl icting and unclear there have been reports of niv being effective in treating patients during an epidemic, reducing the need for intubation • niv should be used especially in a pandemic scenario when the demand for mechanical ventilation support is overwhelming health care workers performing niv during an airborne epidemic should use standard, contact, and airborne protection, including respirators of n- standard or higher exhaled air dispersion distances during noninvasive ventilation via different respironics face masks exhales air an aerosolized droplet dispersion during application of a jet nebulizer airfl ow an droplets spreading around oxygen mask: simulation model for infection control research evaluation of droplet dispersion during non-invasive ventilation, oxygen therapy, nebulizer treatment and chest physiotherapy in clinical practice: implications for management of pandemic infl uenza and other airbone infections aerosol generating procedures and risk of transmission of acute respiratory infections to healthcare workers: a systematic review effectiveness of noninvasive positive pressure ventilation in the treatment of acute respiratory failure in severe acute respiratory syndrome noninvasive mechanical ventilation. theory, equipment and clinical applications the critical ill avian infl uenza a (h n ) patient avian infl uenza (h n ): implications for intensive care mechanical ventilation in an airbone epidemic pandemic infl uenza: implications for preparation and delivery of critical care services clinical management of pandemic infl uenza a (h n ) intubation of sars patients: infection and perspectives of healthcare workers should noninvasive ventilation be considered a high-risk procedure during an epidemic? key: cord- -q ry vp authors: de oliveira, p. m.; mesquita, l. c. c.; gkantonas, s.; giusti, a.; mastorakos, e. title: evolution of spray and aerosol from respiratory releases: theoretical estimates for insight on viral transmission date: - - journal: nan doi: . / . . . sha: doc_id: cord_uid: q ry vp by modelling the evaporation and settling of droplets emitted during respiratory releases and using previous measurements of droplet size distributions and sars-cov- viral load, estimates of the evolution of the liquid mass and the number of viral copies suspended were performed as a function of time from the release. the settling times of a droplet cloud and its suspended viral dose are significantly affected by the droplet composition. the aerosol (defined as droplets smaller than m resulting from seconds of continued speech has o( h) settling time and a viable viral dose an order-of-magnitude higher than in a short cough. the time-of-flight to reach m is only a few seconds resulting in a viral dose above the minimum required for infection, implying that physical distancing in the absence of ventilation is not sufficient to provide safety for long exposure times. the suspended aerosol emitted by continuous speaking for hour in a poorly ventilated room gives . - % infection risk for initial viral loads of ^ - ^ copies/ml, respectively, decreasing to . - % for air changes per hour by ventilation. the present results provide quantitative estimates useful for the development of physical-distancing and ventilation controls. by modelling the evaporation and settling of droplets emitted during respiratory releases and using previous measurements of droplet size distributions and sars-cov- viral load, estimates of the evolution of the liquid mass and the number of viral copies suspended were performed as a function of time from the release. the settling times of a droplet cloud and its suspended viral dose are significantly affected by the droplet composition. the aerosol (defined as droplets smaller than µm) resulting from seconds of continued speech has o( h) settling time and a viable viral dose an order-of-magnitude higher than in a short cough. the time-of-flight to reach m is only a few seconds resulting in a viral dose above the minimum required for infection, implying that physical distancing in the absence of ventilation is not sufficient to provide safety for long exposure times. the suspended aerosol emitted by continuous speaking for hour in a poorly ventilated room gives . - % infection risk for initial viral loads of - copies/ml l , respectively, decreasing to . - % for air changes per hour by ventilation. the present results provide quantitative estimates useful for the development of physical-distancing and ventilation controls. as the scientific debate on the droplet-related mechanisms allowing for the global spread of the sars-cov- virus evolves, attention has been shifting from droplet transmission towards aerosol as a possible additional route of transmission [ ] . illness caused by the inhalation of smallsized virus-laden droplets that can remain in the air long after being emitted by an infected (symptomatic or asymptomatic) individual, seems to explain a number of known outbreaks where safety measures put in place by local authorities were adopted, but contagion still occurred [ ] . due to the limited information on how respiratory droplet clouds evaporate while settling by gravity, the values and decay rates of the suspended viral dose emitted in respiratory releases are yet unknown. as a result, a great deal of uncertainty might be associated with current modelling practices used to define emergency control policies to minimise the damage caused by the covid- disease as it develops. this work sheds light on the droplet-versus-aerosol debate by providing a theoretical characterisation of the time evolution of droplets from the moment of their emission, bridging these estimates to our current knowledge of the sars-cov- characteristics [ ] [ ] [ ] [ ] [ ] in order to provide a metric of viral dose levels and decay. although significant efforts were made to investigate the time scales associated with single respiratory droplets undergoing the combined action of evaporation and gravity (starting from [ ] and refined more recently by [ ] ), only recently a full experimental account of the actual range of droplet sizes produced in a respiratory release was possible. due to fast atomisation processes happening at the mouth, vocal chords, and lungs, during breathing, speaking, or coughing, a wide range of droplets from sub-micrometer to millimetre size are emitted, requiring various experimental techniques combined to account for such wide-ranging sizes [ ] [ ] [ ] . in addition to previous efforts, evidence that the evaporation process of a sputum droplet might be significantly affected by the droplet composition was shown very recently for a -µm diameter droplet [ ] . as a multi-component droplet evaporates, the concentration of non-volatile components increases, affecting evaporation rates and ultimately dictating the final "equilibrium" diameter reached by the droplet. hence, the final droplet diameters found in [ ] were between - % of the initial value, approximately, depending on the assumed concentration of protein modelled in the droplet. such large variation leads to considerable errors in the modelling of airborne transmission, which assumes the resulting droplet nuclei to lie within the aerosol class, that is, below µm [ ] . additionally, such effects could also impact the short-range, short-time scale problem of droplet transmission. here, an evaluation of the evaporation and settling of droplet clouds emitted in respiratory releases is carried out, providing information on the time between the short-time scale problem of droplet transmission up to the long-time scale problem of aerosol transmission. state-of-the-art models are used for the prediction of evaporation and to account for droplet size distribution and concentration in two modes of droplet exhalation: by coughing and speaking. in this paper, we: • evaluate the size distribution and life-time of the suspended droplet cloud and the effects of ambient conditions on these quantities. droplet cloud; only droplets within the aerosol category; and each of these two groups excluding "dry" droplet nuclei. • evaluate the emitted viral dose from sick individuals through coughing and speaking, and investigate the evolution of the suspended viable viral dose. to demonstrate the impact of such metrics for physical distancing/ventilation, three canonical problems are considered: uniform flow from the emitter to the receptor, jet decay simulating the short-range flow pattern from the emission, and the well-mixed room focusing on the long timescales of the aerosol and on the risk of infection. the sputum droplets are assumed to be spherical particles. the trajectory of the centre of mass is computed using the so called 'lagrangian' approach where the equations of motion (balance of momentum) are solved for each particle independently. both the gravity and buoyancy forces are considered together with the aerodynamic drag. all the other forces, such as basset, magnus and saffman forces, as well as virtual mass are neglected [ ] . the governing equations in a lagrangian specification that describe the motion of the k-th droplet are as follows: where t indicates the time, g is the acceleration of gravity, d k is the diameter of the droplet, x k and v k are the position and velocity vectors of the droplet, u is the velocity vector of the gas, ρ is the density, and the subscripts g and l refer to the gas and liquid phase, respectively. the parameter c d,k in the aerodynamic drag term of eq. . is a function of the reynolds number of the droplet re k , calculated based on the relative velocity between the particle and the carrier phase, i.e., re k = ρgd k |u − v k | /µg, where µg is the dynamic viscosity of the gas phase. here, the . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. (which was not certified by peer review) the copyright holder for this preprint this version posted july , . . https://doi.org/ . / . . . doi: medrxiv preprint schiller-naumann correlation for drag is used [ ] , further, mass and temperature equations for an evaporating droplet are given according to the model proposed by [ ] , assuming an infinite conductivity for the droplet. the evaporation model accounts for the effect of stefan flow on heat and mass transfer between the droplet and the surrounding gas, assuming a dilute spray (i.e., volume fraction of the droplets below . %this allows us to use for each particle the models developed for isolated droplets) in an infinitely large domain: wheredg,ρg,kg, andc p,f are the average binary diffusion coefficient of the mixture, density, thermal conductivity, and specific heat in the film. the parameters b m and b t are the spalding mass and heat transfer numbers, and the modified nusselt and sherwood numbers are given as, these are calculated based on the actual nusselt and sherwood numbers, obtained with the widely used frossling's correlations [ ] , and then corrected for the film thickness of the surrounding gas by the correction factors f m and f t proposed in [ ] . given the low biot number of the droplets in all conditions, bi k = hd k /( kg) < . , where the convective heat transfer coefficient h is computed from the nusselt number, a convection-controlled process is assumed and, in turn, a uniform internal droplet temperature t k can also be assumed. the rate dt k /dt can be obtained by an energy balance at the droplet, in the present calculations, it is assumed that the air is initially at a homogeneous temperature ta and pressure pa, and contains moisture characterised by the volume fraction of water vapour xw, which is related to the relative humidity by xw = rh p w,sat /pa. such conditions constitute the far-field (i.e., a region sufficiently far from the droplet surface, where the evaporation process has negligible effect) boundary conditions for droplet computations. the initial conditions of the spray are described next, in sec. (c). in an initial approach, the liquid composition is considered to be pure water. to mimic the formation of a "droplet nucleus" (i.e. what remains after evaporation has ended), the effect of non-volatile content diluted in the droplet is implemented by simply limiting evaporation of each droplet down to % of its initial mass, that is, m k /m k, = . . this value is representative of the equilibrium diameter for the range of relative humidity between % and % verified by [ ] for a model sputum droplet containing mg/ml of nacl, . mg/ml surfactants, and high protein concentration of mg/ml. nevertheless, it is worth noting that the equilibrium diameter as evaluated in the model is approximately % smaller for a model sputum droplet with low protein concentration ( mg/ml) within the same relative humidity range [ ] . in sec. (b), we provide the additional models to evaluate the effect of the droplet composition on evaporation. it should be noted, however, that neither approach considers the effect of hygroscopic growth of the droplet nuclei that may happen at high relative humidity for a recently emitted droplet, or could also be observed in a droplet nucleus undergoing changes in the relative humidity in the environment. . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. (which was not certified by peer review) the copyright holder for this preprint this version posted july , . . https://doi.org/ . / . . . doi: medrxiv preprint it has been mentioned that the effects of solute and of the droplet curvature can determine the equilibrium size of the aerosol [ ] . to account for the increase in the water vapour pressure due to the curvature of the droplet surface, kelvin's equation [ ] is employed, where m is the molecular weight, σ is the surface tension, r is the universal gas constant, and the subindex w represents water. the effect of the surface curvature may be enhanced due to a surface tension increase in the presence of nacl and other components in the liquid [ ] , and at the same time be suppressed by the presence of surfactants which lowers the surface tension [ ] . thus, the surface tension of pure water was used as an approximation. the saturation pressure of the water at the droplet interface is decreased by the presence of soluble as well as by insoluble substances in the droplet. to account for this in a multicomponent sputum droplet, eq. . becomes, [ , , ] , where νz is the number of ions into which a solute molecule z dissociates, Φz is its practical osmotic coefficient, and yz its mass fraction in terms of the total dry mass. we consider the presence of nacl, proteins, and surfactants in the liquid. details for the calculation of the ioninteraction parameterisation of Φz for nacl and osmotic pressure parameterisation of Φz for bsa proteins are given in [ ] . the latter was also used for the evaluation of that parameter in dipalmitoylphosphatidylcholine (dpcc) surfactant, considered here. finally, assuming the water as the only volatile component in the liquid droplet, it is possible to demonstrate that the rate of change of the mass fraction of water in the droplet due to evaporation is, where m n,k, is the initial mass of non-volatile (dry) components in the droplet k, respectively. three different initial liquid compositions were considered, reflecting directly on the evaluation of the water vapour pressure at the droplet surface (eq. . ): pure water, a high protein sputum and low protein sputum. the initial concentrations and molecular weight of each component are given in table (b) . the sputum compositions used in this study are those considered in [ ] , which are low protein content found in the nasal surface airway fluid [ ] , and high protein content found in breath aerosols [ ] , both considering a small concentration of dppc as surfactant [ ] . a homogeneous composition across all droplet sizes is considered for each case, although in reality different droplet compositions may be found depending on the origin of the droplets. . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. (which was not certified by peer review) the copyright holder for this preprint this version posted july , . . https://doi.org/ . / . . . doi: medrxiv preprint size distribution of droplets escaping the mouth, associated with coughing and normal paced speaking, are given as probability density functions (pdfs) of droplet diameter. these functions were obtained using the tri-modal log-normal distribution provided by [ ] . the model was named by the authors as the bronchiolar-laryngeal-oral tri-modal model, as it considers droplet production associated with three distinct modes: one occurring in the lower respiratory tract, another in the larynx, and a third in the upper respiratory tract and oral cavity, respectively. here, we consider an initial droplet distribution in the range µm- mm. the number concentration of droplets of size k produced in each of these modes is given as a sum over each mode i [ ] : where the droplet number concentration cn i , geometric standard deviation gsd i , and count median diameter cmd i for i-th mode are given in table . the total number and liquid concentrations per unit volume of exhaled gas can be directly obtained by sum of cn i and cm i , respectively, for the three modes. the mass concentrations were evaluated by [ ] assuming perfectly spherical droplets and the density of pure water. we model the virus decay in a droplet assuming an exponential decay at a rate λ such that [ ] , where n k,v is the total number of viable viral copies (i.e., plaque forming units, or pfu) in a single droplet k. as an approximation, an exponential decay constant of λ = . h − is used for all droplet sizes and compositions. this value was obtained from the experiments performed by [ ] , which verified the stability of the sars-cov- virus as an aerosol, formed of µm droplets released in % relative-humidity ambient air. in that work, a virus half life of . h was observed. one should note that with this approach, local droplet effects such as change in solute concentrations with evaporation on virus activity are neglected. further, the initial viral copies in each droplet is defined as, where v k is the volume of the droplet. the initial viral load n v, has been recently reported for sars-cov- , with typical values found in sputum and throat swabs ranging between to copies/ml l as the disease develops in sick individuals [ , , ] , who were tested daily from the on-set of the symptoms of the disease and up to several days later. still, values as high as copies/ml l were observed [ ] , and even copies/ml l in patients who recently died [ ] . . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted july , . . https://doi.org/ . / . . . doi: medrxiv preprint additionally, evidence of transmission caused by an asymptomatic individual has also been suggested; following the outbreak, a viral load of copies/ml l was detected in the individual's sputum [ ] . the total suspended viable viral copies and viable viral load in copies, or plaque forming units, per unit volume of liquid are: finally, in order to put the results of sections (a)-(b) in context of physical distancing rules, the infection dose of virus in viable copies needed per individual n v id leading to the disease must be defined as a reference. this value is normally reported as the amount of plaque forming units which will result in a given percent responses (illness) over x% of a population -e.g. n v for infection of % of a population. in the lack of these values for sars-cov- , we used the infection dose model by [ ] for sars-cov- due to the claimed similarity of this virus with sars-cov- and as it is in the same genetic group as other coronaviruses such as hcov- e (human common cold), mhv-s and hev- n (animal coronaviruses) for which the model also demonstrated a good agreement with experimental data [ ] . the intervals of n v id = - pfu and n v id = - pfu are reported for a % confidence interval. the settling of human exhaled droplet clouds is analysed in the absence of turbulence and of mean air flow, so that the effects of gravity and evaporation on various ensemble quantities of interest can be independently investigated. the lagrangian framework, given in sec. (a), is considered in one (vertical) dimension and droplet clouds for two exhalation modes, speaking and coughing, are released at the height of the emitter's mouth ( . m) and then let settle by gravity while evaporating in ambient air. in this section, the effect of composition was not taken into account, hence droplets were considered as pure water with evaporation limited down to the equilibrium size corresponding to % of its initial mass. so as to provide an overview of the evaporation-settling process, the probability density functions (pdfs) of droplet size for coughing and speaking are provided in terms of the time after emission for an ambient condition of ta= • c and rh= % (fig. ) . in this analysis, all droplets or droplet nuclei that remain suspended in air in a given time are considered. this ensemble average is denoted by the subscript s in the quantities of interest (e.g. Ψs). the tri-modal bronchiolar-laryngeal-oral characteristic pdfs of droplets produced during speech and cough [ ] are given at t= s. within one minute, most of the large droplet portion of the distribution ( µm- mm) progressively disappears as these droplets reach the ground. one hour after emission, only droplets smaller than µm remain suspended, that is, those typically defined as aerosol. interestingly, at this point, the total number of particles in the sub-micrometre range is an order of magnitude higher for coughing than speaking. next, we evaluate the pdfs of droplet size for a suspended and evaporating droplet cloud -that is, considering only droplets that have not yet reached their equilibrium size or, in other words, ignoring any droplet nuclei. this condition is defined by the superscript * , as Ψ s * . figure shows the evolution of speech-emitted droplet pdfs evaluated for (a) the total suspended droplet cloud and (b) those evaluated for the suspended cloud minus the droplet nuclei. these are reported for the same ambient condition of fig. . a fast change to the coughing and speaking droplet clouds occurs within the first second from emission, as droplets of the order of µm fully evaporate. these small droplets quickly reach their minimum (equilibrium) size, hence determining earlyon in the process the aerosol dispersion that might remain suspended in the air for much longer . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted july , . times. the effect of evaporation on droplet size and the resulting time scales for full evaporation for each droplet class can be more easily seen in (b), as the lower limit of the given pdfs moves towards higher values as evaporating droplets reach equilibrium. the droplets within the bronchiolar mode of the probability density curve, centred at approximately - µm, have a ms evaporation time scale, while those in the laryngeal mode a characterised by a longer, -s time scale. moreover, fig. b illustrates that the long-time scale problem may be reduced to -s time scale and droplets produced in the oral-mode in a virus transmission problem through droplets produced by normal, paced speech and where the presence of water is vital to the viability of the virus in the droplet. this could be, for example, due to an increasing concentration of surfactants, . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted july , . salts, and other non-volatile components that can enhance viral decay [ ] . in that case, droplet sizes range between - µm, as no droplets within the aerosol class are observed after ms and any droplets larger than µm are quickly deposited by gravity. figures to provide insight on the time scales needed for viral removal from the ambient air due to settling of the droplets through gravity. first, the effect of relative humidity is shown on the evolution of two ensemble quantities of the droplet clouds exhaled by speaking and coughing: mass and number of suspended droplets, both quantities normalised by their respective values at t = (fig. ) . for reference, the total mass of liquid emitted in a single cough, lasting approximately . seconds, is equal to that of a -s speech; as evaluated from the concentration . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted july , . distributions provided in [ ] and the exhalation gas flow rates for speaking ( . l/s) [ ] and coughing ( . l/s) in [ ] . for both exhalation modes, a significant portion of the emitted droplet cloud mass lies in the large droplets. in fact, % of the initial mass is concentrated in the droplet diameter range between nm- mm (fig. ) . thus, it is not surprising that the decay of the total mass suspended relative to the initial emitted liquid mass (ms,a/m , fig. ) behaves similarly in both exhalation modes. nevertheless, what is interesting to observe in terms of the effect of evaporation and relative humidity on ms,a/m concerns the ensemble quantities for the resulting aerosol. as discussed previously, evaporation affects the small droplets in the aerosol within the first second after emission. thus, the effect of lower (far-field) relative humidity which enhances evaporation is only noticed in the aerosol droplets within that time frame. while a decrease of the relative mass occurs due to the evaporation of the droplets in the aerosol class, a combined increase in the aerosol mass and droplet number also occurs as larger droplets evaporate and shrink below µm. further, the number droplets within the aerosol class relative to the initial number of droplets rises from % to % due to this effect, while for coughing only a small increase is observed (from % to %, roughly). the increase in ns,a/n due to evaporation in speech-emitted droplets is typically neglected but can be relevant when one assumes aerosol transmission only, say, in a well-mixed room type of ventilation problem (similar to [ ] ) where the intention is to evaluate risk of infection. this is aggravated by the fact that, relative to the initial emitted cloud, the number of droplets and the respective suspended mass after one hour is an order of magnitude higher for speaking than for coughing. this analysis illustrates the risk associated with constant speaking in closed environments (as for example, in a lecture hall) due to a higher mass fraction of liquid resulting in small droplets during speaking (fig. ) . the effects of evaporation and gravity on the time evolution of the ensemble quantities of interest are now discussed with a focus on transmission through evaporating droplets only. in fig. , the relative mass and droplet number are evaluated for the total droplet cloud minus droplet nuclei, as well as for droplets in the aerosol minus droplet nuclei. in contrast with fig. , where droplets and droplet nuclei are considered, full decay of the evaporating aerosol mass occurs roughly between - ms following exhalation. in terms of total mass emission, . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted july , . . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted july , . virtually no change is observed relative to the value shown in fig. , as the mass decay is mostly controlled by deposition of large droplets on the ground, as previously discussed. in an attempt to provide an assessment of the uncertainty associated with the results given in sec. (a), we assess the effect of different droplet compositions on evaporation and, in turn, on the resulting equilibrium size of the droplets. this is discussed in terms of the ensemble quantities and time scales discussed previously. first, this issue is analysed in the context of a single droplet. figure illustrates the problem through (a) evaporation and (b) settling of a -µm diameter droplet. the colour lines represent different relative humidities (rh= - %), while the short dash, long dash, and continuum lines represent each of the compositions used: that of pure water, high-protein and low-protein sputum, respectively. for the sake of comparing the sputum droplets with pure-water droplets in fig. , no hard limit is imposed on the minimum droplet size of pure water in this case. hence, water droplets undergo full evaporation in less than a second, except in the case of % relative humidity. as the droplet evaporates, the concentration of non-volatile components increases in the droplet, thus reducing the the vapour pressure at the droplet interface. thus, a larger equilibrium diameter is reached for the case of high-protein sputum composition. as expected, evaporation is limited by the vapour pressure in the ambient. thus, the closer to saturated air (rh= %), the higher is the equilibrium diameter of the droplet. although a large variation of the equilibrium diameter was expected, observed here between % and % of the initial diameter, its impact on the settling time is quite significant. this can be seen for the -µm droplet by taking the respective time at the crossing of each line with the x-axis in fig. b . as discussed in the context of a single -µm droplet in fig. a , the combined effect of composition and relative humidity can have a major impact on the settling time of a droplet. next, fig. , we discuss this issue for the entire range of droplet sizes typically found in respiratory releases. the absolute settling time is shown in (a) in terms of the droplet size and for high-and low-protein sputum droplets. the relative difference between the two is given on the right-hand axis. settling times of droplets in the - -µm range are strongly affected by composition, while . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted july , . . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted july , . this effect is negligible in droplets larger than µm. in the transition range between - µm, the deposition and evaporation time scales are very similar, hence the effect of composition swiftly disappears once the settling time due to gravity becomes much shorter than the droplet evaporation time scale. further, fig. b shows the aerosol droplet size distribution for coughing and speaking, where the total number of droplets for each size normalised by the total number of emitted droplets is given. by lowering the equilibrium diameter, more droplets are found in the aerosol category. the shape of the distribution is similar between the two droplet compositions, with the high-protein sputum droplets just shifted towards smaller diameters. there are key implications of such findings. although, at a first glance, one would be tempted to neglect the composition effect in the gravity-controlled short-time scale viral transmission problem (i.e. the ballistic and exhaled gas-driven motion of large droplets), significant differences in settling time and size in the - -µm range can be critical. such droplets might remain longer in air at face height, being more likely to be inhaled by someone near a sick individual. this problem has a direct impact on the uncertainty of methods to evaluate the safe physical distancing and, therefore, should be further investigated for better understanding, for example by means of high-fidelity flow simulations. besides the short-time scale implications, the large differences in deposition times of droplets in the aerosol class, as an effect of both relative humidity (fig. a ) as well as composition (fig. b) , might also affect the long-time scale problem, that is, the virus removal by ventilation in indoor spaces. this large difference can be clearly seen at large times in terms of ms/m and ns/n (fig. ) not only due to the significantly longer deposition times of such droplets, but also due to the difference in the mass that can remain suspended. some of these issues are explored next, in sec. (c) in this section, the evolution of the total number of suspended viable viral copies is evaluated for speaking and coughing. we consider a single cough in which all droplets are assumed to be released instantly, and continuous speaking in which the droplets are considered as uniformly emitted over its duration. assuming a short . -s cough with a mean volumetric gas flow rate of . l/s [ ] , the total emitted liquid can be directly obtained from the total exhaled volume of gas and the liquid concentration values available in table . similarly, we consider the case . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted july , . presented in terms of the saliva composition: low protein (sputum mg/ml nacl, mg/ml protein) and high protein (sputum mg/ml nacl, mg/ml protein) -t= • c, rh= %. in terms of the composition: low protein (sputum mg/ml nacl, mg/ml protein) and high protein (sputum mg/ml nacl, mg/ml protein) -t= • c, rh= %. of continuous, paced speech at an average volumetric gas flow rate of . l/s [ ] . hence, both exhalation modes result in the same emitted liquid mass. additionally, for this analysis, we consider two sputum compositions (high-and low-protein sputum) and assume a range of low and high viral loads at the emission source to be that of a symptomatic person in: (i) a few days after the symptoms appear (typically copies/ml l ) and (ii) at a severe stage in the disease ( copies/ml l ). the evolution of the total number of suspended viable copies of virus ns,v is given for those conditions and and % relative humidity (fig. ) . as a reference value, the infection doses n id v , n id v , and n id v are also given. for speaking, an additional plot is given with a time scale relative to the end of the -s speech (fig. b) . . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted july , . figure . evolution of the suspended viable viral dose following a short cough in terms of two droplet compositions (lowand high-protein sputum), rh= and %, and low ( copies/ml) and high ( copies/ml) initial viral load n v, . one of the key differences in the decay of suspended virus emitted from (a) coughing in comparison to (b) speaking can be seen in respect to n id v in fig. . for a cough and the worstcase viral load scenario ( copies/ml l ), the viral inactivation and removal through gravity will quickly bring the total ns,v down to values below those needed for % risk of infection (if the whole amount is inhaled by person) in about - min. in contrast, min are needed for reduction to the same ns,v levels in speaking. due to the small droplets produced in speaking, a high viral dose can still be suspended up to one hour -although this is approximately the half-life of the virus -being one order of magnitude higher than in coughing at that time. to discuss the evolution of the total number of suspended viable copies of virus in the context of indoors activities, we consider just droplets at face height (between . - . m) in fig. . based . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted july , . on the results of fig. , here, we assume a worst-case scenario in terms of droplet removal by gravity, that is, a droplet composition of low-protein sputum and relative humidity of %. in terms of the virus load in sputum, a typical case of the disease is considered, that is, a high viral load in a patient after a few days of the first symptoms of the disease (n v, = copies/ml l ). three cases of upward, zero, and downward flow are then evaluated by setting the mean vertical gas velocity as + . , , and − . m/s. these simple cases aim to illustrate possible flow conditions that may arrive in indoors activities (e.g. thermal plume, heating systems or flow streams caused by ventilation systems). the effect of the mean flow on viral removal at face height is evident: downward flow can reduce the suspended viral dose to safe levels in only a couple of seconds, while upward flow may actually worsen the problem by keeping a higher viral dose suspended at face height for several minutes longer than no flow at all. moreover, fig. also illustrates the risk associated with speech-emitted droplets in the short-time scale problem; this will be discussed in detail in the next section, as we consider the gas exhaled during speech. in a setting where the initial velocity of the exhaled gas carrying the droplets can be ignoredthis might be a good assumption in, say, slow speaking or exhalation in the presence of a strong background airflow -the above time scales can be easily translated into information on space. for example, assuming a uniform velocity u ab from emitter a to receptor b located a distance l from a in the airflow direction, the total suspended liquid mass can be found by simply setting t = l/u ab in fig. . for instance, for u ab = . m/s and l = m, t = s and hence about × − to × − of the initial liquid is still in the air, depending on the ambient conditions. similarly, in terms of virus dose, (fig. ) , an amount up to pfu could be available at face height, depending on specific flow conditions, which illustrates that a -m safe distance may not be adequate without the use of protective mask/respirator for the case of strong convection from the emitter to the receptor. . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted july , . . https://doi.org/ . / . . . doi: medrxiv preprint (ii) jet decay speaking or coughing involve high velocities at the mouth, which then decay as the flow evolves downstream from the emission source. here, we model a respiratory emission as a continuous round jet in stagnant ambient air. although, in reality, the emission is not continuous and the jet is buoyant and behaves like a starting jet of finite duration, the duration of the release, especially for speaking or breathing out, could last of the order of seconds. for such duration, therefore, it may not be a bad approximation to consider the decay of a continuous round jet, which allows us to build an easy-to-use connection between the settling times of section (a) with a time-of-flight estimate to reach the safe distance l sf . the mean velocity u at the centreline of an axisymmetric turbulent jet decays as: where l is the distance from the jet's source, d the jet diameter, u the velocity at the release, and c ≈ is an empirical constant from experiment [ ] . (the non-circular mouth opening can be absorbed as a first approximation into the value of the constant c). following a fluid particle travelling along the central streamline of the jet, which relates the mean time of flight t fl needed to reach a distance l. for l = l sf = m, u = m/s, d= mm, values typical of speaking [ ] , the physical distancing limit l sf = m is reached at t fl = . s. the results of section (a) suggest that for speaking more than about − of the emitted release has not yet fallen on the ground at m. assume that the steady-state velocity decay (eq. . ) is also valid for a cough. using u = m/s and d = mm, a distance of l = m is reached at about t fl = . s. figure shows that by that time there has been virtually no gravitational removal when considering the total suspended liquid, and fig. shows that between . and . m, at face height, an order of magnitude removal is observed. hence, the receptor will receive a significant proportion of all viral load directly at face height. safe levels are reached only after s- min of flight time for either zero or downward flow, which suggests that an unprotected cough is not safe at any reasonable distance. speaking for s (fig. ) with the high-concentration estimate of viral load releases enough virus particles that even after min, the particles that have not settled through gravity are still above the smallest dose needed for % risk of infection. however, with the copies/ml l estimate, the suspended viable dose within a few minutes has fallen by about two orders of magnitude. for aerosol droplets in particular, removal by gravity starts only after min with the gravitational settling rate reaching a steady-state value of about . h − ( . h − for suspended aerosol droplets by coughing) after min. both viral inactivation and removal by gravity have a small cleansing effect for the aerosols; hence ventilation removal must be added if continuous speaking is to be safe. furthermore, recent work suggests that the voice loudness can enhance droplet production during speaking [ ] , and that a high viral replication and the highest viral loads of sars-cov- were found to occur in the throat -where fine droplets are produced -in the early stages of the disease (or in asymptomatic individuals) [ ] . considering such findings in a worst-case scenario of virus loads and potentially greater amounts of droplets emitted in a loud environment, the potential of speaking as a mechanism of indoor as well as outdoor viral transmission becomes even more evident. this corroborates the suggestion that aerosol transmission was the main contagion mechanism in a number of cases, such as the restaurant in guangzhou (china) and the choir rehearsal in valley chorale (usa) as recently suggested in [ ] . in the case of mixing ventilation -for instance through ceiling-placed a/c systems, fan-assisted, or jet-induced ventilation -it may be assumed that the air in the room is homogeneously . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted july , . . https://doi.org/ . / . . . doi: medrxiv preprint mixed very quickly, typically of the order of the turbulent turnover time t turb = l turb /u , where l turb is the integral length scale (perhaps of the order of . - m for a typical room) and u the characteristic turbulent velocity (perhaps of the order of . - . m/s). hence, the mixing timescale may be of the order of to s. this is short compared to a typical purge time of the room by fresh air, which is the inverse of the "air changes per pour" (ach) that typically characterises ventilation systems. targets for well-ventilated rooms are - ach, which suggests an average purge (or residence) time tres of - s. therefore, considering the typical ach used currently, the well-mixed approximation is fair. the nv,s would be removed by ventilation according to dnv,s dt = − nv,s tres where tres = v/q, with v the volume of the room and q the ventilation volume flow rate. this gives an exponential decay with tres as the characteristic timescale.for example, a removal of − of the original nv,s, associated with the aerosol would be reached at a time t ≈ tres. consider an indoor environment with a total volume v= m , simulating a lecture room, and one infected individual continuously speaking for h. let us also assume a range of - copies/ml l virus load in sputum. the well-mixed approximation results in an uniform concentration of suspended viral aerosol droplets that are generated by speaking and reduced via simultaneous ventilation removal, viral inactivation and gravity, similar to fig. (b) . for an occupant inhaling . l/s [ ] , the infection dose model by [ ] yields an infection risk of about . - . % at the end of emission when the room is ventilated with ach, whereas the infection risk may increase to . - % if the occupant spends another hour in the same room. for a well-ventilated room with ach, the infection risk reduces to . - . %, which confirms the importance of ventilation in mitigating risk from long-time emission, especially when the emitter is pre-symptomatic or asymptomatic, i.e. having a lower virus load. however, to ensure a higher cleansing effect and reduce risk to levels well below . % for any virus load in the considered range, one would need o( ) ach, that is, an order of magnitude stronger than current practice in most residential, professional, and even hospital settings. a comprehensive modelling strategy of the evaporation and settling of droplets emitted in respiratory releases (speaking, coughing) was provided in a lagrangian framework, which included state-of-the-art models for droplet evaporation, effects of the sputum composition on heat and mass transfer, and droplet size distributions. by considering characteristics of the sars-cov- virus, such as its decay rate, viral load in infected individuals, and estimated infection dose from sars-cov- , theoretical estimates were given for the evolution of the droplet cloud in terms of suspended mass and droplet number and its associated viable viral dose, for a short cough and in continuous, paced speech. such metrics were then used in the context of canonical problems providing insights on physical distancing and ventilation. the evolution of the probability density functions of droplet size given by the bronchiolarlaryngeal-oral tri-modal model for speaking and coughing were evaluated. evaporation time scales of approximately ms and s were observed for droplets within the bronchiolar mode (centred at - µm) and the laryngeal mode (centred at - µm), respectively. large droplets produced in the oral mode (centred at - µm) were observed to settle by gravity within just a few minutes. evaporation and settling time scales of the droplets were strongly impacted by the sputum composition, which limited the resulting equilibrium size of the generated droplet nuclei (i.e. "dry droplets"). varying the droplet composition and the ambient relative humidity, resulted in % relative differences in the settling times for droplets up to approximately µm, thus impacting the evolution of the droplet cloud and its associated viral dose. about one hour after emission, virtually all mass lied in droplets within the aerosol class between . - µm in diameter. although, in absolute terms, a short cough emitted as much liquid mass as seconds of continued, paced speaking, the resulting aerosol contained an order of magnitude more mass for speaking than coughing. further, the effect of an upward mean . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. (which was not certified by peer review) the copyright holder for this preprint this version posted july , . . https://doi.org/ . / . . . doi: medrxiv preprint ventilation flow was observed to sustain a higher viral dose at face height, increasing to min the time at which an infection dose for % infection risk was found suspended, in relation to s and s for speaking and coughing when only gravity was considered. at min after emission, the largest droplets in the cloud were just above µm. these results stress the need for air change through ventilation to reduce the risk of disease transmission in indoors activities, and emphasise the importance of the direction of displacement ventilation and precise account of the aerosol characteristics. due to the high associated mass and viral dose in large droplets (∼ % of the emitted value), both a short cough and continued speaking were found to be unsafe within m without personal protective equipment. in this case, the problem is governed by the settling of large droplets (d k > µm) produced in the oral mode, hence the effect of droplet evaporation and composition were negligible. upward air streams resulting from displacement ventilation could increase the distance travelled by droplets, while downward streams (e.g. from under-floor negative pressure ventilation systems) could be used to enhance droplet removal from face height. as ventilation is of utmost importance for aerosol removal, personal protective equipment is crucial to reduce the risk of short-range contamination in ventilation systems inducing upward flows. the implications of the present findings for virus transmission control measures are: • standing m opposite an infected speaker is not safe without the use of a protective mask or respirator. in the presence of a constant mean flow (u ab = . m/s), it was found that up to viable viral copies were within face height after just a few seconds. in the absence of such flow, jet-decay calculations demonstrated that a similar viral dose can be found at face height at the same -m distance, corresponding in % risk of infection, while for a short cough the suspended dose would lead to % risk. • an unprotected cough is not safe at any reasonable distance close to an infected individual. jet decay estimates showed that even for an initial viral load of copies/ml l , equivalent of that found in infected asymptomatic individuals, safe levels of infection at m from emission are only attained after s- min of flight time at face height. • settling of the aerosol by gravity was found to be small compared to the viral decay. for the suspended aerosol resulting from speaking, removal by gravity started only after min and stabilised at settling rate of ≈ . h − after min ( . h − for coughing). therefore, gravitational settling cannot be relied upon for reducing the infection risk posed by aerosols. • the presence of air currents strongly affects the suspended viral dose regardless of the exhalation mode. a . -m/s downward flow can remove completely suspended virus in less than s, while a . -m/s upward air stream can maintain at face height a viral charge corresponding to % infection risk for ≈ min, and a viral charge corresponding to % infection risk for ≈ min. • an infected person speaking for h in a model room may lead to infection risk levels of - % with inadequate ventilation, but the risk can be reduced by, at least, a factor of three if air changes per hour are employed. however, an order of air changes per hour are needed if the risk for continuous emission is to fall below . % for high viral emission (e.g. from symptomatic emitters). therefore, ventilation (in terms of both magnitude and direction) is of utmost importance in minimising infection risk indoors. the present results illustrate the need of addressing the problem between the short and the long time-scale settling, that is, between what is commonly defined as droplet transmission and aerosol transmission (d k < µm, [ ] ). the concerning time scales observed are s- min, in which the droplet cloud is characterised, in addition to the aerosol class, by - µm droplets. although these droplets represented just under % of the total initial mass and viral dose emitted, this value is roughly times more than what lies in the aerosol class. within this time scale, effects of composition and of relative humidity played an important role resulting in order-of-magnitude variations of the estimated suspended mass and viral dose. . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. (which was not certified by peer review) the copyright holder for this preprint this version posted july , . . https://doi.org/ . / . . . doi: medrxiv preprint putting a balance on the aerosolization debate around sars-cov- estimation of airborne viral emission: quanta emission rate of sars-cov- for infection risk assessment temporal profiles of viral load in posterior oropharyngeal saliva samples and serum antibody responses during infection by sars-cov- : an observational cohort study virological assessment of hospitalized patients with covid- transmission of -ncov infection from an asymptomatic contact in germany viral load of sars-cov- in clinical samples sars-cov- viral load in upper respiratory specimens of infected patients on air-borne infection: study ii. droplets and droplet nuclei how far droplets can move in indoor environments the size distribution of droplets in the exhaled breath of healthy human subjects size distribution and sites of origin of droplets expelled from the human respiratory tract during expiratory activities modality of human expired aerosol size distributions mechanistic insights into the effect of humidity on airborne influenza virus survival, transmission and incidence natural ventilation for infection control in health-care settings -world health organization molecular dynamics simulation of the surface tension of aqueous sodium chloride: from dilute to highly supersaturated solutions and molten salt physico-chemical characteristics of evaporating respiratory fluid droplets evaporation and combustion of sprays Über die grundlegende berechnung bei der schwerkraftaufbereitung. zeitschrift des vereins deutscher ingenieure droplet vaporization model for spray combustion calculations uber die verdunstung fallender tropfen microphysics of clouds and precipitation surface tensions of inorganic multicomponent aqueous electrolyte solutions and melts surface tension in human pathophysiology and its application as a medical diagnostic tool interaction of aerosol particles composed of protein and salts with water vapor: hygroscopic growth and microstructural rearrangement modeling the evaporation and dispersion of airborne sputum droplets expelled from a human cough expression of c-reactive protein in the human respiratory tract dilution of respiratory solutes in exhaled condensates role of pulmonary surfactant components in surface film formation and dynamics aerosol and surface stability of sars-cov- as compared with sars-cov- an analysis of sars-cov- viral load by patient age development of a doseresponse model for sars coronavirus characterizing exhaled airflow from breathing and talking flow dynamics and characterization of a cough turbulent flows aerosol emission and superemission during human speech increase with voice loudness acknowledgements. the authors thank dr m.p. sitte for his assistance with the abramzon-sirignano model and also acknowledge dr adam boies (university of cambridge) for useful discussions. authors' contributions. e.m. and p.m.o. conceived the work. all authors contributed to the calculations, analysis, and writing of the manuscript.competing interests. we declare we have no competing interests.funding. none. key: cord- -rimpulm authors: eaton, w. a.; bax, a.; netz, r. r. title: physics of virus transmission by speaking droplets date: - - journal: nan doi: . / . . . sha: doc_id: cord_uid: rimpulm droplets of oral fluid emitted by speaking are a long-recognized mechanism of respiratory virus transmission. while there have been many simulations of droplet evaporation to determine whether droplets containing virions remain floating in air or rapidly fall to the ground, they typically conceal the fundamental mechanisms because of the use of numerics. to make the physics of emitted oral fluid droplets easily understood, we present simple and transparent algebraic equations that capture the essential physics of the problem. calculations with these equations provide a straightforward way to determine the airborne lifetime of emitted droplets after accounting for the decrease in droplet size from water evaporation. at a relative humidity of %, droplets with initial radii larger than about microns rapidly fall to the ground while smaller, potentially-virus containing droplets shrink in size and remain airborne for many minutes. rough estimates of airborne virion emission rates while speaking support the proposal that covering the mouth can help end the pandemic more quickly. the physics of water droplets is a well-studied subject and its relevance to virus and transmission long known ( - ). it is a subject that has aroused renewed interest because of the covid- pandemic and has motivated scientists to perform new kinds of experiments. just published laser light-scattering experiments of anfinrud et al. ( ) show that the number of oral fluid droplets are emitted into the air while speaking is orders of magnitude larger than previously detected using less sensitive methods ( ) and that blocking such droplets is easily accomplished with a cloth mouth cover ( )(youtu.be/qzarpgx cve). previous physics calculations of droplet evaporation to determine whether droplets containing viruses remain floating in air or rapidly fall to the ground typically involve numerical simulations, which hide the fundamental mechanisms ( , , ) . in addition, the mathematics employed is too complex to be understood by other than physical scientists. we have investigated all aspects of this physics problem and present simple and transparent algebraic equations that capture the essential physics. our equations answer two important questions. first, how long does it take for a viruscontaining droplet of a given size to fall to the ground by gravity to potentially contaminate a surface? second, for each relative humidity, how much time does it take for water evaporation to reduce a virus-containing droplet to a size that leaves it floating in air for a sufficiently long time to allow direct transmission of the virus to another person? the answer to the first question is easily obtained by simply equating the gravitational and stokesian viscous forces on a falling object (mg = πηrv) to obtain the terminal velocity (v). this simplistic treatment is justified in ref. ( ) . the mean time for a particle to reach the ground is then: where τsed is the mean time for a droplet of radius, r, to reach the ground from a height, z , with both r and z in units of µm ( µm = - m). the prefactor, φ = η/( ρg) = . x - µm s, is calculated from the viscosity of air at o c, η = . x - g/µm s, water density, ρ = - g/µm , and the gravitational constant, g = . x µm /s . a few examples are instructive. droplets placed initially at . m (the average height above ground for the mouth of a standing human adult) with radii of µm, µm, or µm will require . x s (~ . hours), s and . s, to settle to the ground, respectively. determining whether or not a virus-containing droplet will remain airborne to cause an infection requires determination of the rate of evaporation of water, which is a more complex problem and is different for different size regimes. the most important effects to consider in the size regime of interest are the cooling of the droplet from the heat loss due to water evaporation, which slows the evaporation rate, and the osmotic effect of the soluble droplet contents, that reduces the water vapor pressure at the droplet surface and therefore decreases the evaporation rate. oral fluid, which is primarily saliva, contains about % by volume water, with the remaining % of volume consisting of proteins, mucus, epithelial cells, white cells, electrolytes, small molecules ( ) , and possibly a virion. we assume that ~ % volume of water is strongly bound to the solutes. the volume fraction of non-volatile solute, which includes the strongly bound hydration water, is then about Φ = . . dehydration of the droplet in less than water vapor-saturated air results in a so-called "droplet nucleus" (dn), which retains additional water. balance of the water vapor pressure of the droplet and the ambient air results in an equilibrium solute volume fraction of Φdn = -rh, where rh is the relative humidity. thus, for rh = . , the initial droplet radius can maximally decrease due to evaporation by about a factor of ( ) the different size regimes that require different theoretical treatments are: droplet radii r < nm, nm < r < µm and > µm. we shall only be concerned with the latter regimes, as < nm radii are in the size regime of a single virion (τsed = several days), which cannot be emitted without a surrounding layer of oral fluid. in the following, we assume that the droplet has escaped from any surrounding water vapor cloud ( ) to be in ambient air. in the intermediate size regime of nm < r < , the result for τev, the time it takes for complete evaporation of a pure water droplet of initial radius r , including cooling, is ( where rh is the relative humidity, θ = αdwcgvw = . x µm /s at c is a constant with units of diffusion and the numerical prefactor, α = . , accounts for evaporation-cooling effects ( ) . the diffusion constant for a water molecule in air, dw, is . x µm /s, the water number concentration, cg, in saturated air is . x µm - , and the water molecular volume, vw, in liquid water is . x - µm , all at o c. notice that the quadratic dependence of τev on r , indicates that evaporation accelerates as the droplet gets smaller and therefore falls more slowly. all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted may , . . https://doi.org/ . / . . . doi: medrxiv preprint the theory is more complex for inclusion of the osmotic effect of the contents of a droplet, the droplet nucleus. in this case, the mean time for a droplet of initial radius r to shrink to a radius r from water evaporation, is given by ( ) where is the equilibrium droplet nucleus radius, which we estimated above to be ~r / . the last term in equation ( ) accounts for the vapor pressure reduction due to solutes. at r < . , the evaporation time enters the solute-dominated regime and diverges, albeit only logarithmically, in the limit → ( ) . therefore, for times prior to achieving perfect equilibrium the logarithmic term is small enough to be neglected and equation simplifies to where. at a relative humidity of rh = . , a common value for room air, the mean evaporation times for droplets with initial radii, r , of , , and µm are ms, . s, and s, while the corresponding sedimentation mean times, τsed, from equation ( ) for rh = . and z = . m, the critical radius is µm. this means that droplets with radii greater than µm will fall to the ground before drying out, while droplets with radii less than µm will remain floating in the air. a more accurate value for the critical radius of ~ µm is obtained by solving equations that take into account evaporation of droplets while sedimenting ( ) . equation ( ) does not apply to the third size regime of ro > µm. at ro > µm, calculating the evaporation rate for droplets at rest (the so-called stagnant approximation) is no longer valid and the evaporation is accelerated by the air flow around the droplet. this effect can be treated by assuming a concentration boundary layer around the droplet. at the same time, non-linear hydrodynamic effects produce a flow boundary layer around the droplet outside of which viscosity effects are negligible. using double boundary layer theory ( ) , the evaporation for ro > µm is shown to be even faster than predicted by equation ( ) . since these modifications only become important for larger radii than our equation ( ) predicts, the estimate of the critical droplet size of µm is not modified by these complex hydrodynamic effects. all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted may , . . can we say anything useful about the number of emitted virions while speaking? anfinrud et al. used their sensitive laser light scattering method to count droplets in each / th s frame of their video, which yields an approximate average droplet emission rate of ~ /s ( ) . we also need to know the concentration of virions in saliva and the volume of the droplets. wölfel et al. reported an average virion concentration of x ( ) virions/cc. there are no reported values for the average volume at droplet count rates comparable to the findings of anfinrud et al. however, all of the distributions determined since the work of duguid ( ) show that the vast majority of droplet diameters are less than microns ( ) (and references therein). we can therefore get an informative estimate of the possible range for the rate of emitted airborne virions by calculating this number for each assumed initial droplet radius. given the many contents of saliva, in addition to the possibility of a virion, we estimate that the smallest possible radius before evaporation is ~ µm. table shows the calculated values for initial droplet radii (r ) from to µm, which predicts that the number of emitted virions while continuously speaking ranges from to ~ per minute. comparing the evaporation times at a relative humidity of % with the sedimentation times in table shows that for all radii in this range droplet nuclei remain airborne for times sufficiently long that their airborne lifetime will be determined by the turnover time of the air handling system. it is not known what fraction of the virions in these concentration measurements are infectious, but it has been argued that in some systems as few as a single active virion can cause an infection ( ) . the very large range of virion emission rates in table calls for both an accurate determination of the fraction of airborne virions that are infectious, as well as accurate droplet size distributions at the high rate of emission determined by laser light scattering ( ) . measurements of droplet sizes at these high rates are currently underway at nih. table . theoretical virion emission rates (k), sedimentation times (τsed) at z = . m, and evaporation times (t(rdn)) at c for initial radii (r ) and for droplet nuclei at % relative humidity (rh = . ). overall, the above analysis strongly supports the concept that simply speaking can be a major mechanism of covid- transmission and that covering the mouth in public, as suggested by the work of anfinrud et al ( ) (youtu.be/qzarpgx cve) and others ( , ) , could help to more rapidly contain and potentially end the pandemic. it also suggests that mouth covering is a more effective way of reducing transmission than maintaining a distance of at least feet from another person. this conclusion is strongly supported by epidemiological evidence. the all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted may , . . majority of the million taiwanese have been wearing masks since the first infections were discovered, which almost certainly has contributed to the low number of deaths -only reported in taiwan as of april (with only in the past weeks) compared to more than , deaths in the state of new york with million fewer inhabitants. even more convincing is vietnam, where the total number of reported deaths is zero and wearing a mask is mandatory in public places for the entire population of million. finally, austria and germany, where face masks are required, are the only large non-asiatic countries where there is marked slowing in the rate of new cases (https://coronavirus.jhu.edu/map.html). on air-borne infection -study ii droplets and droplet nuclei the size and duration of air-carriage of respiratory droplets and droplet nuclei evaporation from drops droplet fate in indoor environments, or can we prevent the spread of infection? how far droplets can move in indoor environments -revisiting the wells evaporation-falling curve theoretical analysis of the motion and evaporation of exhaled respiratory droplets of mixed composition influenza virus aerosols in human exhaled breath: particle size violent expiratory events: on coughing and sneezing airborne spread of expiratory droplet nuclei between the occupants of indoor environments: a review infectious virus in exhaled breath of symptomatic seasonal influenza cases from a college community disease transmission via drops and bubbles respiratory virus shedding in exhaled breath and efficacy of face masks visualizing speech-generated oral fluid droplets with laser light scattering fluid dynamics and transport of droplets and sprays evaporation and droplet growth in gaseous media lifetime of virus-containing droplets diffusing and evaporating in air saliva sampling: methods and devices. an overview virological assessment of hospitalized patients with covud- nature one is enough: in vivo effective population size is dose-dependent for a plant rna virus airborne transmission of sars-cov- : the world should face the reality key: cord- - vln erl authors: bhardwaj, rajneesh; agrawal, amit title: likelihood of survival of coronavirus in a respiratory droplet deposited on a solid surface date: - - journal: phys fluids ( ) doi: . / . sha: doc_id: cord_uid: vln erl we predict and analyze the drying time of respiratory droplets from a covid- infected subject, which is a crucial time to infect another subject. drying of the droplet is predicted by using a diffusion-limited evaporation model for a sessile droplet placed on a partially wetted surface with a pinned contact line. the variation in droplet volume, contact angle, ambient temperature, and humidity are considered. we analyze the chances of the survival of the virus present in the droplet based on the lifetime of the droplets under several conditions and find that the chances of the survival of the virus are strongly affected by each of these parameters. the magnitude of shear stress inside the droplet computed using the model is not large enough to obliterate the virus. we also explore the relationship between the drying time of a droplet and the growth rate of the spread of covid- in five different cities and find that they are weakly correlated. previous studies have reported that infectious diseases such as influenza spread through respiratory droplets. the respiratory droplets could transmit the virus from one subject to another through the air. these droplets can be produced by sneezing and coughing. han et al. measured the size distribution of sneeze droplets expelled from the mouth. they reported that the geometric mean of the droplet size of sneezes of healthy subjects is around μm for unimodal distribution and is μm for bimodal distribution. liu et al. reported around % longer drying time of saliva droplets as compared to water droplets deposited on a teflonprinted slide. they also predicted and compared these times with a model and considered the solute effect (raoult's effect) due to the presence of salt/electrolytes in saliva. the slower evaporation of the saliva droplet is attributed to the presence of the solute in it. xie et al. developed a model for estimating the droplet diameter, temperature, and falling distance as a function of time as droplets are expelled during various respiratory activities. they reported that large droplets expelled horizontally can travel a long distance before hitting the ground. in a recent study, bourouiba has provided evidence that droplets expelled during sneezing are carried to a much larger distance (of - m) than the distance previously found. the warm and moist air surrounding the droplets helps in carrying the droplets to such a large distance. while the role of virus-laden droplets in spreading infectious diseases is well-known, the drying time of such droplets after falling on a surface has not been well-studied. in this context, buckland and tyrrell experimentally studied the loss in infectivity of different viruses upon drying of virus-laden droplets on a glass slide. at room temperature and % relative humidity, the mean log reduction in titer was reported to be in the range of . - . for viruses they considered. the need for studying the evaporation dynamics of virus-laden droplets has also been recognized in the recent article by mittal et al. furthermore, to reduce the transmission of covid- pandemic caused by sars-cov- , the use of a face mask has been recommended by who. the infected droplets could be found on a face mask or a surface inside the room, which necessitates the regular cleaning of the surface exposed to the droplets. therefore, the present study examines the drying times of such droplets, which correlates with the time in which the chances of the transmissibility of the virus are high. , first, we present different components of the model that are used to estimate the drying time and shear stress. we consider aqueous respiratory droplets that are on the order of - nl on a solid surface. the range of the volume is consistent with previous measurements. the corresponding diameters of the droplets in the air are around μm and μm, and the probability density scitation.org/journal/phf function (pdf) of the normal distribution of the droplet diameter in the air is plotted in fig. . the mean diameter and standard deviation are μm and μm, respectively. droplets smaller than μm are not considered in this study because such droplets are expected to remain airborne, while the larger droplets being heavier settle down. the droplet is assumed to be deposited as a spherical cap on the substrate. since the wetted diameter of the droplet is lesser than the capillary length ( . mm for water), the droplet maintains a spherical cap shape throughout evaporation. the volume (v) and contact angle (θ) of a spherical cap droplet are expressed as follows: where h and r are droplet height and wetted radius, respectively. we consider diffusion-limited, quasi-steady evaporation of a sessile droplet with a pinned contact line on a partially wetted surface (fig. ) . the assumption of quasi-steady evaporation is valid for t h /tf < . , as suggested by larson, where t h and tf are heat equilibrium time in the droplet and drying time, respectively. t h /tf scales as follows: where d, α, h, r, csat, and ρ are diffusion coefficient of liquid vapor in the air, thermal diffusivity of the droplet, droplet height, wetted radius, saturation liquid vapor concentration, and droplet density, respectively. in the present work, the maximum value of t h /tf is estimated to be around . at ○ c, the maximum water droplet temperature considered in the present work, and a contact angle of ○ (h/r = ). the values of d, α, and ρ are set as . × − m /s, . × − m /s, and kg/m , respectively. therefore, the assumption of quasi-steady evaporation is justified. the mass lost rate (kg/s) of an evaporating sessile droplet is expressed as follows: where h and θ are relative humidity and static contact angle, respectively. the saturated concentration (kg/m ) at a given temperature for water vapor is obtained using the following third order polynomial: , where t is the temperature in ○ c ( ○ c ≤ t < ○ c). the dependence of the diffusion coefficient (m /s) of water vapor on temperature ( ○ c) is given by , ). assuming a linear rate of change in the volume of the droplet for a sessile droplet pinned on the surface, , the drying time of the droplet is given by where v and ρ are the initial volume and density of the droplet, respectively. the properties of pure water have been employed in the present calculations to determine the drying time and shear stress. since the thermo-physical properties of saliva are not very different from water, the present results provide a good estimate of the evaporation time under different scenarios and shear stress. furthermore, we obtain the expression of the maximum shear stress (τ) on the nm diameter sars-cov- , suspended in the sessile water droplet, and estimate its range for the droplet size considered. the shear stress on the virus would be maximum for a virus adhered to the substrate surface (fig. ) . assuming a linear velocity profile across the cross section of the virus, the expression of τ is given by where μ, u, and dv are the viscosity of the droplet, flow velocity on the virus apex ( fig. ) , and virus diameter, respectively. the flow inside the droplet is driven by the loss of liquid vapor by diffusion. we neglect the flow caused by marangoni stress, since an evaporating water droplet in ambient does not exhibit this stress. , , the expression of the non-uniform evaporative mass flux on the liquid-gas interface, j, (kg m − s − ), is given by where λ(θ) = . −θ/π and r is the radial coordinate (fig. ) . the above expression exhibits singularity at r = r, and the maximum value of j (say, jmax) occurs near the contact line region (say, at r = . r). the magnitude of the evaporative-driven flow velocity (m s − ) is expressed as follows: the following expression of the maximum shear stress (τ) is therefore obtained: using eqs. ( ) and ( ) second, we present the effect of ambient temperature, surface wettability, and relative humidity on the drying time of the droplet. in this context, we examine the drying time of a deposited droplet in two different ambient temperatures, ○ c and ○ c. the chosen temperatures are representative of temperatures inside a room with air-conditioning and outdoors in summer. figure shows the variation in evaporation time with the droplet volume at the two different ambient temperatures considered. the contact angle and humidity for these simulations are set as ○ and %, respectively. at ○ c, the evaporation time for small droplets is about s, which increases to s for large size droplets. the evaporation time increases as the square of the droplet radius or / power of volume. an increase in the ambient temperature reduces the evaporation time substantially (by about % for ○ c rise in temperature). therefore, an increase in the ambient temperature is expected to drastically reduce the chance of infection through contact with an infected droplet. the effect of the surface on which the droplet can fall onto is modeled here through an appropriate value of the contact angle. the contact angle of ○ corresponds to a water droplet on glass, while ○ corresponds to a water droplet on the touch screen of a smartphone (table i) . the results of the simulations corresponding to these two contact angles are plotted in fig. . the ambient temperature and humidity are set as ○ c and %, respectively. figure shows that the effect of the surface can be quite profound; the evaporation time can increase by % for a more hydrophobic surface. the droplet spreading on the surface is larger as the contact angle decreases and thereby, enhancing the mass loss rate of liquid from the droplet to the ambient. therefore, for a surface with a smaller contact angle, the evaporation time of the droplet is smaller. the effect of the surface can further be manifested by a difference in temperature in different parts of the surface. such inhomogeneity in the surface temperature can be brought about by the difference in the surface material (leading to the difference in the emissivity) or differential cooling (for example, due to the corner effect). even a slight difference in the surface temperature can further aggravate the surface effect by influencing the evaporation time. sars-cov- has a lipid envelop, and in general, the survival tendency of such viruses, when suspended in air, is larger at a lower relative humidity of %- %, as compared to several other viruses that do not have a protective lipid layer. here, we examine the effect of the relative humidity on the survival of the virus inside a droplet deposited on a surface. figure shows that the relative humidity has a strong effect on the evaporation time. the contact angle and ambient temperature for these calculations are set as ○ c and ○ c, respectively. the evaporation time of a droplet increases almost sevenfold with an increase in humidity from % to %. furthermore, the evaporation time becomes greater than min for large droplets at high humidity. with the increase in humidity in coastal areas in summer and later in other parts of asia in july-september with an advent of monsoon, this may become an issue as there will be sufficient time for the virus to spread from the droplet to new hosts upon contact with the infected droplet. therefore, higher humidity increases the survival of the virus when it is inside the droplet; however, it decreases its chances of the survival if the virus is airborne. finally, we discuss the relevance of the present results in the context of covid- pandemic. the evaporation time of a droplet is a critical parameter as it determines the duration over which the spread of infection from the droplet to another person coming in contact with the droplet is possible. the virus needs a medium to stay alive; therefore, once the droplet has evaporated, the virus is not expected to survive. the evaporation time can, therefore, be taken as an indicator of the survival time of the virus. in general, it is regarded that a temperature of ○ c maintained for more than min inactivates most of the viruses; however, contrary reports about the effect of temperature on the survivability of sars-cov- has been reported. , our results indicate that the survival time of the virus depends on the surface on which the droplet has fallen, along with the temperature and humidity of the ambient air. the present results are expected to be of relevance in two different scenarios: when droplets are generated by an infected person by coughing or sneezing (in the absence of a protective mask) or when fine droplets are sprayed on a surface for cleaning/disinfecting the surface. a wide range of droplet sizes is expected to be produced in these cases. the mutual interaction of the droplets such that they interfere in the evaporation dynamics is, however, expected to be weak because of the large distance between the droplets, as compared to their diameter. the virus inside a droplet is subjected to shear stresses due to the generation of the evaporation-induced flow inside the droplet. the magnitude of this shear stress has however been estimated to be small, and the virus is unlikely to be disrupted by this shear stress inside the droplet. to determine the likelihood of the droplet and the virus on the surface, we find the mean and standard deviation of the probability density function (pdf) of the normal distribution of the droplet drying times for different cases of ambient temperature, contact angle, and relative humidity. the values of the mean and standard deviation are plotted using the bar and error bar, respectively, in fig. . the likelihood lifetime is in the range for ( - ) s for h ≤ %, while it is in the range of ( - ) s for h = %. this result shows that the drying time is likely to be larger by around five times in the case of large relative humidity values, thereby increasing the chances of the survival of the virus. furthermore, we examine the connection between the drying time of a droplet and the growth of the infection. a similar approach was recently tested for suspended droplets in air in ref. . we hypothesize that since the drying time of a respiratory droplet on a surface is linked to the survival of the droplet, it is correlated with the growth of the pandemic. since the drying time is a function of weather, we compare the growth of infection with the drying time in different cities. the cities were selected based on cold/warm and dry/humid weather. the growth of the total number of infections is plotted for cities with different weather conditions during the pandemic in fig. . the data of the infections were obtained from public repositories. , the data were fitted with linear curves using the least-squares method, and the slope of the fits represents the growth rate (the number of infections per day) of the respective city. the growth rate of new york city and singapore is the highest and the lowest, respectively. for different cities, we compute the drying time of a droplet of nl volume, which is the mean volume obtained using the pdf of the distribution (fig. ) . the ambient temperature and relative humidity are taken as a mean of the respective ranges listed in table ii . as discussed earlier, the drying time increases with an increase in humidity; however, it decreases with an increase in ambient temperature. thus, the combined effect of humidity and temperature dictates the final drying time. this can be illustrated by comparing the drying time of singapore and new york city plotted in fig. . the time is shorter for the former as compared to the latter despite with a large humidity for the former ( %- %) as compared to the latter ( %- %). finally, fig. compares the growth rate and drying time in different cities using vertical bars and symbols, respectively. the growth rate appears to be weakly correlated with the drying time, i.e., a larger (lower) growth rate corresponds to larger (lower) drying time. qualitatively, these data verify that when a droplet evaporates slowly, the chance for the survival of the virus is enhanced and the growth rate is augmented. we recognize that our model has limitations, which can be improved in subsequent studies. in particular, air has been assumed to be stationary; the evaporation time is expected to reduce in the presence of convective currents. therefore, the value of the predicted evaporation times is on the conservative side, and the actual evaporation time will be smaller than that obtained here. the effect of the solute present (i.e., raoult's law) in saliva/mucus has not been modeled, and the contact angle and drying of these biological fluids could be slightly different from that of pure water on a solid surface. however, the impact of these latter effects on the drying time is expected to be small. furthermore, the model does not consider the interaction of the droplets. it is likely that the respiratory droplets, expelled from mouth and/or nose, deposit adjacent to each other on a surface and could interact while evaporating. they may interact while falling, and a falling droplet may coalesce on an already deposited droplet on a surface. in addition, receding of the contact line may influence the drying time, which is not considered in the present work. in sum, we have examined the likelihood of the survival of sars-cov- suspended in respiratory droplets originated from a covid- infected subject. the droplet is considered to be evaporating under ambient conditions on different surfaces. the droplet's volume range is considered as ( , ) nl. the datasets of the drying time presented here for different ambient conditions and surfaces will be helpful for future studies. the likelihood of the survival of the virus increases roughly by five times under a humid condition as compared to a dry condition. the growth rate of covid- was found to be weakly correlated with the outdoor weather. while the present letter discusses the results in the context of covid- , the present model is also valid for respiratory droplets of other transmissible diseases, such as influenza a. the data that support the findings of this study are available from the corresponding author upon reasonable request. characterizations of particle size distribution of the droplets exhaled by sneeze evaporation and dispersion of respiratory droplets from coughing how far droplets can move in indoor environments-revisiting the wells evaporation-falling curve turbulent gas clouds and respiratory pathogen emissions potential implications for reducing transmission of covid- loss of infectivity on drying various viruses the flow physics of covid- a review of coronavirus disease- (covid- ) inactivation of influenza a viruses in the environment and modes of transmission: a critical review aerobiology and its role in the transmission of infectious diseases transport and deposition patterns in drying sessile droplets crc handbook of chemistry and physics evaporation of a sessile droplet on a substrate pattern formation during the evaporation of a colloidal nanoliter drop: a numerical and experimental study a combined computational and experimental investigation on evaporation of a sessile water droplet on a heated hydrophilic substrate evaporative deposition patterns: spatial dimensions of the deposit analysis of the microfluid flow in an evaporating sessile droplet self-assembly of colloidal particles from evaporating droplets: role of dlvo interactions and proposition of a phase diagram dynamics of water spreading on a glass surface wetting of wood on the collision of a droplet with a solid surface water wetting and retention of cotton assemblies as affected by alkaline and bleaching treatments preparation and adhesion performance of transparent acrylic pressure sensitive adhesives for touch screen panel the effect of environmental parameters on the survival of airborne infectious agents high temperature and high humidity reduce the transmission of covid- no association of covid- transmission with temperature or uv radiation in chinese cities modeling ambient temperature and relative humidity sensitivity of respiratory droplets and their role in determining growth rate of covid- outbreaks evaporation-induced transport of a pure aqueous droplet by an aqueous mixture droplet effect of viscosity on droplet-droplet collisional interaction coalescence dynamics of a droplet on a sessile droplet on the lifetimes of evaporating droplets with related initial and receding contact angles key: cord- - nl js x authors: kumar, vivek; nallamothu, sravankumar; shrivastava, sourabh; jadeja, harshrajsinh; nakod, pravin; andrade, prem; doshi, pankaj; kumaraswamy, guruswamy title: on the utility of cloth facemasks for controlling ejecta during respiratory events date: - - journal: nan doi: nan sha: doc_id: cord_uid: nl js x the utility of wearing simple cloth face masks is analyzed using computational fluid dynamics simulations. we simulate the aerodynamic flow through the mask and the spatial spread of droplet ejecta resulting from respiratory events such as coughing or sneezing. without a mask, a turbulent jet forms, and droplets with a broad size distribution are ejected. large droplets (greater than about {mu}m in diameter) fall to the ground within about m, while turbulent clouds transport a mist of small aerosolized droplets over significant distances (~ m), consistent with reported experimental findings. a loosely fitted simple cotton cloth mask (with a pore size ~ microns) qualitatively changes the propagation of the high velocity jet, and largely eliminates the turbulent cloud downstream of the mask. about % of the airflow leaks around the sides of a mask, considering a uniform gap of only mm all around, between the face and the mask. the spread of ejecta is also changed, with most large droplets trapped at the mask surface. we present the viral load in the air and deposited around the person, and show that wearing even a simple cloth mask substantially decreases the extent of spatial spread of virus particles when an infected person coughs or sneezes. there is consensus , , , that the use of surgical facemasks and n respirators help control the transmission of respiratory diseases such as influenza. therefore, the use of these personal protective equipment (ppe) has been recommended for health care personnel, infected patients and their care givers. to ensure that surgical masks and n respirators are available to those at greatest risk of infection, the world health organization and national agencies have recommended against their use by the general public. even so, greatly increased demand during the covid- pandemic has seen a global shortage of such ppe. since surgical masks and n respirators are not readily available to the public, the use of simple homemade reusable cloth facemasks has been suggested , as a protective measure, especially due to the possibility of asymptomatic disease transmission. however, there has been considerable controversy , , , over the efficacy of home-made reusable cloth face masks. one report suggests that the use of a homemade face mask would be better than "no protection at all". in south east asian countries, the practice of using face masks for combating pollution or for personal hygiene is widespread. this has been cited as an important factor in controlling the transmission of covid- infections. however, there are concerns that the use of facemasks may decrease the rigour in following strict physical distancing and handwash hygiene. further, incorrect use of masks, for example, wearing masks incorrectly or touching the outer surface of masks can result in adverse outcomes. sars-cov has been found on the surface masks worn by infected patients, and has been shown to remain viable on the surface of surgical masks for several days. therefore, a detailed understanding of the benefits of wearing homemade cloth masks would be useful in determining policy on their recommended and possible mandatory use. sars-cov , the virus responsible for the covid- pandemic, infects cells in the upper respiratory system. transmission of covid- is currently believed , , to happen primarily through shedding of virus particles in droplets ejected as infected people speak, cough or sneeze, or through contact with viable infective virus deposited on surfaces. when people cough or sneeze (or even simply talk loudly , ) , they eject droplets of mucosal fluid. large droplets ~o( µm) fall due to gravity and, under no wind conditions, are transported over lateral distances of the order of m. however, turbulent flows resulting from violent expulsions during sneezing or coughing suspend finer droplets and transport them over large distances, of the order of - m. , , therefore, it has been suggested that transmission of infection through fine droplets be investigated. , , the effect of surgical masks and n respirators on airflows (but not spread of droplet ejecta) during expiratory events has been experimentally imaged. here, we employ computational fluid dynamics (cfd) simulations to address the influence of homemade face masks on the turbulent clouds that result due to sneezing events, and on the lateral extent of spread of ejecta. our emphasis is on understanding the effect of face masks in altering the flow field and droplet dispersion due to the respiratory event. respiratory events (sneezing or coughing) and the resultant spread of ejecta are modeled as two-phase flow using ansys fluent software r . the carrier fluid (air) is represented as a continuum phase, and mucosal droplets are represented as the discrete phase. mucosal droplets are assumed to have properties of water. we model the dynamics of turbulent air jets using timeaveraged navier-stokes mass and momentum conservation equations. the renormalization group (rng) k-epsilon model is used to model the turbulence, allowing us to span high velocity turbulent flows to lower velocity flows. we employ the enhanced wall treatment model in combination with rng k-epsilon model to account for the viscous sublayer near the wall surface. a detailed description of the equations and models is given elsewhere, and a brief summary is provided in the supporting information (section a). for the discrete droplet phase, equations of motion are solved for each droplet to model its trajectory. droplets can exchange mass (due to vaporization), momentum and energy with the continuous fluid phase. droplets are convected by the continuous phase and can, in turn, affect the flow of the continuous phase (two way coupling between the fluid and droplet phase). to reduce computational time, half the domain is simulated assuming symmetry in geometry and flow features. ambient conditions ( o c, % relative humidity) representative of summer conditions in india are assumed. in our simulations, a human face is included in the domain m from the left surface, at a height of m from the ground level, and the mouth is represented as a cm opening facing right. experimentally, it has been observed , , that respiratory events result in jets angled towards the ground, with some variability in the angle. we followed previous simulations that model the respiratory event as a jet emanating from the mouth in the horizontal direction. for this jet, a time dependent velocity profile is applied with the peak velocity of m/s at . s. values for the peak flowrate (= l/s) and the total volume expelled (= l) are obtained from gupta et al. we do not describe the detailed breakup of the ejecta into droplets. rather, we prescribe the size distribution of droplets in the ejected spray as a rosin-rammler distribution with droplet sizes ranging from to µm. droplets ejected are not allowed to coalesce or break-up. based on previous work, we consider that % of injected droplet mass can evaporate and the remaining % represents non-volatile matter. following aliabadi, we inject . mg of droplets over equal injections with initial droplet positions staggered over cm. the cloth mask is not tightly fitted around the face, representative of homemade masks. therefore, we model the mask as covering % of the face area around the nose and mouth and model air leaks by considering a uniform gap of mm all around, between the face and the mask. the area of the gap around the mask is about % of the mask area. to model the resistance presented by the mask to the flow of air, we consider the mask as an isotropic porous medium, with darcy and inertial contributions to the pressure drop, given by: where si is the source term in the momentum equation, µ is the fluid viscosity, vi is the velocity, α is the permeability and c is the inertial resistance factor. we consider a mask made of cotton cloth, and obtain α and c from a fit to experimental data presented in the literature (details in si -section a). to model the permeation of droplet ejecta, we follow experimental reports of the penetration efficiency of fabric. we consider an effective pore size of µm for the cotton cloth and impose a trap condition so that all droplets larger than the pore size are trapped by the mask. more details about the governing equations, computational method and validation can be found in the supporting information (section a). the instantaneous flow field . s after the respiratory event without and with masks, respectively, is shown in figures a, b (close ups: figures c, e) . we represent the flow field using streamlines and present data in the symmetry plane passing through the face. without a mask (figure a, c) , the respiratory event results in an air jet with a fast moving turbulent core that entrains ambient air and slows down as it propagates from the face. as the surrounding air is entrained, the jet forms a conical shape with a cone angle = tan - (radius/height) ≈ tan - ( . ) = . o , corresponding to an entrainment coefficient slightly lower than that reported in the literature there is a qualitative change in the airflow when a mask is worn (figure b, e). here, the turbulent jet and strong recirculating flows are eliminated by the mask and about % of the air flow is diverted through the openings at the sides of the mask to create a qualitatively different flow around the face. we reiterate that the area of the openings (considering a uniform gap of mm all around, between the face and the mask) represents only about % of the area of the mask. this leakage flow is similar to experimental reports of flows using surgical masks (which are also not tightly fitted). correspondingly, we observe a drastic change in the spatial distribution of the turbulent kinetic energy when a mask is worn (compare figure d with f, plotted through the symmetry plane at t = . s). without a mask, a highly turbulent jet with large mean square velocity fluctuations propagates axially away from the face (figure d) . this is virtually eliminated by the mask (figure f) . at t = . s, the centerline velocity through the face decreases from ≈ m/s to ≈ m/s over . m. we note that the velocity reported here is exactly at the centreline. therefore, these values are higher than the experimentally measured peak velocities of the jet, that are likely averaged around the centreline. at . s after the respiratory event, the centreline velocity immediately after the face is about m/s, and decreases to about m/s at . m. in contrast, the centreline velocities drop to less than m/s within . m when a mask is worn (figure f) . correspondingly, when no mask is worn, the centerline turbulent kinetic energy decreases from about m /s to m /s at . m from the face at t = . s, and then rises to m /s at a distance of . m from the face as the entrained air forms a turbulent cloud (figure h). when a mask is worn, the turbulent kinetic energy rises near the mask due to the increase in mean square velocity fluctuations as the expelled jet impinges on the mask. however, due to the resistance to the flow presented by mask, it rapidly decreases immediately after the mask and approaches m /s at . m from the face. the dissipation of the turbulent flow field tracks the trend in the turbulent kinetic energy. without a mask, it decreases by about -fold over . m (for t = . s) and then rises reaching a maximum at . m, while wearing a mask results in a rapid decrease by over orders of magnitude over a distance of . m (figure i) . wearing a mask has a significant impact on the spread of cough ejecta. we observe the time dependent trajectories of large and small droplets with time from the respiratory event (figure ). without a mask (figure , top panel) , large drops are not convected by the flow and rapidly fall to the ground: drops > µm fall within a lateral distance of . m, while drops > µ m extend to about m (si, figure s ). in contrast to the large drops, smaller drops (< µ m in size) are convected by the turbulent cloud. they shrink in size as their water content is completely evaporated, and are transported to significant distances, as far as m from the face (si, figure s ). we observe that the non-volatile content in these drops continues to stay suspended for as long as s. our data is consistent with the experimental literature. wearing even a simple cotton mask restricts the spatial transport of droplets (figure , bottom panel). large droplets (> µm) are trapped by the mask while smaller droplets are transported by the flows through the surface of the mask and through the openings on the sides. at t = . s, droplet ejecta is transported over less than . m (as compared to well over m, without a mask). thus, large droplets are trapped by the mask while the damping of the turbulent flow field by the mask leads to smaller droplets being transported only over relatively short distances. flow through the openings around the mask convects small droplets along the face, in contrast to the case without a mask. we estimate the potential viral concentrations suspended in the air and deposited on the floor due to propagation of droplets from the respiratory event of an infected person. recent literature indicates that the sars-cov load in throat swabs on patients within the first days of the infection averages . x rna copies/ml. for sputum samples, an average of x rna copies/ml was observed. based on these, in these simulations we assume a representative viral concentration of particles/ml in the ejecta, to estimate the potential spatial dispersion of the virus. when an infected person not wearing a mask sneezes or coughs, virus particles in the large droplets rapidly drop to the floor. by t = s, ≈ % of the potential viral load in the ejecta is deposited on the floor while ≈ % remains in the air. most of the virus particles that are deposited on the floor are within m from the person, with a maximum virus density ≈ cm - at about . m from the person (figure a, d) . the suspended aerosolized virus particles form a low density cloud that extends from to m. at the centerline passing through the face, the suspended concentration ≈ - cm - (figure a, c) . when a mask is worn, most of the virus-laden droplets (nearly %) are deposited on the mask. flow through the mask surface and leakage flows from the openings around the mask result in generating a cloud, potentially conveying virus to a distance of about . m from the face. at the centerline passing through the face, this cloud has a density of - cm - within about . m from the person (figure b, c) . however, the suspended concentration drops significantly after . m from the person, and there is virtually no deposition of droplets on the ground (figure b, c) . thus, there is a clear qualitative difference in the distribution of virus particles when the infected person wears a mask. without a mask, high concentrations of potentially virus-laden droplets are deposited on the floor within m of the person and a dilute suspended cloud is observed over - m. in contrast, when a mask is worn, there is no deposit on the ground since most of the virus is deposited on the mask. virus particles stay suspended within . m of the person, but this suspended concentration falls off sharply after that distance. our simulation results conclusively demonstrate that wearing even just a simple cotton mask has a dramatic influence on the air flow and spread of ejecta after a respiratory event. when a person not wearing a mask coughs or sneezes, the emanating jet sets up turbulent flows at distances of several meters from the person. while the large mucosal droplets fall to the floor within a distance of m, the turbulent clouds continue to suspend aerosols at distances up to m, for over a minute after the respiratory event. when an infected person coughs or sneezes, most of the virus deposits on the floor within a meter of the person. however, a dilute aerosol stays suspended, potentially carrying virus particles. in contrast, wearing a mask dissipates the turbulent flows passing through the mask, and diverts about % of the flow to the openings at the sides of the mask. the vast majority of the virus particles are retained on the mask and face. at t = s, a cloud of virus particles ( -fold higher in density compared to the case without the mask) stays suspended within . m of the person. our results strongly suggest that airborne transmission from patients (especially asymptomatic or presymptomatic patients) can be greatly reduced by wearing a simple cotton mask and maintaining strict physical distancing of m. the fluid phase is treated as a continuum by solving the navier-stokes equations, while the dispersed phase is solved by tracking droplets through the calculated flow field. the dispersed phase can exchange momentum, mass, and energy with the fluid phase. the dispersed phase is treated by the lagrangian approach, where a large number of droplet parcels, representing a number of real droplets with the same properties, were traced through the flow field. by representing droplets by parcels, one can consider size distribution and simulate the measured liquid mass flow rate at the injection locations by a reasonable number of computational droplets. the trajectory of each droplet parcel is calculated by solving the equation of motion for a single droplet. the droplets in the dispersed phase are modelled using the discrete phase model (dpm). in this approach, a lagrangian frame of reference is used to calculate the trajectories of a large number of droplets representing real droplets with the same properties, by integrating the forces acting on droplets. the droplets can exchange mass, momentum and energy with the fluid. the force balance on each droplet can be written as: where is the particle mass, ⃗ is the fluid velocity, ⃗ is the droplet velocity, ρ is the fluid density, ρp is the density of the droplet, ⃗ is an additional force, ⃗ ⃗ is the drag force, and is the droplet relaxation time calculated by = here, µ is the molecular viscosity of the fluid, and dp is the diameter of the droplet. the relative reynolds number re is defined as the drag coefficient is calculated considering spherical particles. the dispersion of droplets due to turbulence in fluid phase is included using the stochastic tracking (random walk) model which includes the effect of instantaneous turbulent velocity fluctuations. for evaporating droplets, inert heating/cooling along with vaporization laws are applied. more information about the energy treatment of the dpm droplets and evaporation rate can be found in ansys fluent r help manual. other fluid-droplet and droplet-droplet interactions are ignored in the study. the droplets are two-way coupled into the continuum fluid phase to make it possible for the droplets to influence the continuous fluid phase. we model the effect of wearing a woven cloth face mask as follows: the mask is included in the cfd model as a thin volume and modeled as porous media. for the current study the media is considered to be homogeneous and the resistances included via this media are considered to be isotropic in nature. porous media are modeled by the addition of a momentum source term to the standard fluid flow equations. the source term is composed of two parts: a viscous loss term (darcy, the first term on the right-hand side of equation , and an inertial loss term (the second term on the right-hand side of equation ) where si is the source term for the i th (x, y , or z ) momentum equation, µ is the dynamic viscosity of fluid , v is the magnitude of the velocity and dij and cij are prescribed matrices. this momentum sink contributes to the pressure gradient in the porous cell, creating a pressure drop that is proportional to the fluid velocity (or velocity squared) in the cell. to recover the case of simple homogeneous porous media where α is the permeability and c is the inertial resistance factor, obtained by specifying d and c as diagonal matrices with diagonal values of /α and c , respectively (and zero for the other elements). we consider a mask prepared from cotton cloth. details of the cloth used are taken from the thesis of saldaeva. details of the construction of the fabric as provided in the thesis are given in table s . pressure drop versus velocity data obtained from the thesis and shown below in figure s can be fitted to obtain the darcy (proportional to v) and non-darcy inertial (proportional to v ) components of the resistance to flow. for the jet coming from the mouth, a time dependent velocity profile is applied with peak velocity time (pvt) of . sec as shown in figure s . cough peak flowrate (cpfr) is derived using the formulation reported by gupta et al. to simulate varied human expirations, various cough expired volume (cev) values are used corresponding to very weak, medium and very strong expirations. to simulate the spray of droplets, a rosin-rammler distribution method is used for the injection. % of injected droplet mass fraction represents evaporating sprays and the remaining % represents the non-volatile matter. a total . mg of droplets are injected using injections with equal distribution among the injections. the initial droplet positions are staggered over . m. conditions used for the baseline simulation are shown in table s . a user defined function (udf) has been used to filter the droplets from the mist generated by the respiratory event. we model filtration by cloth with reference to reported experimental literature. guyton et. al. measure the filtration efficiency of a single layer of fabric typical of bath towels, cotton shirts, handkerchiefs, etc. and report the penetration efficiency of µm particles. rengasamy et. al. report the penetration efficiency of cotton cloth for a range of particle sizes (up to m in size). we use a conservative estimate for the penetration efficiency of the cotton mask used in this work and implement a simplified filtering mechanism such that all droplets above µm diameter are filtered out while droplets below m are allowed to pass through the mask. this boundary condition is applied when the droplets hit the surface of the mask. the baseline case is created to validate the methods used simulate near field cough, particle dispersion, heat and mass transfer in a still environment. the results from the baseline cfd simulation are verified against results from aliabadi et. al. in figure s (a) , average droplet diameter in each of the diameter bins are plotted against time. figure s (b) shows the vertical penetration of the droplet plumes in the gravity direction. in the current work, penetration is computed as the location where % of the total mass of the droplet is contained. the exact approach taken by aliabadi et. al. to compute penetration length is not known. some differences may be expected because of this uncertainty as wells as the uncertainty about the exact location of the duct. we employ a geometry representing a m x m x m domain with a small duct of . m x . m placed opposite side of the inlet plane. half of the computational domain is simulated by placing a symmetry boundary condition in the middle. the computational domain is discretized into . million elements with a mix of polyhedral and hexahedral elements using ansys fluent r mesh creation tools as shown in figure s . the conditions used for the simulation presented in this paper are shown in table s . b. additional simulation results, as referred to in the main manuscript are presented here. respiratory virus shedding in exhaled breath and efficacy of face masks potential utilities of mask wearing and instant hand hygiene for sars-cov- a cluster randomised trial of cloth masks compared with medical masks in healthcare workers effectiveness of n respirators versus surgical masks in protecting health care workers from acute respiratory infection: a 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configurations through thickness air permeability and thermal conductivity analysis for textile materials simple respiratory protection-evaluation of the filtration performance of cloth masks and common fabric materials against - nm size particles virological assessment of hospitalized patients with covid- through thickness air permeability and thermal conductivity analysis for textile materials cfd simulation of human coughs and sneezes: a study in droplet dispersion, heat and mass transfer flow dynamics and characterization of a cough emergency respiratory protection against radiological and biological aerosols simple respiratory protection-evaluation of the filtration performance of cloth masks and common fabric materials against - nm size particles key: cord- - gqxajw authors: bahl, prateek; de silva, charitha; bhattacharjee, shovon; stone, haley; doolan, con; chughtai, abrar ahmad; macintyre, c raina title: droplets and aerosols generated by singing and the risk of covid- for choirs date: - - journal: clin infect dis doi: . /cid/ciaa sha: doc_id: cord_uid: gqxajw choral singing has become a major risk during covid- pandemic due to high infection rates. our visualisation and velocimetry results reveal that majority of droplets expelled during singing follow the ambient airflow pattern. these results points toward the possibility of covid- spread by small airborne droplets during singing. singing in group settings has become an apparent risk for outbreaks of covid- [ ] . while social distancing is effective in normal social interactions, singing can produce a substantially larger number of respiratory droplets and aerosols than speaking, as it is louder and sustained for longer durations [ ] . this may require further measures to be put into place to mitigate risks. in contained smaller spaces, the transmission risk may be higher, as respiratory aerosols may saturate the whole indoor environment [ ] . despite this, at present there is not a collective approach or response to the potential risks of group singing. certain countries, including germany and the netherlands, have banned all group singing activities [ ] . choir-related outbreaks of covid- in berlin, amsterdam, and washington state had high attack rates of . %, . % and . % respectively [ , , ] . since restrictions have eased globally, a rise in outbreaks related to singing has been reported [ ] . a large proportion of these documented outbreaks associated with singing (approx. %), were reported from the united states resulting in over cases [ ] . covid- is assumed to be transmitted through respiratory and contact routes; and transmission by respiratory droplets is believed to occur only in close contact (within - m) with someone who is infectious [ ] . however, there is uncertainty about the dynamics of respiratory emissions during singing. additionally, studies have shown that droplet and airborne transmission may not be mutually exclusive modes of transmission and exist as a continuum [ ] . hence, unravelling the spread of respiratory particles during singing, especially in closed environments, could inform infection control policy and practice. to quantify and understand the spread of infection during singing we performed a detailed flow visualization of aerosols and droplets expelled during singing using an image-based flow diagnostic system. the visualisation technique employs a led based light source (gs vitec multiled pt) with a spherical lens to control the divergence of the light beam, along with a high-speed camera (nac memrecam hx- s) to capture the light scattered by the droplets expelled during singing. to capture the video, the head of the subject was adjusted in front of black backdrop/background and the light was positioned in a forward scatter arrangement to maximize the scattering from expelled droplets ( figure ). once the position is adjusted, the subject was asked to sing a major scale using the solfège system and the high-speed video was captured with an exposure of µs per frame at a resolution of megapixels. in addition to singing, the subject also counted from to and coughed voluntarily. the horizontal field of view captured in the high-speed video, from the mouth of the subject, was cm approximately. frames obtained from the video were first calibrated and a -axis stabilisation was applied to subject's head (further details on this procedure can be found in [ ] ). thereafter, all the frames were processed with a hybrid particle tracking velocimetry technique [ ] . this technique first performs a particle image velocimetry (piv) procedure to estimate flow velocity and these estimates are subsequently refined using a particle tracking algorithm applied to each droplet. specifically, for the piv step we used a variable interrogation window with an initial size of × pixels and a final size of × pixels with an overlap of %. for particle tracking we used a correlation window of pixels and particle size range of to pixels in order to cover the entire size range of visible droplets. the flow visualisation together with detailed particle tracking results are included in supplementary video. the results of detailed particle tracking (in supplementary video) reveals that the maximum velocity of droplets expelled, specifically for certain syllables such as 'do', 'fa' and 'ti', is approx. m/s, which is similar to the velocities reported for speaking [ ] . upon further examining the motion of droplets at a distance of cm from the mouth, we observed that almost % of the droplets are moving at velocities less than m/s (figure a) . the droplets moving with velocities greater than m/s are moving in the direction between ° - ° (θ = ° towards subject (figure ) ) and move away from the mouth. moreover, approx. % of droplets observed are moving at velocities less than . m/s and the motion is equally distributed in all the directions, which implies that they do not settle rapidly and may follow the ambient airflow pattern. these results points toward high aerosol generation, as the behaviour of these droplets is like airborne particles [ ] . nevertheless, to accurately quantify the size, future work using particle counters, is essential to better understand the dynamics of these droplets. figure b shows the distribution of droplet velocities obtained at cm from the mouth for syllable 'fa' and the direction in which these droplets are moving. approximately % of the droplets are moving at velocities less than . m/s and more than % are moving away from mouth (θ = ° to °), which is also evident in the supplementary video. figure c shows the velocity distribution of droplets that are visible while the subject was singing syllable 'sol' & 'la' and the direction in which these droplets are moving. it can be observed that all droplets are moving at velocities less than . m/s and are equally distributed in all directions. the direction in which these droplets are moving is important because it implies that for a normal choir configuration with multiple rows and heights, these droplets can pose a risk to those in the adjacent rows as well as to those in the distant rows. figure d and e shows the distribution for counting and coughing, respectively. in the case of coughing approximately % of the detected droplets were moving at velocities greater than m/s whereas in case of speaking only % were moving at velocities greater than m/s. we note, the loudness measured during singing was within the range of - decibels. further, it is also worth noting that some degree of variability is expected in the number of droplets expelled between different individuals, and due to other parameters, such as loudness, notes, consonants, and duration of each note sung. nevertheless, the droplets observed do not appear to be settling down rapidly and without adequate ventilation, these droplets can potentially saturate the indoor environment which can likely explain the very high attack rates of covid- seen in choirs in the us and europe (almost % in skagit county, washington) [ ] . we note the present study only provides visual evidence of the droplets and aerosols expelled during singing and compare the associated velocities and directions with speaking and coughing. however, these droplets have the capacity to potentially transmit viruses such as sars-cov- . we only used a basic major scale for our experiments and during singing various other factors comes into play, such as pitch, rhythm, diction, etc. and it would be valuable to investigate all these aspects for future studies to have a better understanding of droplet and aerosol generation while singing. nonetheless, the data presented combined with high infection rate among the choir members ( - %) [ ] points towards the possibility of airborne spread of covid- during singing events, hence, should be considered when designing safety guidelines for public singing events. these findings could inform safety guidelines for restarting choirs during and after the covid- pandemic and other similar respiratory infection outbreaks. for example, rehearsals could be done with fewer people, greater physical distancing between singers, or face coverings and masks to reduce droplet and aerosol expulsion [ ] . in addition to that either well ventilated large spaces or outdoor performances should be utilised to minimize the risk of infection. high sars-cov- attack rate following exposure at a choir practice -skagit county aerosol emission and superemission during human speech increase with voice loudness indoor aerosols: from personal exposure to risk assessment german choirs silenced as singing branded virus risk concertgebouw chorus is devastated after pre-covid bach passion church-related coronavirus outbreaks reported as trump pushes for reopening modes of transmission of virus causing covid- : implications for ipc precaution recommendations airborne or droplet precautions for health workers treating coronavirus disease an experimental framework to capture the flow dynamics of droplets expelled by a sneeze a hybrid digital particle tracking velocimetry technique characterization of expiration air jets and droplet size distributions immediately at the mouth opening aerosol technology: properties, behavior, and measurement of airborne particles face coverings and mask to minimise droplet dispersion and aerosolisation: a video case study none of the authors has any potential conflicts to disclose. key: cord- -tmc aa authors: cummins, c. p.; ajayi, o. j.; mehendale, f. v.; gabl, r.; viola, i. m. title: the dispersion of spherical droplets in source–sink flows and their relevance to the covid- pandemic date: - - journal: phys fluids ( ) doi: . / . sha: doc_id: cord_uid: tmc aa in this paper, we investigate the dynamics of spherical droplets in the presence of a source–sink pair flow field. the dynamics of the droplets is governed by the maxey–riley equation with the basset–boussinesq history term neglected. we find that, in the absence of gravity, there are two distinct behaviors for the droplets: small droplets cannot go further than a specific distance, which we determine analytically, from the source before getting pulled into the sink. larger droplets can travel further from the source before getting pulled into the sink by virtue of their larger inertia, and their maximum traveled distance is determined analytically. we investigate the effects of gravity, and we find that there are three distinct droplet behaviors categorized by their relative sizes: small, intermediate-sized, and large. counterintuitively, we find that the droplets with a minimum horizontal range are neither small nor large, but of intermediate size. furthermore, we show that in conditions of regular human respiration, these intermediate-sized droplets range in size from a few μm to a few hundred μm. the result that such droplets have a very short range could have important implications for the interpretation of existing data on droplet dispersion. the transport of inertial particles in fluid flows occurs in many problems arising in engineering and biology, such as the build-up of microplastics in the ocean and respiratory virus transmission through tract droplets. [ ] [ ] [ ] the maxey-riley equation describes the motion of a finite-sized spherical particle in an ambient fluid flow. the equation is a representation of newton's second law in which the forces acting on the particle include a stokesian drag force, an added mass force, a gravity force, the force due to the undisturbed flow, and a basset-boussinesq history term. the equation takes the form of a second-order, implicit integro-differential equation with a singular kernel and with a forcing term that is singular at the starting time. the equation has been applied to model the dynamics of aerosol comprising particles of various density ratios, the feeding mechanism of jellyfish, , and the dynamics of inertial particles in vortical flows. [ ] [ ] [ ] the equation has also been applied to droplet-laden flows with a phase change at sub-kolmogorov scales. the basset-boussinesq term accounts for the drag due to the production of vorticity as the particle is accelerated from rest. it is difficult to include this term numerically and is often omitted on the assumption that particles move in a quasistatic manner. this assumption breaks down in bubbly and slurry flows, where the basset-boussinesq term accounts for a quarter of the forces on the particle when the density ratio r = ρ ′ f /(ρ ′ f + ρ ′ p ) is greater than / , where ρ ′ f is the fluid density and ρ ′ p is the particle density. recent advances have shown that the full maxey-riley equation can be represented as a forced, time-dependent robin boundary condition of the d diffusion equation. here, the authors found that a particle settling under gravity relaxes to its terminal velocity according to t − / ; however, if the basset-boussinesq term is neglected, it relaxes exponentially quickly. in this paper, we examine the transport of inertial particles in source-sink flows. such a flow could represent the trajectories of water droplets emitted from coughing, sneezing, [ ] [ ] [ ] or breathing and in the presence of extraction, such as an air-conditioning unit or air current. our simplified mathematical model yields to analytic treatment in certain limits of large and small droplets. this enables us to provide important physical insight into this complex problem, but we remark that the effects such as drag non-linearity and turbulent dispersion are not taken into account. since the dynamics of settling droplets is significantly affected by their size, it is important to understand the impact that the emitted droplet size has on the destination of such a droplet in a source-sink flow. in particular, since droplets are vectors for infectious diseases such as covid- , it is imperative that we understand the droplet dynamics in such flows to mitigate the spread of the disease. this paper is organized as follows: in sec. ii, the mathematical model is presented and non-dimensionalized. the results are presented in sec. iii for small (sec. iii a) and intermediate-sized (sec. iii b) droplets in the absence of gravity. gravitational effects are considered for small droplets in sec. iii c and for intermediatesized droplets in sec. iii d. in sec. iv, we present applications of our results for human breathing without (sec. iv b) and with (sec. iv c) the inclusion of extraction. finally, we discuss our findings in sec. v. consider a source producing air of density ρ ′ air and viscosity ν ′ air , with volume flux of q ′ , containing spherical liquid droplets of density ρ ′ drop , which are emitted with a characteristic velocity u ′ . let us represent the d velocity field u ′ source (x ′ ) at a position x ′ of the emitted air as a point source of strength q ′ , centered at the origin in the cartesian coordinates, we include an extraction unit as a point sink of strength q ′ located at a position x ′ as follows: the resulting airflow is given by the linear superposition of these two flows, the natural timescale of the problem emerges as t ′ = |x ′ |/u ′ . we non-dimensionalize ( ) according to which gives the non-dimensionalized expression for the airflow velocity with where x(t) is the position of the droplet at time t, v(t) =Ẋ(t) is its velocity, the dot indicates the time derivative, and with a ′ being the droplet radius, g ′ being the acceleration due to gravity vector, re = u ′ |x ′ |/ν ′ air is the reynolds number, and st is the particle stokes number. note here that the faxén correction terms have not been omitted: they are identically zero since Δu = . the approximate ratio of the basset history drag to stokes drag is o(st / ), which, for the range of st we are interested in, is generally much less than one. in the remainder of this paper, we neglect the basset history term since we anticipate that its magnitude is negligible compared to the stokes drag term for the parameters of interest to us, and the resulting equations arė subject to the initial conditions v( ) = u(x( ), ), where x( ) lie on a circle surrounding the origin of radius |x( )|. in ( ), taking the limit hence, we can ensure that the non-dimensional initial velocity has unit magnitude by requiring |x( )| = √ Λ. the resulting equations ( ) are a set of three coupled secondorder non-linear ordinary differential equations (odes) for the position vector x(t). the algebra involved in computing the material derivative in ( ) is straightforward, but cumbersome, and it is omitted here. this set of equations does not admit analytical solutions, in general, and so it must be solved numerically. we solved the equations by expressing them as a system of six first-order odes using the matlab ® ode s algorithm, a variable-step, variable-order solver based on the numerical differentiation formulas. this was performed on a laptop equipped with in ( ), for small droplets (st ≪ r) emitted from the source, the balance is between the first term on the left-hand side and the righthand side so that the velocity rapidly adjusts to the background flow v ≈ u| x . we are interested in whether droplets move away from or toward the sink. to this end, we look for trajectories for which if we take x = [ , , ], then the trajectory that emerges from the source and travels in the direction of the negative x-axis is the one that gets the greatest distance away from the sink. hence, let us consider this inequality in the first component, and along the line y = , we are interested in where the flow field changes direction, since this indicates the maximum distance the droplets emitted at the source can travel before moving toward the sink. to this end, let us choose a point x = −λ along y = and z = ; then, this inequality tells us that this inequality can hold only if γ > . this makes sense, since the flow is directed toward the sink only if the sink is stronger than the source. figure shows the trajectories for small droplets (st ≪ r) in the presence of a source-sink pair: the source is located at the origin (green disk) and the sink is located at x = along the x-axis (red disk). for γ = [ fig. (a) ], we have equal strength and droplets can take large excursions from the source before returning to the sink. as γ increases, the trajectories emanating from the source occupy an increasingly compacted region [figs. (b)- (d)]. we can use this inequality above to define a region such that small droplets do not get further than a distance |λ| before traveling toward the sink. the circle with radius |λ| is shown in fig. (dashed curve). observe that, as one gets increasingly close to the source (λ → ), the inequality tends to meaning that in order to maintain trajectories moving away from a given test point, the sink strength needs to increase quadratically with the distance of the test point to the source. b. intermediate-sized droplets in the absence of gravity which represents a balance between inertia and drag forces. provided γ > , and in the absence of gravity, in the long-term, the droplet will always migrate toward the sink. however, in the case of intermediate-sized droplets, the maximum distance traveled by the droplet before it moves toward the sink is given by |v( )|/(r/st). since the initial velocity of the droplet is chosen to be the same as the surrounding fluid, then we can write the maximum distance as |u(x( ), )|/(r/st). as explained above [see ( ) ], in our nondimensionalization, our characteristic velocity u ′ was chosen to be that of the outlet. hence, in this non-dimensionalization, |u(x( ), )| = . figure shows the trajectories of intermediate-sized droplets for γ = in the absence of gravity. the striking feature of the plot is the shift from a regime where the maximal extent of the trajectories as predicted by ( ) is no longer valid and must be replaced with a circle of radius st/r. in fig. (a), st/r = . so that the droplets are slowed down rapidly before following the fluid flow. in fig. (b), st/r = , meaning that the droplets are slowed down over the area covered by the unit circle, before being brought to the sink as ideal tracers. finally, in fig. (c), st/r = so that the droplets travel a non-dimensional distance of before being slowed down enough to be pulled into the sink. hence, we find that, in the absence of gravity, we can have two very different behaviors depending on whether we have small droplets st ≪ r or intermediate-sized droplets st ≥ r. small droplets cannot get further than a distance ( √ γ + )/(γ − ) from the source before traveling toward the sink, but intermediate-sized droplets are not restricted by this and can travel further than this, provided as the droplets move from the source to the sink, gravity attempts to pull them vertically downwards. over the timescale of the problem, i.e., the average time it takes for a droplet to travel from the source to sink, gravity may or may not have an appreciable effect. intuitively, one would imagine that smaller droplets are influenced more by the airflow than gravity: for stronger sinks, the effect of gravity is comparatively less. intuitively, one would also expect that this holds true, provided that the source and sink are not too far away. the gravitational vector is non-dimensionalized according to the dashed circle indicates the predicted maximal distance that a droplet can travel in this regime, calculated using the inequality ( ) . the source is indicated by a green filled circle, and the sink is indicated by a red filled circle. u ′ /|x ′ | as shown in ( ) so it depends on the initial speed and the distance between the source and sink. for st ≪ r < / , and in the absence of gravity, there are three fixed points: the source, the sink, and a saddle point located at x = −|λ| along the x-axis (fig. ) . when gravitational effects are included, the fixed point at x = −|λ| moves clockwise about the origin as the effect of gravity is increased [see fig. (a)]. a fourth fixed point (saddle) is created far from the source-sink pair, which gradually moves toward the sink [figs. (b) and (c)] as the effect of gravity is increased. in fig. (d) , the separatrices (indicated as the red dashed-dotted curves) show that there is a wedge of trajectories that escape the pull of the sink. as might be expected, these trajectories are those that point directly away from the sink. our results show that even for small droplets, gravity can be important if either the sink is far away or if the ejection speed is too low. small droplets are deflected by gravity but generally feel the pull of the sink. whether or not they are pulled in is determined by the interaction of gravity, the angle of their trajectory, and γ. as the droplets become larger, gravitational effects dominate and the sink becomes ineffective. in fig. , we show how the droplet trajectories behave as st is increased. figure (a) shows the familiar situation where the droplets are so small that gravity does not appreciably affect their trajectory over the characteristic lengthscale. as st is increased, fig. (b) shows that there are a range of trajectories with ejection angles α (defined with respect to the positive sense of the x-axis) around the source, which are deflected downwards away from the sink. this is consistent with sec. iii c. in these plots, r = . , Λ = . , and |g| = . the dashed circle indicates the predicted maximal distance that a droplet can travel in this regime, calculated using the inequality ( ) . the dashed-dotted circle indicates the maximal distance predicted by the inertia-drag balance, giving radius equal to st/r. the source is indicated by a green filled circle and the sink is indicated by a red filled circle. however, at a critical st ≈ . × − , each trajectory is deflected downwards by gravity [ fig. (c) ]. in this case, the maximum horizontal distance traveled by the droplets is very small. interestingly, this trend is not monotonic. further increasing st, the trajectories adopt a ballistic trajectory [ fig. (d) ]. such droplets can move in very close proximity to the sink but are not pulled into it [ fig. (d) ]. a. background on respiratory virus transmission one of the possible applications of this paper is to underpin more sophisticated analytical or numerical models to study the transmission of respiratory viruses. in medical applications, it is common practice to categorize the emitted fluid particles as larger droplets from μm to mm in diameter, which have a ballistic trajectory, and aerosol that remains airborne. droplets smaller than μm and the desiccated droplet nuclei are known as aerosol, which can remain airborne for several hours. [ ] [ ] [ ] respiratory viruses are transmitted from the virus-laden fluid particles to the recipient through ( ) aerosol inhalation, ( ) droplet deposition on the recipient's mouth, nose, or conjunctiva, or ( ) droplet deposition on a surface and successive transmission through physical contact. the sars-cov- virus, for example, has a diameter of nm- nm, and it is carried by droplets and aerosol. , the model proposed in this paper can provide new insights into the aerosol transmission, i.e., through those particles whose stokes number is not sufficiently large to have a ballistic trajectory. the relative importance of aerosol ( ) and droplet [ ( ) and ( )] virus transmission is not always known, and it is yet to be established for sars-cov- . counterintuitively, it has been argued that aerosol could be more dangerous than larger droplets. smaller droplets (≤ μm) suspended in aerosol might carry a higher concentration of virus than larger droplets (> μm). , , the largest droplets are less likely to penetrate deeply in the respiratory system and might be deactivated by the effective first structural and defense barrier of the mucosa. conversely, aerosolized virus half-life exceeds h and can be transported airborne through inhalation deep into the lungs, [ ] [ ] [ ] [ ] avoiding the defense mechanisms of the upper respiratory system. furthermore, aerosol inoculation has been shown to cause more severe symptoms than droplets administered by intranasal inoculation, and the dose of influenza required for inoculation by the aerosol route is - orders of magnitude lower than the dose required by intranasal inoculation. , , to apply our model to aerosol dispersion, we consider the particles ejected by a person talking. a person ejects about tens of fluid particles per second with diameters between . μm to mm and with a speed of the order of m s − . because this is the most frequent source of aerosol, this accounts for most of the aerosol inhaled by other people. , coughing leads to the ejection of - fluid particles per second with a speed around m s − , while sneezing generates - fluid particles per second with a speed of up to m s − . the values presented in this paragraph should be taken as indicative because there is a significant variability between different experimental studies. , , , , [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] some of the physics that is not considered in this work is the particle-particle interaction and evaporation. in fact, fluid particles are ejected through a jet that transports particles in the range of μm- μm, , , i.e., the aerosol, while the largest droplets have a ballistic trajectory independent of the surrounding flow. , , the jet can be either laminar or turbulent when breathing and speaking, while coughing and sneezing always results in a turbulent jet with a diameter-based reynolds number higher than . once ejected, the air jet extends along a straight trajectory; its diameter increases linearly with the traveled distance, while the mean velocity linearly decreases, and the turbulent statistics remain constant (i.e., the jet is self similar ). once the largest particles with a ballistic trajectory have left the air jet, the jet bends upwards due to the buoyancy force caused by the temperature and thus density difference. smaller size particles (≤ μm) are transported by the jet while they evaporate. once a droplet exits the jet, it falls at its settling speed. for a particle with a diameter of μm and μm, the settling speed is less than . m s − and . m s − , respectively. the smallest of these two droplets is likely to land in the form of a desiccated nucleus. in fact, while a droplet with a diameter of μm evaporates in about s, a μm droplet evaporates in less than , . s, although their survivability also depends on the ambient temperature and relative humidity. once these droplets leave the jet, they can still be transported by ambient air currents, which have speeds typically in excess of . m s − . these currents are modeled by the sink-source flow field discussed in this paper. a key issue that is discussed in this study is the extent to which the cloud of droplets and aerosol are displaced into the neighboring environment, as this is associated with virus transmission risk. previous studies estimated that the overall horizontal range of the droplets generated while breathing and coughing before they land on the ground is around m- m. [ ] [ ] [ ] these studies led to the centers for disease control and prevention (cdc) and world health organization (who) social distancing guidelines. nonetheless, the complex physics involved, which includes knowledge of the particle size distribution, their speed of evaporation, the viral charge of droplets of different size, the diffusivity of the virus-laden particles, etc., makes it difficult to assess what is the effective dispersion of the virus-laden fluid particles into the environment once ejected. it was found that the largest droplets generated by sneezing can reach a distance as far as m, , , while aerosol dispersion is highly dependent on the temperature, humidity, and air currents. for these reasons, this paper does not aim to provide definitive measures for the aerosol displacements but contributes to building a body of evidence around this complex question. currently, there is a large amount of disagreement in the reported spectra of droplet sizes in respiratory events. the analysis is complicated by various factors including the evaporation of the droplets as they travel from the source, which, in turn, is influenced by ambient humidity and temperature. recent mathematical modeling of droplet emission during talking have categorized droplets into one of the three groups: small (< μm), intermediate ( μm- μm), and large (> μm). small droplets approximately follow the air and can travel a great distance by weakly feeling the effects of gravity. large droplets can also travel a large distance due to their inertia. however, the intermediate-sized droplets feel strongly both gravity and drag, and their trajectory is a complex interaction of , b taken from wind tunnel experiments. these effects. similar trends were observed in computational fluid dynamics simulations of previous authors. in this section, we examine the problem from a much simplified perspective: we ignore evaporation entirely. we model the situation as a point source emitting droplets of various sizes in the presence of gravitational forces and compute the maximum horizontal distance traveled by these droplets. in this case, q ′ = l min − , and other quantities such as jet speed, direction, and spread are taken from recent experimental studies of the authors: these quantities are summarized in table i . we find that for both heavy and quiet breathing, the maximum distance traveled by droplets l ′ (and the corresponding flight time τ ′ ) depends strongly on the droplet diameter (see fig. ). as expected, small droplets can travel many meters; however, we see that there is an intermediate range of droplet diameters where the horizontal distance is minimized. for quiet breathing, this minimum occurs between μm < d < μm, while for heavy breathing, this minimum occurs between μm < d < μm. this multi-modal behavior is reminiscent of that in previous experimental studies that measured the size distributions of droplets in various respiratory events such as talking and coughing , and sneezing. the multimodal behavior observed in experiments is attributed to the different generation modes: bronchiolar, laryngeal, and oral. in our simplified model, we do not have any assumption on the biological origin of the droplet: the existence of the minimum is a characteristic of the droplets themselves and cannot be used as an indicator of the underlying droplet size distribution. the time it takes τ ′ decreases monotonically with increasing droplet diameter, as shown in figs. (b) and (c). in order to unpick the physics, observe that the drag force scales with the diameter of the droplet, but the weight of the droplet scales with the diameter cubed; hence, for large droplets, the drag force is negligible in comparison with the inertia of the droplet. as shown before, the droplets are slowed down exponentially in the horizontal direction and are accelerated in the vertical direction by gravity, giving the maximum horizontal range of the droplet (when nominally y = − ), for large droplets (st ≫ r), we can then estimate that the maximum meaning that the trajectories are ballistic, and we expect that, for st ≫ r, the maximum distance becomes independent of st, in agreement with the observation that large droplets' trajectories are independent of the surrounding flow. , , for small droplets st ≪ r, the drag decreases linearly with decreasing droplet diameter, but the weight rapidly decreases cubically with decreasing diameter. hence, small droplets follow the airflow faithfully with little influence from gravity. such droplets can get great distances before falling, as shown in the left-hand side of fig. (a) . in the case of small droplets, the horizontal component of the droplet's trajectory follows the airflow like a tracer, and the droplet falls at its stokesian settling velocity. upon inspection, we find that the maximum horizontal distance l (when nominally y = − ) tends to the following asymptote as st → : we can therefore estimate that droplets for which l > or, equivalently, (i.e., the droplets travel farther in the horizontal direction than the vertical direction) weakly feel gravity. in between these two extreme cases, the drag force on the droplet is the same order of magnitude as the gravitational force. by balancing these two effects, we can approximate the upper bound of st where the droplets become ballistic, such droplets are not light enough to get carried any great distance by the ambient airflow but do not have large enough inertia to become ballistic. hence, we have the following designations: (i) small droplets with st satisfying st < rΛ reverting to dimensional quantities, we have the following range of intermediate-sized droplets: plugging in the numbers from table i , we have the approximate range for quiet breathing and for heavy breathing. our upper bound is in good agreement with previous categorizations of droplets, although our lower bound seems to be smaller than those found by previous authors. scitation.org/journal/phf for breathing, and the typical speed of a jet in normal breathing conditions is of the order of u ′ = m s − . in violent respiratory events, such as sneezing or coughing, these values could be significantly higher. finally, the extraction unit is located a distance of |x ′ | = . m from the person. these quantities are summarized in table ii. based on these numbers, the non-dimensional parameters that govern the trajectory of the droplet are determined to be r = . , re = , , Λ = . , and |g| = . , and the stokes number ranges approximately from − to − . the parameter γ relates the flux of the extraction unit to the flux of a human's breath, and its effect will be examined. in particular, if we suppose that the envisaged extraction unit has a volume flux approximately equal to that of a standard vacuum cleaner ( l min − ), then we can approximate that γ ≈ . in fig. , we show the efficacy of such extraction for a range of st. extraction is very effective at low st; however, for st > . × − , such extraction is ineffective. this upper bound of the stokes number corresponds to water droplets of diameter μm. droplets larger than this will not be collected by extraction. in the droplet classification of sec. iv b, the effective range of extraction corresponds to nonballistic droplets. in this paper, we have presented a simplified mathematical model for droplet dispersion from a source and in the presence an aerosol extractor. in the absence of gravity, and for st ≪ r, droplets behave as ideal tracers, and the maximum distance that they can travel before being extracted is a function of γ only. in this case, there are two (source, and sink if γ = ) or three (source, sink, and saddle if γ > ) fixed points. the fixed points in this study are colinear, and the position of the saddle depends on γ alone, for any given distance between the source and sink. for moderate st, the droplets' inertia carry them far away from the source until they are slowed down by drag forces and pulled into the sink. in this case, the maximum distance that the droplets can travel is given by r/st. when gravity effects are taken into account, the saddle point for st ≪ r is no longer colinear but moves on an arc, clockwise about the source, and a fourth fixed point (saddle) emerges approximately below the sink fixed point. for fixed γ, this fixed point moves closer to the source as the magnitude of gravity is increased. in this case, there is a set of trajectories that are pulled away from the sink by gravity. for moderate st, gravity plays an increasingly important role, and there is a critical value of gravity that pulls all trajectories vertically downwards away from the source. for yet larger st, the trajectories adopt a ballistic trajectory, with even those that travel close to the sink not being pulled in. covid- has brought increased awareness of the risks of aerosol generating procedures (agps) across all fields of medicine, highlighting the need for a deeper understanding of droplet dispersion and categorization during respiration and agps. clinicians recognize that our historical approaches to protection during agps are no longer adequate and that many additional precautions are necessary. in order to develop the most effective solutions, a critical first step is understanding the behavior of droplets generated during agps. this paper allows us to predict this behavior and inform our understanding of "at risk" zones in the vicinity of an agp. in particular, we performed simulations relevant to human respiration, as well as simulations to inform the development of an aerosol extractor for use in clinical settings. these simulations can help to guide recommendations on maximum safe distances between the source and sink. additionally, these models provide a better understanding of the behavior of individual droplets of various sizes, which may be present in a wide range of aerosols contaminated with viruses or other pathogens. this may help clinicians to make better informed decisions regarding safety while performing agps and in their choices of the type of ppe they wear. finally, these models provide a basis on which aerosol and droplet contamination from a wide range of surgical, medical, dental, and veterinary agps can be modeled while taking into account airflows in confined clinical spaces. in this case, we found that, for st ≤ . × − , all of the aerosol is extracted and that gravity has a minimal effect; this st corresponds to droplets with approximate diameter equal to . mm. droplets larger than this are affected by gravity, and for st = − , corresponding to droplets equal to . mm, none of the droplets are extracted. such large droplets would be typically captured by personal protective equipment (ppe), such as ffp masks that have pore sizes typically smaller than μm. we determined the maximum range of droplets ejected from the source in the absence of a sink and found that the range is minimized for intermediate-sized droplets. we find that, in human respiration, this pertains to droplets within the observed range of the ejected droplets. this could have implications for the interpretation for data obained from experiments on biological subjects, in particular, those that attribute observed bi-and tri-modal droplet dispersion to biological functions. our studies suggest that the bi-modal nature of the curve is a function of the droplet's stokes number and not necessarily linked to a specific biological function. in our model, we neglected the basset history term in the maxey-riley equation. the basset history term is of significant importance for bubbly flows, where it can account for a quarter of the instantaneous force on a bubble. generally speaking, for r ≪ / , this term can be safely ignored for small and intermediatesized droplets. recent studies have also shown that neglecting it in the modeling of raindrop growth leads to a substantial overestimate of the growth rate of the droplet. hence, for the solutions that become ballistic, we expect that such trajectories would be influenced by the basset history term that should be included. to do this efficiently, there is a very promising method developed recently. since this is not the focus of our study (such droplets can be captured by other forms of ppe), we do not perform such a study here. if the aerosol route of transmission is confirmed to be important by the world health organization, , we will need to reconsider guidelines on social distancing, ventilation systems, and shared spaces. to ensure that we put in place the correct mitigating measures, for 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management of severe acute respiratory infection (sari) when covid- disease is suspected short-range airborne route dominates exposure of respiratory infection during close contact study on transport characteristics of saliva droplets produced by coughing in a calm indoor environment face coverings, aerosol dispersion and mitigation of virus transmission risk aerosol dispersion and mitigation of infection risk -dataset of [dataset characterizing exhaled airflow from breathing and talking situation report key: cord- -gbhjke authors: meccariello, giuseppe; gallo, oreste title: what ent doctors should know about covid‐ contagion risks date: - - journal: head neck doi: . /hed. sha: doc_id: cord_uid: gbhjke nan a general consensus exists on coronavirus diffusion by droplet transmission, especially the aerosolization during hospital procedures like intubation or bronchoscopy might represent a big concern, exposing other patients and healthcare staff to an increased risk of infection. in this context, the general otolaryngology procedures may determine an aerosolization with nosocomial amplification of the infection. in particular, flexible and/or rigid nasolaryngoscopy may include some maneuvers such as puffing out cheeks, talking, swallowing some colored water, or poking out tongue. furthermore, the introduction of the endoscope may cause sneezing and cough. these risks can increase when in-office surgical procedures are applied to cure urgent and emergent pathologies such as epistaxis, removal of foreign bodies in upper aerodigestive tract, cricothyroidotomy as well as elective procedures such as biopsies, inferior turbinoplasty, and so on. based on the available evidence, it appears that sars-cov- can be transmitted by asymptomatic carriers, which contributes to its basic reproduction number and pandemic potential. zou et al showed higher viral loads after symptom onset, with higher viral loads detected in the nose than in the throat. further in the asymptomatic patients, the viral load was similar to symptomatic patients, which suggests the transmission potential of asymptomatic or minimally symptomatic patients. the common workloads of an ent are symptoms related to upper airways inflammations or infections. sore throat with or without fever, sneezing, hoarseness may be prodromic symptoms of a covid- infection in the incubation period. moreover, the coughing patients with a negative chest x-ray is one of the most consultation required. direct contact of droplet spray produced by coughing, sneezing, or talking involves relatively large droplets containing organisms and requires close contact usually within m. indirect contact may take place after the droplets are removed from the air by surface deposition. han et al studied the dynamic features of bioaerosolization by sneezing. the velocity of the airflow exhaled by sneeze is much larger than that of breath and cough. moreover, the total number of droplets generated during sneeze is also larger than that of other respiratory activities. according to the study on flow dynamics and characterization of cough, the maximum velocity of exhaled airflow can be found at t = to milliseconds for different persons which is most likely to occur at milliseconds. usually, sneeze lasts . to seconds, so t = milliseconds is in the duration of the sneeze. as the velocity of the airflow exhaled by sneeze is really high, it can be assumed that the droplets that are exhaled at t = to milliseconds will not reenter the measurement zone before t = milliseconds. the high-speed airflow and corresponding turbulence produced by sneeze may also lead to a large number of droplets, that is, the number of the droplets generated by sneeze is about times larger than that of cough. furthermore, the size of sneezing droplets is . to . μm for unimodal distribution and . to . μm for bimodal distribution. after the droplets are exhaled into the indoor environment, the evaporation effects will strongly influence the size and mass of the droplets. the final equilibrium diameter of expiratory droplets after evaporation is highly dependent upon the temperature and relative humidity of the environment. in the indoor environment, the relative humidity and temperature are much lower than those in the respiratory tract. so the volatile content of these droplets will keep evaporating and result in the shrinkage of the droplets. definitively, these findings demonstrate that the routine activities of an otolaryngologist are constantly at high risk of contagion in covid- epidemic areas. taking a look at the current italian situation, the experience of the region veneto demonstrated that the application of covid- screening also in asymptomatic people can reduce the contagion spreading. thus, it seems clear that extend the screening to all health workers included otolaryngologists could be a valid strategy to reduce the onset of a worst case scenario, the hospital outbreak. in conclusion, the professional exposure to sars-cov- is really high for the otolaryngologist and nurse staff, even in in-office settings. personal protective equipments are strongly recommended as well as for health workers in close contact with infected patients. orcid giuseppe meccariello https://orcid.org/ - - - initial clinical features of suspected coronavirus disease in two emergency departments outside of hubei sars-cov- viral load in upper respiratory specimens of infected patients the incubation period of coronavirus disease (covid- ) from publicly reported confirmed cases: estimation and application respiratory infections during air travel transport and removal of expiratory droplets in hospital ward environment characterizations of particle size distribution of the droplets exhaled by sneeze what ent doctors should know about covid- contagion risks key: cord- - zl pm authors: tan, vanessa y. j.; zhang, edward z. y.; daniel, dan; sadovoy, anton; teo, neville w. y.; kiong, kimberley l.; toh, s. t.; yuen, heng‐wai title: respiratory droplet generation and dispersal during nasoendoscopy and upper respiratory swab testing date: - - journal: head neck doi: . /hed. sha: doc_id: cord_uid: zl pm respiratory particle generation and dispersal during nasoendoscopy and swab testing is studied with high‐speed video and laser light illumination. video analysis reveals droplet formation in three manoeuvres during nasoendoscopy ‐ sneezing, vocalization, and nasal decongestion spray. a capillary bridge of mucus can be seen when a nasoendoscope exits wet nares. no droplet formation is seen during oral and nasopharyngeal swab testing. we outline the following recommendations: pull the face mask down partially and keep the mouth covered, only allowing nasal access during nasoendoscopy; avoid nasal sprays if possible; if nasal sprays are used, procedurists should be in full personal protective equipment prior to using the spray; withdrawal of swabs and scopes should be performed in a slow and controlled fashion to reduce potential dispersion of droplets when the capillary bridge of mucus breaks up. when a nasoendoscope exits wet nares. no droplet formation is seen during oral and nasopharyngeal swab testing. we outline the following recommendations: pull the face mask down partially and keep the mouth covered, only allowing nasal access during nasoendoscopy; avoid nasal sprays if possible; if nasal sprays are used, procedurists should be in full personal protective equipment prior to using the spray; withdrawal of swabs and scopes should be performed in a slow and controlled fashion to reduce potential dispersion of droplets when the capillary bridge of mucus breaks up. precautions, prevention, transmission the current covid- pandemic has major implications on the examination of the respiratory tract. due to the high viral load, there are concerns regarding potential aerosol generation during upper respiratory procedures such as nasoendoscopy and swab testing. various safety recommendations have been proposed for such procedures. , high-speed video with laser light illumination has been used to study respiratory particle dispersal patterns during coughing and sneezing. here, we used a similar technique to assess respiratory droplet generation and dispersal during nasoendoscopy and swab testing. the sagittal plane dispersal patterns of respiratory droplets were captured using a digital camera (panasonic lumix gh ) at frames per second in a low-airflow light-controlled laboratory. illumination was provided through a green laser light ( nm wavelength, mw, cm beam-size). to visualize the droplets' trajectories, we combined the relevant frames into one image. nasal, nasopharyngeal, and oral swab testing were first performed, followed by nasoendoscopy with and without cophenylcaine spray decongestion, on three volunteers. maneuvers performed during nasoendoscopy included swallow, tongue protrusion, vocalization, cough, and sneeze. video analysis revealed droplet formation only in three maneuvers during nasoendoscopy-(a) sneezing ( figure a) , (b) vocalization ( figure b) , and (c) nasal decongestion spray ( figure c) . a capillary bridge of mucus was seen when the nasoendoscope exited the wet nares in one volunteer. no droplet formation was demonstrated during oral and nasopharyngeal swab testing. video s shows the droplets produced when the patient exhales out through the nose following nasal spray. video s shows the droplets produced when the patient sneezes during nasoendoscopy. video s and video s have been slowed down times. video s shows the droplets produced while vocalizing plosives and a cough. there are more droplets seen while vocalizing than coughing. covid- is transmitted through droplet spread, with limited evidence of aerosol spread through droplet nuclei. polymerase chain reaction testing of nasal, nasopharyngeal, and oropharyngeal swabs remain the gold standard for diagnosis, and is performed worldwide. nasoendoscopy is a common procedure performed by otolaryngologists. till date, there has been no definitive evidence of droplet or aerosol generation during nasoendoscopy or upper respiratory tract swabs. our study demonstrates that droplets clearly form only under three scenarios during nasoendoscopy. from this, we suggest the following ways to reduce droplet dispersal. firstly, when only nasal access is required, the face mask should only be pulled down enough to expose the nares. secondly, while adequate topical nasal decongestion and anesthesia can reduce the tendency of sneezing, nasal sprays are in itself an aerosol generating procedure, and exhalation through the nose during a spray results in large amounts of droplet production. hence, use of nasal sprays should be avoided if possible, and if used, procedurists should be in full personal protective equipment prior to performing the nasal spray. patients should be instructed to inhale gently during the spray and avoid immediate exhalation. adequate time should be given for sufficient anesthesia prior to commencement of nasoendoscopy. thirdly, droplets formed from speech can be mitigated with the face mask over the patient's mouth. lastly, withdrawal of the swabs and scope should be performed in a slow and controlled fashion, to reduce potential dispersion of droplets when the capillary bridge of mucus breaks up. a technical limitation of our study is that our equipment can only adequately assess droplet formation. aerosols below μm ( μm) are unlikely captured in the images. studies on aerosol production during similar procedures are ongoing, with the caveat that significant f i g u r e a, sneeze; b, vocalization. bilabial plosives "per" created the most droplets, followed by lingual alveolar plosives "tee," and fricatives "fer." common sounds patients were often made to elicit during nasoendoscopy such as "eee," tonal glides, and "sniff-hee," maneuver did not produce droplets. c, most droplet production occurred with nasal expiration immediately after nasal decongestion spray [color figure can be viewed at wileyonlinelibrary.com] aerosol transmission has yet to be proven in the spread of covid- . nonetheless, this will provide crucial complementary information as aerosols remain suspended in air longer and have a higher risk of penetrating deeper in the airway. acknowledgments dr loh xian jun-director, institute of materials research and engineering, a*star, singapore; a/prof mariko koh siyue-senior consultant, respiratory and critical care medicine, sgh; olympus (singapore). vanessa y. j. tan https://orcid.org/ - - - detection of sars-cov- in different types of clinical specimens safety recommendations for evaluation and surgery of the head and neck during the covid- pandemic flexible laryngoscopy and covid- violent expiratory events: on coughing and sneezing modes of transmission of virus causing covid- : implications for ipc precaution recommendations institute of medicine committee on personal protective equipment for healthcare personnel to prevent transmission of pandemic i, other viral respiratory infections. current research i additional supporting information may be found online in the supporting information section at the end of this article. key: cord- -ndfoppoq authors: bahl, prateek; doolan, con; de silva, charitha; chughtai, abrar ahmad; bourouiba, lydia; macintyre, c raina title: airborne or droplet precautions for health workers treating covid- ? date: - - journal: j infect dis doi: . /infdis/jiaa sha: doc_id: cord_uid: ndfoppoq cases of covid- have been reported in over countries. thousands of health workers have been infected and outbreaks have occurred in hospitals, aged care facilities and prisons. world health organization (who) has issued guidelines for contact and droplet precautions for healthcare workers (hcws) caring for suspected covid- patients, whilst the us centre for disease control (cdc) has recommended airborne precautions. the – m (≈ – ft) rule of spatial separation is central to droplet precautions and assumes large droplets do not travel further than m (≈ ft). we aimed to review the evidence for horizontal distance travelled by droplets and the guidelines issued by the world health organization (who), us center for diseases control (cdc) and european centre for disease prevention and control (ecdc) on respiratory protection for covid- . we found that the evidence base for current guidelines is sparse, and the available data do not support the – m (≈ – ft) rule of spatial separation. of ten studies on horizontal droplet distance, eight showed droplets travel more than m (≈ ft), in some cases more than meters (≈ ft). several studies of sars-cov- support aerosol transmission and one study documented virus at a distance of meters (≈ ft) from the patient. moreover, evidence suggests infections cannot neatly be separated into the dichotomy of droplet versus airborne transmission routes. available studies also show that sars-cov- can be detected in the air, hours after aeroslisation. the weight of combined evidence supports airborne precautions for the occupational health and safety of health workers treating patients with covid- . m a n u s c r i p t coronaviruses are respiratory pathogens, and the sars-cov- has been identified in both upper and lower respiratory tract samples from patients [ ] . fever, dry cough, malaise, lethargy, shortness of breath, myalgia are the commonest symptoms [ ] . less common symptoms are headache, productive cough and diarrhoea. mild cases may present with a common cold like syndrome, whilst severe cases may develop severe acute respiratory distress syndrome and pneumonia. according to the who % of cases in china have a severe illness [ ] . early estimates of the reproduction number, r , give values around . with a mean incubation period of . days [ ] , and a range up to days. a review found the average r value for covid- to be up to . and median value to be around . [ ] . a more recent study estimated the maximum-likelihood (ml) value of r to be . for the diamond princess cruise ship [ ] . all these estimates are similar to r estimates for sars [ ] . in the past epidemics of sars and mers coronavirus, health care workers (hcws) have paid a heavy toll. during sars, hcws comprised % of all cases and in some countries, such as hong kong, singapore and canada, more than half the cases were hcws, with deaths reported among them [ ] . hcw deaths have already been reported with a c c e p t e d m a n u s c r i p t the who has issued guidelines for protection of hcws which recommend contact and droplet precautions for hcws caring for suspected covid- patients [ ]. specifically, a medical mask is recommended for routine care, while a respirator (airborne precautions) is recommended if hcws are conducting an aerosol-generating procedure such as endotracheal intubation, bronchoscopy or airway suctioning, along with droplet precautions [ ] . droplet precautions includes the recommendation to maintain spatial separation of m (≈ ft) with an infected patient, in the belief that large droplets can only spread horizontally to a maximum of m (≈ ft) [ ] . the initial guidelines released by us centers for disease control recommended a more precautionary approach, which includes the use of a mask by the patient (source control [ ] ), and airborne precautions for hcws [ ] . we aimed to review the evidence supporting the rule of m (≈ ft) spatial separation for droplet precautions in the context of guidelines issued by the world health organization (who), us center for diseases control (cdc) and european centre for disease prevention and control (ecdc) for hcws on respiratory protection for covid- . a systematic review was conducted for evidence of horizontal distance travelled by respiratory droplets, using the prisma criteria [ ] we found papers in the initial search. after reviewing the titles and abstracts papers were selected for full text review. finally, papers were included in the review (figure ). eight of the ten studies discussed a horizontal trajectory greater than m (≈ ft) for a range of droplet sizes of less than µm [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] . seven out of ten studies are based on modelling and a c c e p t e d m a n u s c r i p t among them the extent of horizontal spread of droplets vary between - m (≈ - ft) [ ] [ ] [ ] [ ] [ ] [ ] [ ] , highlighting differing findings between them, which can be partially attributed to the methodologies employed. specifically, four of these studies rely on computational fluid dynamics (cfd) approaches that do not account accurately for the multiphase particle-flow interaction physics [ , , , ] and three of them model cough as a turbulent jet (continuous ejection with conservation of momentum flux) instead of a turbulent puff (short sudden ejection with conservation of momentum) [ , , ] . the fourth study used lagrangian modelling for the droplet dispersion and it was acknowledged that this approach assigns a larger momentum to air hence, making it difficult to translate the results into relevant settings for hospital infection control [ ] . two studies used analogous water tank experiments to validate the mathematical modelling developed and reported distances up to . m (≈ . ft) and . m (≈ . ft) [ , ] . one of these two studies modelled coughs as turbulent jets (continuous emission) [ ] despite contrary evidence showing that the physics of violent exhalations is captured by puffs, sudden high momentum emission of moist and hot air [ ] . five studies performed experiments on human subjects [ , , , , ] , four of them generated undisturbed/natural sneezes and coughs, without injestion of fluid or powders by the human subjects [ , , , ] . out of five, two studies used the human subject measurements to develop and validate the mathematical modelling of the droplet dispersal and showed the importance of the exhaled gas cloud of hot and moist air in trapping and extending the range of all droplets [ , ] . one involved injection of powder in the mouth of the human subject potentially shifting the natural droplet sizes ejected [ ] . the other two used still photographs [ ] and particle counters [ ] and the distance reported among these two vary from - m (≈ - ft). table the interim guidelines for covid- appear to assume only droplet and contact spread and the general risk limit defined for healthcare workers is m (≈ ft) from the patient [ , ] . the transmission of covid- is not well characterised, but is likely to be similar to sars, which was spread by contact, droplet and airborne routes [ ] . given the presence of sars-cov- viral loads in both the lower and upper respiratory tract [ ] , as well as persistence of the virus in the air hours after aeroslisation [ ] , airborne transmission is possible. a recent study showed that seasonal coronaviruses were more commonly emitted in aerosols than in droplets, a c c e p t e d m a n u s c r i p t even through normal tidal breathing [ ] . it is timely to review the evidence informing the - m (≈ - ft) rule of infection control, which drives guidelines for droplet precautions. most studies of horizontal transmission of droplets show distances of greater than m (≈ ft). the maximum distance recorded in the few available studies is m (≈ feet) [ , ] . we note, although the studies employed very different methodologies and should be interpreted cautiously, they still confirm that the spatial separation limit of m (≈ ft) prescribed for droplet precautions, and associated recommendations for staff at ports of entry [ ] , are not based on current scientific evidence. the horizontal distance of droplet spread depends on various factors such as viscoelasticity of the expiration fluid, type of ventilation, velocity of expiration, rate of evaporation and the dynamics of turbulent cloud generated during exhalations, sneezing, or coughing [ , [ ] [ ] [ ] . the - m (≈ - ft) limit is based on very limited epidemiologic and simulated studies of some selected infections [ ] . some studies cite jennison ( ) [ ] as the evidence in support of the - m (≈ - ft) risk limit. this study used high speed exposure to capture still photographs of the atomising secretions generated by human sneezing, coughing and talking, imaged very close to the mouth. it was concluded that the distance to which the majority of droplets were expelled is - ft (≈ m) but, no details were provided about how they reached this conclusion. the study acknowledges that the motion picture film used for the experiments was not sensitive enough to capture all the droplets. the lighting technique used inherently selects for the largest sizes of droplets and fluid ligaments, not capturing the rest of the emissions and gas cloud carrying them. the author used still photographs, in which many droplets move out of focus and become unrecordable very quickly, especially using photographic technology from the s. more recent studies have shown the extent of droplet spread to be greater than m (≈ ft) [ ] [ ] [ ] [ ] [ ] [ ] ] , and that infection risk exists well beyond the recommended range of spatial separation. a c c e p t e d m a n u s c r i p t further, there is no agreement on the definition of "droplet" route of transmission. there is some agreement that particles with diameters less than µm are airborne particles but, there is significant variation in the literature when it comes to the classification of the lower size limit of droplets. wells ( ) [ ] considered µm as the cut-off limit for the droplet route. but, later studies considered a cutoff particle diameter of more than µm to more than µm [ , , ] . the world health organization (who) employs a cut off limit of µm to differentiate between aerosols (≤ µm) and droplet (> µm) [ ] transmission routes. however, even particles with a diameter of more than µm can remain airborne long enough to not fall under the framework of classification of "droplet" route [ ] . in addition, the size of a droplet is dynamic and changes within seconds during the transit from the respiratory tract to the environment due to evaporation [ ] . a large droplet expelled during coughing or sneezing can become an airborne particle in less than a second [ ] and that timescale changes depending on the cloud dynamics of exhalation [ , ] . hence, it is not possible to characterize droplet and airborne spread as separate, mutually exclusive modes of transmission and further studies of the risks accounting for combined ambient conditions and patient exhaled cloud are needed. indeed, another important consideration is the effect of temperature, relative humidity, ventilation etc. on the extent of droplet spread which has been examined by only a few studies. to summarise, they have shown that relative humidity plays an important role in the evaporation of the droplets and the distance a droplet can travel. they report that as the relative humidity increases the extent of droplet spread decreases [ , ] , yet the horizontal range of the cloud propelling the drops was found to increase with increase in relative humidity, due to the role of buoyancy of the exhaled cloud [ ] . for droplets less than µm in diameter, local airflow field due to body heat is an important factor in determining the extent of spread since it can lift the droplets upwards into the breathing zone [ ] . studies have also shown that depending on the flow direction and airflow pattern, increasing ventilation rate can effectively a c c e p t e d m a n u s c r i p t reduce the risk of long range airborne transmission [ ] . most patients spend the majority of time in normal breathing and can saturate the room air with airborne particles expelled during breathing. moreover, despite negative pressure isolation conditions, airflow due to door motion can cause breakdown in isolation conditions and as a result pathogen can escape the room and there is probability of infection spread outside the room [ ] . in general recent studies show distances reached by potentially pathogen-laden droplets of a continuum of sizes to be far greater than m (≈ ft) [ ] [ ] [ ] [ ] [ ] , therefore the probability of infection well beyond the defined risk limit can be significant. for example, sars was classified as predominantly transmitted through contact and droplet modes, but, aerosolised transmission well beyond m (≈ ft) was reported in the amoy gardens outbreak [ ] . the ability of countries to respond effectively depends on the safety and confidence of the health workforce, especially in low income countries with low ratios of hcws per head of population and protective measures are crucial to ensure a functional health workforce. we have previously shown that masks do not have clinical efficacy against respiratory infections [ , ] , and that intermittent use of respirators (which depends on hcws to assess their own risk and use the device when they judge they are at risk) is as equally ineffective as mask use [ ] . a recent trial confirmed there is no difference between targeted respirator use and surgical mask use, but did not have a control arm and so may have shown equal efficacy or inefficacy [ ] . proven efficacy of a respirator is seen when the device is worn continually during the shift [ ] . the sars-cov- has been found in both upper and lower respiratory tract specimens, often early in the upper and later in the lower respiratory tract [ ] , which means it can potentially be dispersed in fine, airborne particles. influenza studies show that in a busy emergency department or hospital ward, airborne particles with viable virus can persist for hours in the air [ ] . a study of sars-cov- in a hospital in wuhan found virus at least m (≈ ft) within a hospital ward, and virus was identified in air samples and on multiple air outlet a c c e p t e d m a n u s c r i p t vents [ ] . other studies have also found sars-cov- on air vents in a patient room [ ] . another study found virus in air samples three hours after aersolisation [ ] . we have also shown that airborne precautions are more efficacious in protecting hcws even against infections assumed to be spread by the droplet route [ ] . this further supports the conclusion that infections cannot be neatly separated into droplet versus airborne transmission routes, and that it is likely both airborne and large droplets, carried by the respiratory cloud, are emitted close to the patient and further away. in light of the lack of definitive transmission data for sars-cov- , as well as persistence of the virus in the air hours after aeroslisation [ ] , the precautionary principle in the initial cdc guidance was justified. this includes use of a mask by the patient, for which the limited evidence is supportive [ ] . guidelines should be precautionary in ensuring protection of the occupational health and safety of health workers treating covid- [ ] . although the majority of the studies reviewed point towards horizontal spread of more than m (≈ ft), these results cannot be translated directly to hospital settings, as the studies used varying range of assumptions. the recent data on sars-cov- in a hospital ward shows a distance travelled by the virus of at least m (≈ ft), double the assumed safe distance [ ] . this review reveals the limited scientific data to inform spatial separation guidelines, and a growing body of evidence that droplet precautions are not appropriate for sars-cov- . hence, future works on carefully documenting and studying the mechanisms shaping transmission distances are warranted, particularly with experiments over a large number of subjects and a variety of conditions, to update current spatial separation guidelines and the current paradigm of droplet and airborne respiratory transmission routes. m a n u s c r i p t novel coronavirus ( -ncov) situation reports virological assessment of hospitalized patients with covid- early transmission dynamics in wuhan, china, of novel coronavirus-infected pneumonia the reproductive number of covid- is higher compared to sars coronavirus estimation of the reproductive number of novel coronavirus (covid- ) and the probable outbreak size on the diamond princess cruise ship: a data-driven analysis transmission dynamics and control of severe acute respiratory syndrome infection prevention and control during health care when novel coronavirus (ncov) infection is suspected world health organization. management of ill travellers at points of entryinternational airports, seaports and ground crossings -in the context of covid- outbreak: interim guidance world health organization cluster randomised controlled trial to examine medical mask use as source control for people with respiratory illness interim healthcare infection prevention and control recommendations for patients under investigation for novel coronavirus preferred reporting items for systematic reviews and meta-analyses: the prisma statement study on transport characteristics of saliva droplets calm indoor environment how far droplets can move in indoor environments -revisiting the wells evaporation-falling curve theoretical analysis of the motion and evaporation of exhaled respiratory droplets of mixed composition violent expiratory events: on coughing and sneezing enhanced spread of expiratory droplets by turbulence in a cough jet evaporation and dispersion of respiratory droplets from coughing. indoor air quantity, size distribution, and characteristics of coughgenerated aerosol produced by patients with an upper respiratory tract infection human cough as a two-stage jet and its role in particle transport atomizing of mouth and nose secretions into the air as revealed by high-speed photography. aerobiology. th ed. american assn. for the advancement of science interim domestic guidance on the use of respirators to prevent transmission of sars infection prevention and control during health care for probable or confirmed cases of middle east respiratory syndrome coronavirus (mers-cov) infection: interim guidance: updated interim infection prevention and control recommendations for hospitalized patients with middle east respiratory syndrome coronavirus (mers-cov) rapid risk assessment: severe respiratory disease associated with middle east respiratory syndrome coronavirus (mers-cov) cdc updates guidance on ppe for health care personnel; covid- declared a pandemic interim infection prevention and control recommendations for patients with suspected or confirmed coronavirus disease (covid- ) in healthcare settings infection prevention and control and preparedness for covid- in healthcare settings -second update evidence of airborne transmission of the severe acute respiratory syndrome virus aerosol and surface stability of sars-cov- as compared with sars-cov- respiratory virus shedding in exhaled breath and efficacy of face masks turbulent gas clouds and respiratory pathogen emissions guideline for isolation precautions: preventing transmission of infectious agents in health care settings on air-borne infection. ii. droplets and droplet nuclei world health organization. infection prevention and control of epidemic-and pandemic-prone acute respiratory diseases in health care aerosol technology: properties, behavior, and measurement of airborne particles thermal effect of human body on cough droplets evaporation and dispersion in an enclosed space ventilation control for airborne transmission of human exhaled bioaerosols in buildings door-opening motion can potentially lead to a transient breakdown in negative-pressure isolation conditions: the importance of vorticity and buoyancy airflows a cluster randomized clinical trial comparing fit-tested and non-fit-tested n respirators to medical masks to prevent respiratory virus infection in health care workers a randomized clinical trial of three options for n respirators and medical masks in health workers n respirators vs medical masks for preventing influenza among health care personnel measurement of airborne influenza virus in a hospital emergency department aerosol and surface distribution of severe acute respiratory syndrome coronavirus in hospital wards surface environmental, and personal protective equipment contamination by severe acute respiratory syndrome coronavirus (sars-cov- ) from a symptomatic patient the efficacy of medical masks and respirators against respiratory infection in healthcare workers. influenza other respi viruses uncertainty, risk analysis and change for ebola personal protective equipment guidelines m a n u s c r i p t wei and li key: cord- -rg br d authors: lai, a. c. k.; tan, t. f.; li, w. s.; ip, d. k. m. title: emission strength of airborne pathogens during toilet flushing date: - - journal: indoor air doi: . /ina. sha: doc_id: cord_uid: rg br d the flushing of toilets generates contaminated aerosols, the transmission of which may cause the spread of disease, particularly in the immunocompromised or the elderly. this study investigated the emission strength of three types of airborne bacteria, namely staphylococcus epidermidis, escherichia coli, and pseudomonas alcaligenes, during toilet flushing in a custom‐built toilet under a controlled environment. flushing was activated by a flushometer operated at two pressure levels, kpa (high pressure [hp]) and kpa (low pressure [lp]), and by a water cistern tank placed cm (high tank [ht]) and cm (low tank [lt]) above the toilet seat. the pathogens emitted by the first flush were calculated, with the correlations between airborne pathogen emissions and droplet concentration (hp, r= . , p<. ; lp, r= . , p<. , ht, r= . , p<. ) and bacterial size (hp, r=− . , p<. ; lp, r=− . , p<. ; ht, r=− . , p<. ) in the different conditions then tested. the emission strength in the hp condition was statistically greater than that in the lp condition, whereas the cistern tank system produced less emissions than the flushometer system, and tank height was not found to be a sensitive parameter. the human-to-human transmission of airborne pathogens, such as tuberculosis, smallpox, severe acute respiratory syndrome coronavirus (sars-cov), middle east respiratory syndrome coronavirus, avian influenza, and ebola, , presents a challenge to the prevention, management, and containment of emerging infectious disease outbreaks and infection control worldwide. a number of studies have investigated human-to-human transmission via expiratory droplets inside built environments with a view to minimizing it, but there are also other airborne pathways that can transmit pathogens. when external energy is used to disintegrate liquid into airborne droplets, the process is referred to as atomization. the splashing of water droplets during the flushing process is commonly observed when toilets are poorly designed or the flushing pressure is too high. in addition to the relatively large droplets that are visible (~ millimeters in size), the toilet flushing process is also known to atomize numerous smaller airborne droplets. it was demonstrated as long ago as the s that droplets with airborne pathogens can be generated during the toilet flushing process, thereby creating infectious hazards. more recent studies have revealed a very high viral load, up to viral particles per gram of fecal matter. if feces containing pathogenic organisms are shed by an infected person and contaminate toilet fluid, the atomized droplets produced may well be infectious. [ ] [ ] [ ] the results of previous studies have raised concern over the aerosolization of excreta containing such intestinal or urinary pathogenic microorganisms as aeromonas sp., bacillus sp., campylobacter sp., clostridium sp., escherichia sp., klebsiella sp., pseudomonas sp., salmonella sp., serratia sp., shigella sp., and staphylococcus sp. presenting either as colonization or infection. among all pathogens concerned, noroviruses have received the greatest attention, particularly in elderly and healthcare settings. in addition, pathogens other than the typical intestinal pathogens, including the deadly sars-cov and ebola virus, have also been detected in excreta, thus further raising concerns about the potentially infectious pathogen-laden aerosols generated by toilet flushing. when the fecal shedding of pathogenic organisms takes place in the toilet bowl of a public washroom, flushing the toilet may expose subsequent washroom users through primary exposure to contaminated aerosols via direct inhalation, and/or secondary exposure may occur via contact with contaminated surfaces. large droplets settle within - m, and are highly likely to contaminate such environmental surfaces as door handles, banisters, and flush handles. small droplets generally refer to droplet nuclei with a diameter in the range of less than μm. as they settle slowly in the air, they can travel farther and for a much longer duration. it has been reported that contaminated droplet nuclei can be dispersed to other areas of a washroom, and they have even been found outside a mock-up toilet cubicle. barker and jones conducted a toilet seeding experiment in which they measured the level of bioaerosols generated by the flushing of a residential toilet. they reported the amount of serratia marcescens in the air to increase sharply from zero colony-forming units per cubic meter (cfu/m ) to cfu/m after the first flush. however, a later study recorded a much smaller number of size-resolved flushinggenerated airborne droplets than that observed by barker and jones. a similar study was recently conducted in a hospital to determine the concentration of clostridium difficile following flushing. it found that even with the toilet lid down, aerosolized droplets could be recovered cm above the seat within minutes of flushing. quantification of the potential transmission risk of pathogen-laden aerosols is important. emission strength is the most important of all known parameters for such quantification, but has rarely been investigated. quantifying the risk of potential transmission based on indirect evidence without carrying out controlled experiments is unreliable. it is believed that flushing systems (and related parameters) exert the strongest effect on airborne pathogen emission. a significant association between bacterial emission strength at different degrees of flushing energy and flushing systems was reported in a recent study focusing on the initial droplet size distribution generated by flushing an experimental toilet system with various flushing mechanisms. however, submicrometer monodisperse spheres were used as surrogates for microorganisms. the flushing of a toilet bowl can be achieved either by supplying water pressure through a flushometer or by gravity through a cistern system. flushometer-valve toilets are typically used in commercial and office buildings because the recharge/refilling time is very short, meaning the toilet is available for the next user almost immediately. cistern systems (or simple tank systems), in contrast, take a few minutes to recharge after each flush, causing inconvenience in high-frequency settings such as shopping arcades or other public buildings. however, cistern systems remain popular in residential and educational buildings, partly because their design and maintenance are simpler and less costly than those for flushometer-based systems. the aim of this study was to investigate the emission strength of the first flush for the two flushing systems. parameters such as water pressure, tank height, and bacterial size were varied, and the correlations between airborne droplet concentration and bacterial emission strength were investigated. the test-rig comprised a toilet bowl incorporating a flushometer, a cistern tank, a storage tank, a booster pump, a pneumatic pressure vessel, and tailor-made pipework ( figure s ). a ceramic wash-downtype toilet bowl was installed (c p, econax) because it is the most common toilet bowl type used in hong kong households. all public housing in hong kong, which accommodates ~ % of the approximately . million population, is equipped with such toilets. the flushometer was designed to supply l per flush (naval exposed water closet, sloan, usa). because no direct pressurized city water was available in the laboratory, the water supply was specially arranged and designed with a closed-loop system. the outlet of the bowl was connected to a stainless steel water tank (with a capacity of l), and a booster pump with a pneumatic pressure vessel was installed to deliver water from the storage tank to the flushometer, thereby forming a closed-loop circuit in which water discharged from the water closet was recirculated. the cistern tank system was simpler in design. a standard cistern tank was purchased from a local plumbing store and filled with l of tap water for each flush. a tailor-made tracking system was fabricated to allow the cistern height to be adjusted with a handle. the two flushing systems could be rendered interchangeable in less than a minute via a few simple valve-changing steps. the temporal profiles of the different-sized droplets generated during toilet flushing were recorded using an optical particle counter • emission strength is probably the single most important parameter for estimating the bacterial exposure risk from toilet flushing. this study found emission strength and bacterial size to be negatively correlated, which is valuable information for estimating the risks associated with small viruses or large bacteria. it also documented a correlation between droplet concentration and emission strength. finally, it found a cistern tank design to be the preferred toilet flushing option because of its minimal generation of potentially infectious small aerosols. to enhance the accuracy of the bacterial counts, instead of random sampling inside the entire environmental chamber, a small transparent acrylic box of × × cm (l×w×h) in size was placed upright on the toilet bowl seat surface, with a -cm-diameter circular opening in one side facing the toilet bowl ( figure ). to ensure that the air was well-mixed inside the box, and to avoid unnecessarily vigorous mixing to prevent high-turbulence deposition loss, preliminary trial tests were run to determine whether any mixing fans were required. four small computer muffin fans were hung in each upper corner to provoke mixing. as the results indicated no significant differences in the air samples, no mixing fans were used subsequently. also, the electrostatic and diffusion losses were found to be negligible, with the smallest droplet size concerned being just . μm. to balance the pressure differential created by the sampling pump, another circular opening of cm in diameter was made in one of the vertical walls. electrostatic filter paper was fixed at the opening to allow filtered air to flow through without affecting the bacterial count. another small opening of . cm in diameter was made to allow particle counter measurements through the conductive sampling tube. finally, a standalone split-type air-conditioning system operated in the chamber throughout the experiments, and thus, the temperature and relative humidity were maintained at ± . °c and ± %, respectively. such parameters as the static pressure of the water supply and cistern height were selected on the basis of practical application. by adjusting the water pressure switch, two levels of water supply pressure, high pressure (hp, kpa) and low pressure (lp, kpa), were achieved, and the pressurized water was fed to the flushometer. this range is the conventional water pressure range for flushometer systems. two cistern heights, as measured from the surface of the toilet seat to the bottom of the tank, were selected: high tank (ht, cm) and low tank (lt, cm). the ht system represented the systems used in old residential buildings, whereas the lt system represented that used in newer residential and commercial buildings. the quantity of water used during flushing was also measured. for the cistern system, such measurement was a straightforward matter of measuring the drop in water level before and after flushing, which was estimated to be l. for the flushometer system, the water used per flush was estimated to be l. similar to a previous study, the selection criteria for the microorganisms were based on biosafety issues and physical characteristics rather than pathogenic properties. three biosafety levels for bacteria of different sizes and shapes were selected as surrogates for the pathogenic species commonly found in bioaerosols. further details can be found in the supporting information (table s ) . bacterial emission strength was measured in the order of s. epidermidis, e. coli, and p. alcaligenes. the first two types of bacteria were tested in all four scenarios (hp, lp, ht, and lt), whereas p. alcaligenes was tested in the hp and lp conditions alone. each type of bacteria was inoculated onto a nutrient agar (na) plate from frozen stock. after incubation at or °c for to hour, a colony from the na plate was inoculated into a ml nutrient broth (bd), and incubated in an orbital shaker at or °c for to hour to reach a stationary phase. the suspensions were used immediately for the emission strength experiments. the input of each bacterial suspension was to cells, and the suspension volumes used are shown in table s in the supporting information. for the background experiment, the acrylic box was placed upright on the toilet seat, and flushing was activated. the andersen sampler was loaded with a -mm petri dish containing na and operated for minutes. the dish was incubated at or °c for to hour. the cfus obtained were counted manually after cultivation. for the bacterial emission experiments, each bacterial suspension was splashed onto the porcelain surface of the toilet bowl using a syringe. the sampling procedure was the same as that for the background experiment. at least three independent experiments were conducted for each flushing scenario. to overcome the main drawback of the closed-loop system, that is, that after flushing a certain amount of bacteria can flow back into the water tank, the entire system was thoroughly disinfected between experiments by pouring ml of household bleach ( . % sodium hypochlorite by mass) into the toilet bowl, followed by ml of % sodium thiosulfate to neutralize the bleach residue, and then flushing with plenty of fresh water. water samples collected after disinfection were found to have no bacterial cross-contamination. an approximately -cm conductive sampling tube was connected from the sampling inlet of the counter to the center of the acrylic box. preliminary observation indicated that minutes was sufficient for the particles to decay back to their background levels (figures and s ). for the first measurement, samples were collected for mins to determine the background level before flushing, and the second flushing was activated minutes after the first. as noted, measurements were repeated at least four times for each scenario. although the particle counter was not calibrated for each specific aerosol examined, and hence, the readings are not the actual gravimetric values, it is believed that such a limitation did not affect the study's results because they were normalized by the results collected by the same counter. comparisons of the emission strengths of the different types of bacteria and the different scenarios were computed by the mann-whitney u test and kruskal-wallis test, respectively. pearson correlation coefficients were used to test the strength of the association between two parameters. the ibm statistical package spss (version . ) was used for all of the statistical computations. before detailed analysis of the size-resolved concentration profiles, preliminary results on the total emissions generated by the different flushing systems in the four scenarios were obtained. figure presents the temporal profile of the total particle emissions of the four scenarios. two salient points can be observed. first, the flushometer system produced a significantly higher droplet concentration than the tank system regardless of the water pressure or tank height. second, emission was detected immediately after flushing was activated, and it took less than seconds for the droplet concentration to increase to peak level. the water pressure for the cistern tank was . and . kpa for the lt and ht conditions, respectively, whereas that for the flushometer was and kpa. hence, the pressure produced by the cistern tank was, at most, % ( . / ) of that produced by the flushometer, which suggests that cistern systems create much less energy for the atomization of droplets, and thus generate significantly fewer droplets. this observation is supported by the results of this study and previous studies. total and size-resolved droplet emissions per flush were determined by the summation of all temporal particle counts minus the background counts for seconds post-flush. because the emission time (~ seconds) was much shorter than the decay time, droplet emissions could be approximated by equation ( ): where e is droplet emissions per flush; q is the air sampling flow of the optical particle counter, that is, . × − m /s; β is the particle loss rate (s − ); and v is the volume of the acrylic box, that is, . m . β depends on such factors as particle size, turbulence intensity, and deposition surface, whereas q+βv is estimated from the decay of the droplet profiles, and falls within the range of . × − m /s to × − m /s. the simple approach of using the average of the range, that is, . × − m /s, was adopted in calculating equation ( ) to obtain more details on the emission characteristics, the temporal profile of the size-resolved droplet concentrations was investigated, with the results presented in figure s the size-resolved droplet concentrations are also shown in table . the ratio of the average droplet emission strength was calculated. the hp to lp ratios for . - . μm, . - μm, . - μm, and - μm were . , . , . , and . , respectively, which are in line with the ratio of . for the total concentration. the magnitude of the ratios for the cistern tanks was very different. for droplet diameters in the range of . - . μm, the hp/ht droplet emission ratio was . times, whereas that for those ranging from . to μm, . to μm, and to μm were . , . , and . , respectively. hence, compared with the flushometer, the droplet emission concentration produced by the cistern tank was only . % for droplets sized ≤ . μm, whereas it ranged from % to % for droplets ≥ . μm. this finding has important implications, showing that an exposure risk still exists even for tank flushing (with a low degree of atomization energy) with a low level of total droplet emissions. the pathogen emission strength of the first flush in the four scenarios was calculated by equation ( ), with the results shown in figure . where cfu is the count in the petri dish with bacteria added to the toilet bowl, and cfu(bg) is the count without bacteria added. positive hole correction was applied for all samples. because the order of magnitude of the cfu counts and bacteria was significantly dispersed, the results were normalized by . the were very low. as similarly low or even lower cfu results were anticipated for p. alcaligenes, only the hp and lp scenarios were tested. the correlations between the airborne pathogen concentrations and quantity of airborne droplets are reported in table . it can be seen that there was a positive correlation between the droplet and pathogen concentrations in the hp, lp, and ht conditions, whereas a non-intuitive result was obtained for lt, that is, the emission strength was higher than in the ht condition. the exact reason for this result is unclear, but may be attributable to the very low concentration of aerosols in the ht and lt conditions. the explanation is further clouded by the highly complex water flow (atomization process). the correlations between emission strength and bacterial size are also shown in table , with a negative such correlation found in both our work confirms the correlation between a threshold droplet size and emission strength, thereby also supporting our hypothesis, that is, that a droplet of diameter d can embed a pathogen whose size is at most diameter d. as shown in table , the emission of smaller droplet overwhelms larger droplets. combining these two observations, it can explain the airborne emission strength of pathogens decreases with the their sizes. it can be inferred from these results that low flushing pressure is better in practice than high pressure. however, additional factors such as refilling time and cleaning performance also need to be considered, and hence, the best level of in-use flushing pressure for minimizing the generation of emissions cannot be determined solely on the basis of these results. in practice, an overly low pressure may be insufficient to remove the waste adhering to the bowl surface, which raises issues of hygiene. nevertheless, drainage system designers would be advised to take our results into consideration in conjunction with the need to provide satisfactory drainage performance, particularly in facilities for the elderly and other special groups and in hospitals and clinical settings, to reduce the risk of transmitting potentially infectious contaminated aerosols to highrisk persons. the world health organization reported that during the sars outbreak inadequate plumbing systems allowed infectious sars droplets to enter buildings via sewage and drainage systems, blaming in particular strong upwards airflows, inadequate traps, and non-functional water seals. it has thus been recommended that drainage systems be designed to prevent the evaporation of fluids within u-traps. however, this preventive measure can minimize the risk of exposure only through the pathways of building drainage systems. even when water seals function properly, the atomization of airborne pathogens occurs on the toilet bowl surface during flushing. there are many commercially available products designed to improve toilet hygiene, including paper toilet seat covers, gel/foam disinfectants, and automatic toilet bowl cleaners or tablets, but none is cfus were found, and the test was therefore discontinued and is not reported in detail. the pilot study reported herein was the first to measure the emission strength of airborne pathogens and to demonstrate a correlation between airborne cfus and flush droplet counts. it investigated the two most popular flushing systems, flushometer and cistern systems, at two different water pressures (hp= kpa and lp= kpa) and tank heights (ht= cm and lt= cm) and tested three types of this paper also highlights the need for greater concern over the transmission via toilet flushing of aerosols containing pathogenic organisms, which poses particular for the immunocompromised, children and the elderly. finally, our findings also imply that a cistern tank design is preferable to a flushometer design with respect to aerosol generation. transmission of ebola viruses: what we know and what we do not know evidence of airborne transmission of the severe acute respiratory syndrome virus infective hazards of water-closets fecal viral concentration and diarrhea in norovirus gastroenteritis 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of clostridium difficile after flushing toilets: the role of toilet lids in reducing environmental contamination risk size-resolved emission rates of airborne bacteria and fungi in an occupied classroom evaluation of cold plasma disinfection efficacy against different airborne bacteria in ventilation duct flow particle deposition indoors: a review positive-hole correction of multiple-jet impactors for collecting viable microorganisms inadequate plumbing systems likely contributed to sars transmission environmental conditions and the prevalence of norovirus in hospital building drainage system wastewater and airflows reduction of microbial aerosols by automatic toilet bowl cleaners the work described in this paper was fully supported by a general additional supporting information may be found online in the supporting information tab for this article. key: cord- -s fm rfa authors: jayaweera, mahesh; perera, hasini; gunawardana, buddhika; manatunge, jagath title: transmission of covid- virus by droplets and aerosols: a critical review on the unresolved dichotomy date: - - journal: environ res doi: . /j.envres. . sha: doc_id: cord_uid: s fm rfa the practice of social distancing and wearing masks has been popular worldwide in combating the contraction of covid- . undeniably, although such practices help control the covid- pandemic to a greater extent, the complete control of viral-laden droplet and aerosol transmission by such practices is poorly understood. this review paper intends to outline the literature concerning the transmission of viral-laden droplets and aerosols in different environmental settings and demonstrates the behavior of droplets and aerosols resulted from a cough-jet of an infected person in various confined spaces. the case studies that have come out in different countries have, with prima facie evidence, manifested that the airborne transmission plays a profound role in contracting susceptible hosts. interestingly, the nosocomial transmission by airborne sars-cov- viral-laden aerosols in healthcare facilities may be plausible. hence, clearly defined, science-based administrative, clinical, and physical measures are of paramount importance to eradicate the covid- pandemic from the world. coronavirus disease was first reported in wuhan, china, in december . the disease is caused by severe acute respiratory syndrome coronavirus (sars-cov- ) and asseverated to be transmitted from human-to-human by multiple means, namely, by droplets, aerosols, and fomites . it has been more than days that covid- , later declared as a pandemic and highly contagious, was first reported. as of may , , there have been more than . million confirmed cases and , deaths by the covid- disease worldwide (who, a) . covid- infection triggers severe acute respiratory illness, with fever, cough, myalgia, and fatigue as common symptoms at the onset of illness judson and munster, ; . infectious agents may spread from their natural reservoir to a susceptible host in different pathways. there are various classifications reported in the literature for modes of transmission of different infectious agents. morawska ( ) has presented a classification for virus transmission, including human-human transmission, airborne transmission, and other means of transmission such as endogenous infection, common vehicle, and vector spread. however, many respiratory viruses are believed to transmit over multiple routes, of which droplet and aerosol transmission paths become paramount, but their significance in transmitting the disease remains unclear (morawska and cao, ; . in general, infected people spread viral particles whenever they talk, breathe, cough, or sneeze. such viral particles are known to be encapsulated in globs of mucus, saliva, and water, and the fate/behavior of globs in the environment depends on the size of the globs. bigger globs fall faster than they evaporate so that they splash down nearby in the form of droplets liu et al., ) . smaller globs evaporate faster in the form of aerosols, and linger in the air, and drift farther away than the droplets do. respiratory particles may often be distinguished to be droplets or aerosols based on the particle size and specifically in terms of the aerodynamic diameter . one could dispute that, unlike larger droplets, aerosols may pose a greater risk of the spread of the covid- disease among many susceptible hosts positioned far from the point of origin. nevertheless, it has been proven that viral disease outbreaks via aerosol transmission are not as severe as one would think, because of dilution and inactivation of viruses that linger for extended periods in the air . there has been no discernable evidence on the minimum infectious viral load for covid- pandemic, but many researchers speculate that a few hundreds of sars-cov- virus would be enough to cause the disease among susceptible hosts. there have been numerous disagreements on the average particle size of droplets and aerosols . the world health organization (who) and centers for disease control and prevention (cdc) postulate that the particles of more than μm as droplets, and those less than μm as aerosols or droplet nuclei who, ) . conversely, there have been some other postulations, indicating that aerodynamic diameter of μm or μm or less should be reckoned to be aerosols, based on their ability to linger in the air for a prolonged period, and the reachability to the respirable fraction of the lung (alveolar region) tellier, ) . small aerosols are more susceptible to be inhaled deep into the lung, which causes infection in the alveolar tissues of the lower respiratory tract, while large droplets are trapped in the upper airways (thomas, ) . for easy apprehension, aerosols can be defined as suspensions of solid or liquid particles in the air, which can be generated by either natural or anthropogenic phenomena (judson and munster, ; tellier, ) . though social distancing would be promising in combatting the covid- , the minimum distances that have been maintained between an infected person and a host are disputable and far from being established based on any scientific evidence. nevertheless, many have believed that droplets predominate over aerosols in terms of contracting the disease; thus, over time, research work has been focused on acquiring better knowledge on the science of droplet transmission (morawska and cao, ; . however, since the recent past, evidence has been provided to refute the former hypothesis and speculated that aerosols also play a major role in transmitting the disease (morawska and cao, ; . as such, the controversy on the modes of transmission of the sars-cov- virus seems to be speculating and puzzled among many researchers, including the who (morawska and cao, ) . no conclusive studies have been conducted on differentiating between the modes of transmission of viruses via droplets and aerosols; hence, unresolved dichotomy. thus, this paper outlines the possible key deliberations cast by many researchers on the possible modes of transmission of previously identified viruses with similar characteristics of sars-cov- . it has also been argued that environmental settings, in which the sars-cov- virus transmits, trigger the disease adversely or beneficially with a susceptible host exposed to more or lesser payloads, respectively (morawska, ; tellier et al., ) . such adverse or beneficial scenarios are based on plausible changes in the fate of the virus in the environment caused by altered transport phenomena. there have been myriads of hypotheses corroborating that certain threshold levels of humidity, temperature, sunlight, and ventilation will speed up the virus-laden droplet and aerosol transmission, aggravating the spread of the sars-cov disease (morawska, ) . thus, this review paper also attempts to hypothesize how the general environmental and geographical settings in sars-cov- -affected countries impacted the susceptible hosts differently. as scientists underpin more conclusive evidence on the modes of transmission via droplets and aerosols, facemasks and respirators worn by billions of people around the globe (both infected persons and susceptible hosts) has become a common sight in day-to-day activities. in the events of the droplet and aerosol transmission, the efficacy of such personal protective equipment in combating the transmission of the sars-cov- has been poorly understood. this review paper attempts to delineate as to how such facemasks and respirators help combat transmission of virus-laden droplets and aerosols to a level less than the so-called minimum infectious dose. ever since the covid- has been declared to be a pandemic with incredibly high morbidities and mortalities worldwide, the database of research on controlling the covid- , especially in the indoor environment, has been updated with several evidence-based studies. however, less attention has been focused on the whole in controlling virus-laden droplet and aerosol shedding, their transport phenomena, and plausible methods of their dilution and destruction in different indoor settings. this review paper, therefore, outlines the best practices that could be adopted to lessen the covid- casualties in different diverse environmental settings. with more covid- cases reported worldwide, evidence-based decisions need to be adhered to in combating the disease, especially for situations in confined environments. the transmission of droplets and aerosols within confined spaces becomes profoundly complex phenomena, and the real trajectories under different micro-climatic conditions are poorly understood. the aggressive nature of the disease is directly connected with the transport phenomena of both droplets and aerosols, and the comprehension of such phenomena is vital in controlling the spread of the disease within such confined spaces. aerodynamic engineers, therefore, need to network with virologists to fully understand the possible trajectories of the viral spread within such confined spaces. in this context, computational fluid dynamics could be made use of, to simulate the trajectories resulting from coughs and sneezes of an infected person within a given space. thus, this paper attempts to illustrate how such transport phenomena of droplets and aerosols of an infected person affect other susceptible hosts. although the direct transmission from infected person/s is the primary source of aerosols and droplets, other scenarios such as medical procedures, surgeries (judson and munster, ) , fast-running tap water and toilet flushes (morawska, ) also generate aerosols contaminated with infectious pathogens. the most common types of viruses causing infections in the respiratory tract through aerosol transmission are influenza viruses, rhinoviruses, coronaviruses, respiratory syncytial viruses (rsvs), and parainfluenza viruses (morawska, ) . tellier ( ) has postulated three modes in which the influenza virus can be transmitted: aerosol transmission, droplet transmission, and self-inoculation of the nasal mucosa by contaminated hands. another classification is presented by judson and munster ( ) , which is often referred to as the term of 'airborne transmission' to describe the disease spread by small droplet aerosols and droplet nuclei, while the term 'droplet transmission' to describe infection by large droplet aerosols. the term 'airborne transmission' defined by morawska ( ) is quite similar to the same apprehended by judson and munster ( ) . besides, the direct contact and fomite transmission produced by aerosol-generating medical procedures (agmps) can also be considered as potential transmission pathways (judson and munster, ) . droplet transmission occurs by the direct spray of large droplets onto conjunctiva or mucous membranes of a susceptible host when an infected patient sneezes, talks, or coughs. in the meantime, direct physical touch between an infected individual and susceptible host and indirect contact with infectious secretions on fomites can cause the contact transmission (boone and gerba, ; brankston et al., ; tellier, ) . it is a well-known fact that covid- is transmitted by human-to-human contact; hence, contagious. one of the predominant mechanisms for covid- to be contagious is selfinoculation from contaminated fomites. self-inoculation could occur by poor hand hygiene (kwok et al., ) or by not following the common disease-controlling etiquettes. the viral transmission because of the frequent touches of contaminated fomites was found to be a source of the disease. consequently, many researchers have paid attention to the airborne transmission directly by virus-laden droplets and aerosols. however, the novelty of this viral outbreak limits the prima facie evidence to determine the potential transmission routes, and thus, it is assumed that sars-cov- also spreads as the other human coronaviruses (cdc, a) . recent studies corroborated that covid- is transmitted primarily between people through respiratory droplets and contact routes cdc, a; chan et al., ; huang et al., ; who, b) . besides, evidence has been found that fecal contamination caused by an infected person is discernible to spread the sars-cov- virus . a recent study in china has investigated , specimens collected from infected patients at three hospitals in the hubei and shandong provinces, and about % of positive cases for covid- have been observed with the transmission through feces . further, they also highlighted the fact that covid- could be transmitted via fecal routes after they detected the live infectious agents of covid- in patients' stools . contrary to what has been stated above, the who, at early hours of manifestation of covid- , has denounced that there was no supporting evidence on the fecal-oral transmission of the sars-cov- virus (who, b) . the same report also highlighted the fact that airborne transmission has not played a significant role in disease transmission from , confirmed covid- cases in china as of (who, c . in contrast to the who study, another study has reported that sars-cov- can survive in the air for many hours, causing potential aerosolized transmission (van doremalen et al., ) . with more infected persons being recorded in many countries, the who has intimated that certain hospital procedures would also generate aerosols under specific circumstances: endotracheal intubation, bronchoscopy, open suctioning, administration of nebulized treatment, manual ventilation before intubation, turning the patient to the prone position, disconnecting the patient from the ventilator, non-invasive positive-pressure ventilation, tracheostomy, and cardiopulmonary resuscitation (who, b) . as precautions to prevent such plausible airborne transmission of viruses, the who has recommended a myriad of management protocols (who, d). besides, healthcare workers are unwittingly exposed to infectious agents through person-toperson contact via respiratory droplets or aerosols and direct handling of contagious secretions (e.g., sputum, serum, blood, feces, etc.) of covid- patients. ong and his coworkers ( ) have studied the sources of covid- that could transmit the infection during the involvement in healthcare services. the results obtained from their study indicate that the samples collected from the personal protective equipment (ppe) worn by the hospital staff (physicians exiting the patient rooms) were negative for covid- . however, the samples from the air outlet exhaust fans in patient-rooms except corridors and anterooms have been reported as positive for covid- , indicating that the airborne transmission is plausible. sean and his co-workers ( ) corroborated that swabs taken from air exhaust outlets in a hospital room of a symptomatic patient of covid- in singapore tested positive, suggesting that small virus-laden aerosols have been displaced by airflows and deposited on equipment such as vents. however, there is no conclusive evidence as to how it is contaminated, and it is presumed that the aerosol particles may have got deposited in the vent. on february , , in inner mongolia of china, there has been a case of covid- reported positive when a person has passed the door of a symptomatic patient several times, giving evidence of the airborne transmission . the sars-cov- is often said to be transmitted through droplets generated when a symptomatic person coughs, sneezes, talks, or exhales (morawska and cao, ) . some of these droplets are too heavy to remain in the air, and rather fall on nearby floors or surfaces. fomites collect droplets contaminated with sars-cov- , and touching of such surfaces by a susceptible host would get infected. however, some droplets, when ejected from an infected person, convert to aerosol particles (also known as bioaerosols) with relatively smaller aerodynamic diameters and, consequently, become airborne (morawska, ) . such virusladen aerosol particles are capable of infecting people who inhale such particles, thereby spreading the disease. further, there have been several transport phenomena where larger droplets become smaller through evaporation so that such smaller particles are called droplet nuclei. such aerosol particles with the encapsulation of viruses could be termed as bioaerosols or droplet nuclei; hence, the term 'aerosol', 'bioaerosol', and 'droplet nuclei' is used in this paper interchangeably. the scenarios in respect of the generation of droplets and aerosol, particularly in the indoor environment, have not been adequately understood, and thus, insights into the plausible mechanisms are worthy of being explored. duguid ( ) , for the first time, has explored the characteristics of droplets and aerosol from human expiratory activities with chest infections, and such information is presented in table . duguid ( ) has observed that % of particles were often smaller than μm, and the majority were between - μm. the findings corroborated that breathing and exhalation originated from the nose have shed up to a few hundreds of droplets of which some were aerosols. in contrast, talking, coughing, and sneezing have produced more aerosols than droplets (table ) . on the contrary to what duguid ( ) has presented, a study conducted by with five healthy individuals has manifested that - % of particles from human expiratory activities were aerosols with the diameter being smaller than μm. the study also corroborated that the highest aerosol densities were generated during coughing and the lowest from nasal breathing, of which exhaled breath would be more responsible in transmitting the viruses (size of the order of . μm) when compared with transmitting the bacteria (> μm). it has been found that vomiting by a sars-cov infected person in the corridor of a hotel in hong kong in has contracted the disease on several people nearby by aerosol transmission (morawska, ) . the physicochemical processes affecting the fate of airborne aerosols constitute evaporation, interaction with other types of particles, transport, and removal from the air by deposition on solid surfaces (morawska, ) . particles in the air are often subjected to brownian motion, gravity, electrostatic forces, thermal gradients, electromagnetic radiation, turbulent diffusion, and inertial forces (baron and willeke, ) . of these mechanisms, the diffusion is a key mechanism of transmitting viruses with particles in the lower sub-micrometer range, together with other aerosol particles (baron and willeke, ) . for droplets larger than μm, gravity becomes significant than brownian motion in deciding the fate of such particles (cox, ) . under the standard atmospheric conditions, droplets smaller than μm often evaporate before reaching the ground, and the evaporated droplet residues linger in the air for prolonged periods (morawska, ) . when the droplets contain infectious bioaerosols, such as viruses, bioaerosols will remain in the air, even after the liquid content evaporates (morawska, ) . however, the time interval that a virus survives in the air varies from one type of bioaerosol to another type. droplets in the range of . - . μm lingering in the air are more likely to be retained in the respiratory tract and produce the infection (mccluskey et al., ) . however, droplets seem to be not present in the air for longer periods; instead, evaporation takes place, transforming droplets to bioaerosol residues, which could linger in the air for extended periods. hui and his co-workers ( ) have investigated that in different indoor environments, sars-cov could be transmitted through the airborne route. another retrospective study has found that the airborne transmission in an aircraft from an infected person to passengers located seven rows of seats ahead, indicating that the sars-cov virus could travel for a distance more than m of horizontally (olsen et al., ) . another case has been reported on infecting more than , persons in an apartment complex in hong kong because of aerosols generated by the building's sewage system (mckinney et al., ) . these observations manifest that the aerosol-laden sars-cov virus transmission is a phenomenon, which would impart greater havoc than one thinks, and precautionary measures are, therefore, of paramount importance. the sars-cov- virus has been found to remain viable in aerosols for three hours, while it, in the form of droplets, was more stable on plastic and stainless steel, copper, cardboard, and glass with durations detected up to , four, , and hours, respectively (van doremalen et al., ) . in comparison, the sars-cov virus was also found to be airborne in the form of aerosols for three hours, indicating that both sars viruses behave more or less in the same manner in the air. nevertheless, the sars-cov virus remains stable and viable in the form of droplets on plastic and stainless steel, copper, cardboard, and glass with durations (half-lives) lasting to , eight, eight, and hours, respectively (van doremalen et al., ) . the halflives of the sars-cov- and sars-cov were almost the same in aerosols, with median estimates of approximately . to . hours, indicating that both viruses have similar stability characteristics in transmitting through the air (van doremalen et al., ) . however, more profound epidemiological sustenance of sars-cov- virus may, therefore, be because of some other factors, including high viral loads in the upper respiratory tract and the capability of persons infected with covid- to shed and transmit the virus while remaining asymptomatic (bai et al., ; zou et al., ) . based on a study carried out by nicas and his co-workers in , it has been estimated that particles emitted from a cough of an infected person of a respiratory illness quickly decrease in diameter (with initial diameters of less than μm) mainly because of the water loss by approximately half of the initial volume, amounting to × − ml. exhaust ventilation, particle settling, die-off, and air disinfection methods are some prominent mechanisms by which the removal of viable airborne pathogens often takes place; each removal mechanism follows a first-order reduction rate . based on -hour viability of sars-cov- in the air (van doremalen et al., ; van doremalen et al., ) , prerequisites for the disease such as exposure, inhalation, and infection could occur minutes or a few hours later near and far from an aerosol source even in a stagnant environment (bourouiba, ) . the actual airborne times for droplets may be greater in an environment where there are significant cross-flows (who, ) . such scenarios could be expected in quarantine and healthcare centers (e.g., with doors opening, bed and equipment movement, and people walking back and forth, constantly). conversely, airborne durations for smaller droplet nuclei or aerosols may be profoundly shorter when they are subject to a significant downdraft (e.g., if they pass under a ceiling supply vent) (who, ) . when the flow of mucus or saliva ejects from an infected person, its trajectory is determined primarily by the size of droplets and airflow patterns that govern the paths of movement (tang et al., ) . the stokes' law describes the resultant trajectory of the droplets subjected to the forces of gravity downwards and air friction upwards, which governs the droplet movement in the air . coughs and sneezes usually constitute a turbulent cloud of buoyant gas with suspended droplets of various sizes. the larger droplets follow a ballistic trajectory irrespective of flow in the gas phase, whereas the aerosols are buoyant to a varying degree within the turbulent gas cloud (bourouiba et al., ) . in general, there exists an accepted notion of a -m safe exclusion zone to prevent possible droplet transmission from an infected person to a susceptible host; however, there are no comprehensive studies to support such a phenomenon. has supported the -m exclusion zone concept taking into account the evaporation-falling curve. has postulated that large droplets (> μm) will fall to the floor within a horizontal distance of m from the source. simple calculations, assumptions, and inadequate empirical data of wells's study have been later speculated by xie and his co-workers ( ) . xie and his coworkers ( ) have corroborated that for respiratory exhalation flows, the larger droplets (diameter between μm and μm) were, depending on the exhalation air velocity and relative humidity of the air, carried away for more than m of horizontal distance with the exhaled air having a velocity of m/s at the point of expiration (figure a ). such scenarios simulate sneezing events. conversely, larger droplets were found to carry for more than m afar at a velocity of m/s reordered at the point of exit, simulating coughing bouts ( figure b ). the same for exhaling events for which the velocity is at m/s was found to carry large droplets only up to about m of horizontally ( figure c ). other studies also have proven that when an infected person of a respiratory illness coughs or sneezes, a cloud of pathogenbearing droplets of different sizes appears to come out and travel even up to - m from the point of source (bourouiba et al., ; bourouiba et al., ) . moreover, recent experiments conducted after covid- contagion by bourouiba ( ) and loh and his co-workers ( ) have been in agreement with the findings of . xie and his co-workers ( ) have reported that pathogens bearing droplets of all sizes can travel for almost - m during sneezes and for more than m (maximum of . m) during coughs. incredibly, there have been contradicting insights on the distance to be maintained between healthcare workers and covid- infected patients [e.g., m (who, e) and m (cdc, b)]. however, most of the studies on the covid- virus mentioned above have been carried out in laboratories with expiration devices set on manikins; hence, no convincing information can be deduced. the most important environmental factors that could impact on the viability of airborne microorganisms are temperature, humidity, radiation (sunlight), and open-air (ventilation) (marthi, ) . the airborne microorganisms vary from large size fungal ( . - μm) and bacterial ( . - μm) aerosols to small size viral ( . - . μm) aerosols (morawska, ) . viruses in aerosols lose or gain the viability and infectivity because of environmental stresses caused by temperature, relative humidity, and sunlight before they reach a susceptible host. environmental tolerance of the viral-laden aerosols depends on the specific phenotype available, the composition of the bioaerosols containing virus and their payload, and physical characteristics in the surrounding environment . as the environmental factors play a major role in transmitting payloads of sars-cov- virus in different geographical locations of outdoor and indoor environments, it is worthy of exploring the effects of environmental factors on the transmission of sars-cov- virus. a retrospective study carried out in beijing and hong kong reports an inverse relationship between the numbers of daily sars-cov cases and daily minimum temperatures with a lagged effect of - days, while air pressure was found to be positively associated with transmission through the air for the data collected from april to may (bi et al., . another study underpins that when high payloads of transmissible gastroenteritis and mouse hepatitis viruses were emitted and deposited, they may have survived for days on surfaces at air temperatures ( °c) and relative humidity (< % or > %) typical of indoor environments . the sars-cov virus on smooth surfaces was found to retain its viability for over five days at temperatures of - °c and relative humidity of - %, which is typical of air-conditioned environments . however, virus viability has rapidly lost (> log ) at higher temperatures and higher relative humidity (e.g., °c, and relative humidity > %) . the higher stability of sars-cov coronavirus at low temperatures and low humidity environment may, therefore, facilitate its transmission faster in a community in the subtropical areas (such as hong kong) during the spring, and in air-conditioned environments . this study suggests evidence why some asian tropical countries (malaysia, indonesia, sri lanka, india, or thailand) with high temperature-and high relative humidity-environments did not have significant episodes of community outbreaks of sars-cov. a similar study has corroborated that there has been a significant negative correlation between the sars-cov cases and the environmental temperature seven days before the onset, and the seven-day time lag has corresponded well with the known incubation period for sars-cov (tan et al., ) . the optimum environmental temperature associated with the sars-cov cases has been in the range of - °c, which may have stimulated the virus growth (tan et al., ) . they have further reiterated that a sharp decrease or increase in the environmental temperature related to unexpected rapid spells of cold and warm days may have led to a rise in the sars-cov cases. such scenarios were because of the possible influence of the weather on the human immune system, indicating that there has been a higher possibility for sars-cov to reoccur in spring than that in autumn and winter. van doremalen and his co-workers ( ) have experimented the stability of mers-cov under different conditions ( °c and % relative humidity; °c and % relative humidity, and °c and % relative humidity) and found out that payloads of mers-cov were more stable and viable at low temperature/low humidity conditions even after hours. casanova and her co-workers in have investigated the effect of air temperature and relative humidity on the survival of coronaviruses in different solid surfaces. the findings of the study were analogous to the previous studies of coronaviruses in aerosols, which clearly stated that there was greater survival of virus at a low relative humidity ( %) than at high relative humidity ( %, % & %) (ijaz et al., ; kim et al., ) , and the viral survival was enhanced by lower air temperatures ( o c) ijaz et al., ) . further, the results of casanova and co-workers ( ) suggest that the relative humidity affects the inactivation of coronavirus than that by the air temperature that could prevail for any given season of the year. however, the interaction between the two factors (relative humidity and air temperature) on virus inactivation seems to be still questionable. in an indonesian study, the average daily ambient temperature prevailing in the period of january to march was significantly negatively correlated with covid- cases, while other components of weather such as minimum temperature, maximum temperature, relative humidity, and amount of rainfall had no significant correlations (tosepu et al., ) . another study on sars-cov has manifested that there was a synergistic effect of high temperature and high relative humidity on inactivation of the virus, whereas lower temperatures and low humidity enhance the survival of the virus and thus, induce the transmission . further, the same study has clearly stated that the showing that the slowest inactivation when exposed to low temperatures in the absence of ultraviolet light and different relative humidity (kormuth et al., ; lowen et al., ; mcdevitt et al., ; . similarly, the strong association of transmission rate of the influenza virus with environmental factors was observed during the winter season in temperate countries, in the rainy season, or where there were sudden seasonal changes in tropical countries (biswas et al., ; chowell et al., ; hemmes et al., ; . have investigated the effect of ambient temperature on covid- infection in cities, including wuhan, china, where the novel coronavirus was first discovered. the findings of their study have manifested that there was a positive association between ambient temperature (< o c) and the daily number of confirmed cases; hence, the temperature could be an essential factor in spreading the infection caused by sars-cov- virus. moreover, they have highlighted the fact that the sars-cov- virus may not perish itself without any public health interventions when the weather becomes warmer, and thus, there was no adequate evidence to confirm that the covid- cases could decline when the temperature increases. conversely, several studies carried out after covid- outbreak have clearly stated that there was a positive association between ambient daily average temperature and the number of covid- cases, where the number of covid- cases significantly decreased with increasing the temperature up to a comparatively lower value (around o c) wang m. et al., ) . however, they also lacked evidence to support the fact that the temperature affects the mortality of this virus. another investigation by ma and his co-workers ( ) manifests a positive relationship between diurnal temperature range and daily death counts of covid- in wuhan, china. a similar argument proposed by ma and his co-workers ( ) has been postulated by the studies of tan ( ) and park and co-workers ( ) for sars-cov and influenza viruses, respectively. a recent study has underpinned that absolute humidity was negatively associated with the daily death counts of covid- (ma et al., ) , which is similar to the study carried out by metz and finn ( ) for the influenza virus. metz and finn ( ) have reported that the absolute humidity significantly negatively correlated with the survival and transmission rate of the virus. lowen and his co-workers in have performed twenty experiments at relative humidity from % to %, and temperature from o c, o c, or o c, and the results indicated that both cold and dry conditions stimulate the transmission, which is, however, rare in tropics. lowen and his co-workers in have reported the lack of aerosol transmission at °c and at all humidity tested, indicating that there is no well-defined, recurrent influenza season affecting tropical and subtropical regions of the world. conversely, the transmission via the contact route was equally efficient at °c and °c. later, , using clausius-clapeyron relation converting relative humidity values into absolute humidity, have manifested that the seasonal cycle is consistent with a wintertime increase in influenza virus transmission and influenza virus survival, and supported the seasonality of influenza. conversely, a similar experiment conducted in the subtropical region has reported that there was no strong correlation between absolute humidity and airborne transmission of the virus, but other environmental factors such as temperature and relative humidity (tang et al., ) . the sunlight significantly negatively affects the survival and infectivity of various microorganisms, including viruses (nelson et al., ; rzeżutka and cook, ; tang, ; qiao et al., ) . the studies of and schuit and his coworkers ( ) have investigated the impact of natural and simulated sunlight on inactivation of influenza virus in liquid suspensions and aerosols, respectively. a significant loss of infectivity was observed under simulated sunlight at a range of relative humidity levels ( %, %); hence, aerosols containing the virus are more likely to transmit at night, indoor or reduced sunlight conditions than they do under direct sunlight . coronaviruses have high sensitivity to natural or simulated sunlight since they possess singlestranded nucleic acids, and are unable to repair the damage in the absence of complementary strand (tseng and li, ; who, ) . by considering this intrinsic characteristic of coronaviruses, several studies have been successfully conducted to decay the viability of the virus using natural sunlight and uv radiation (karapiperis et al., ) . duan and his colleagues ( ) have observed that the sars-cov virus lost its viability after minutes of exposure to > w/cm of uv-c light at a distance of cm. however, in a similar study of darnell and his colleagues ( ) found that the efficiency of inactivation was quite high, with the inactivation time being minutes under high intensity of uv-c light (> w/cm ) at a closer distance (< cm), while there was no effect of uv-a light on the inactivation. for natural ventilation, minimum hourly averaged ventilation rates of l/s/patient for airborne precaution rooms, l/s/patient for general wards and outpatient departments, and . l/s/m for corridors and other transient spaces without a fixed number of patients need to be provided (who, ). an airborne precaution room is defined to be a room with > air changes per hour (ach) (e.g., equivalent to > l/s for a m -room) and must have controlled direction of airflow (aia, ; mayhall, ; who, ) . a mechanically ventilated room is often provided to an airborne infection isolation room and should have a negative pressure of > . pa, an airflow having a difference between the exhaust to supply > cfm ( l/s), clean-to-dirty airflow, > ach for a new building, and > ach in existing buildings for an old building, and exhaust to the outside, or a hepa-filter if room air is recirculated (cdc, ) . the transmission of droplets and aerosols has significant implications on healthcare workers and caretakers managing patients infected with covid- , and providing appropriate personal protective equipment (ppe) is, therefore, of utmost importance. the facemasks play a major role in preventing both droplets and aerosols from transmitting the disease from an infected person to a host. facemasks are popular in controlling and preventing virus transmission, especially in connection with severe respiratory syndromes such as sars-cov, mers-cov, and covid- , since the absence of any vaccination or specific anti-infective treatments (long et al., ) . the surgical mask, n respirator, and elastomeric respirator have been popular among many countries with a different degree of success against the covid- virus. besides, with greater demand for masks in many countries, more sophisticated masks have been experimented by various researchers (balachandar et al., ; leung and sun, ) . surgical masks and n respirators are very popular and ubiquitous among millions of people worldwide as the ppe for covid- , but surgical masks are believed to be not preventing aerosol transmission, and n respirators are recognized to be preventing aerosol and droplet transmission (derrick and gomersall, ; leung et al., ; sandaradura et al., ) . the live influenza virus in the air from, in front, and behind all surgical masks have been tested, and the results indicate that a surgical mask will reduce the exposure to aerosolized infectious influenza virus (average -fold), depending on the design of the mask (booth et al., ) . another study on masks has manifested that when applied to outpatient healthcare personnel, there was no significant difference in the performances between n respirators and medical masks for the incidence of laboratory-confirmed influenza (radonovich et al., ) . long and his co-workers ( ) have corroborated that the use of n respirators compared with surgical masks was not associated with a lower risk of laboratory-confirmed influenza. this study pronounced that n respirators were not necessary for the general public and non-high risk medical staff those who were not in close contact with influenza patients or suspected patients (long et al., ) . unresolved dichotomy on the route of transmission by virus-laden droplets and aerosols suggested that the use of respirators for healthcare workers against sars was much advisable than conventional surgical masks that were ineffective against aerosols . with the unexpected escalation of the covid- cases worldwide, there has been a dearth in supply of masks, and consequently, the center for disease control and prevention, usa, has modified its guidelines on masks with the inclusion of homemade cloth or fabric masks to be worn in public areas. use of masks can be -fold: control the penetration of droplets from an infectious person into the respiratory tract of a susceptible host, and control the droplets going out from an infected patient. nevertheless, the effectiveness of the use of masks for the control of sars-cov- -laden aerosol transmission from an infected person to a susceptible host is uncertain and not fully conceivable. it has been a known fact that different commercial masks have different efficiencies in controlling the transmission of infectious agents. in general, n respirators are provided to prevent users from inhaling small airborne particles (aerosols) and need to fit tightly to the user's face. surgical masks are often used to protect people from larger droplets transmission and fit loosely to the user's face (lawrence et al., ; zhiqing et al., ) . complying with european standard en : , three different types of disposable particulate respirators known as filtering facepiece (ffp ), ffp , and ffp have been in use for controlling sars-cov- . the ffp refers to the least filtering of the three masks with an aerosol filtration of at least % and leakage to the inside of a maximum of %. this mask is mainly used as a dust mask. the ffp masks have a minimum of % filtration and a maximum of % leakage to the inside. healthcare professionals often wear them against influenza viruses, believing that they guard against aerosol transmission. the ffp masks are also used for protection against the sars-cov- . the ffp masks are the best in filtering particles and are recommended against the contraction of sars-cov- . with a minimum filtration of % and a maximum % leakage to the inside, the ffp masks protect the susceptible host against the contraction of the disease caused by very fine particles such as viral-laden aerosols from an infected person. another study comparing the efficiency of homemade masks, surgical masks, and standard ffp masks has corroborated that surgical masks provided about twice as much protection as homemade masks (van der sande et al., ) . the ffp masks were observed to provide adults with about times as much protection as homemade masks, and times compared to surgical masks (van der sande et al., ) . similarly, another study has elaborated that a surgical mask (that filtered % of viral particles) was about three times better in controlling the viral transmission than that of a homemade mask made of a tee-shirt and cotton towel (davies et al., ) . davies and his co-workers ( ) have further iterated that a homemade mask should only be considered as a last resort to prevent droplet transmission from infected individuals, but with limited success. elastomeric respirators serve as an alternative to disposable n respirator use in healthcare, as both have similar efficiencies in filtering sars-cov- . the primary advantage of elastomeric respirators is the reuse potential with proper cleaning. leung and his co-workers ( ) have carried out experiments in developing a novel charged pvdf nanofiber filter to capture aerosol particles effectively. leakage of droplets and a cloud of aerosols could be expected (figure c and d). none of these masks is guaranteed to cut off sars-cov- ; hence, social distancing is vital to be adopted, especially in the indoor environment. with the onset of the covid- pandemic, many researchers have been in the development of effective filtering mechanisms to combat sars-cov- -laden aerosol transmission; however, until early may , there have been no promising ppe developed to curtail such transmission. in the meantime, it is imperative to explore situations where an infected patient coughs without any mask worn, and a susceptible host inhales the resultant plume of droplets and aerosols with different masks worn at a distance of m ( figure ). as shown in figure a , the host without a mask worn receives a considerable payload of viruses so that it is very likely that he gets infected. however, with a surgical mask worn, he may, during inhalation, filter in - % of the payload of viruses with a lower propensity of getting infected ( figure b ). such a payload may have more than a couple of hundreds of sars-cov- , which is believed to be adequate to instill the covid- among exposed people. the host wearing n or reusable elastomeric respirator may not receive in more than %, which may, however, constitute more than a few hundreds of payloads of the virus (figure c and d). the probability of getting infected under such a scenario is still positive, although it is very minute. none of these masks is, however, guaranteed against sars-cov- . many people are reported to contract the covid- in confined spaces. thus, it is worthwhile to describe how such phenomena help intensify the mass occurrence of the covid- in different confined spaces under varying microclimatic conditions. in this respect, three confined spaces such as inside the cabin of an airplane, interior space of a car, and common dormitory-type space of a healthcare or isolation center were selected. since over two billion people travel on commercial flights each year (silverman and gendreau, ) , the behavior of sars-cov- in the cabin is paramount to be understood. air travelers spend extended periods in enclosed spaces, even for more than hours, which usually facilitates a conducive environment for the spread of infectious diseases. extensive aerodynamic modeling has been performed to get an insight into how the buoyant jet of coughing by an infected person of a respiratory illness spreads in the cabin of a flight (redrow et al., ; yang et al., ) . the hypothesis on the most affected zones within the cabin is, therefore, highlighted below. the cabin of a flight is usually provided with airflow from cabin air outlets and individual outlets located in the overhead compartment that runs the length of the cabin (figure ) . a sheet of airflow typically in the form of a jet with lower temperatures (< °c) is projected down, and finds its way towards the bottom of the cabin (return air grills located on the sidewalls) from which it goes to the underfloor area ( figure ). however, looking at a more detailed picture, there are two typical airflow fields developed ( figure a ). the first zone called the jet zone, established in the upper deck areas of the cabin, is characterized in terms of large-scale circulations, while the collision zone found in the middle and lower floor area is characterized by interactions of two lateral jets (li et al., ) ( figure a ). in general, about . - . l/s of air per passenger is provided, of which half of the volume is the filtered and recirculated air, and the other half is outside air (bagshaw and lllig, ). such an arrangement brings in a complete cabin air exchange every two to three minutes ( to air changes per hour (ach)) (bagshaw and lllig, ). the high air exchange rate controls the temperature gradients, prevents stagnant cold areas, maintains air quality, and dissipates payloads of viral-laden droplets and aerosols. in a typical aircraft, the recirculated air is passed through high-efficiency particulate air (hepa) filters, with which in excess of . % of particles characterized by aero-diameter of . μm could be removed from the ingress of cabin air. exhaled droplets and aerosols from passengers and crew often increase the humidity to an average of - %, which is below the % normally accepted as comfort level (de ree et al., ) . in the flight cabins, because of the densely packed environment, the cough-jet released by a sars-cov- infected person is expected to break the local airflow, particularly the jet zone, and travels both forward and backward directions in the proximity of the point of exit ( figure b ). since the velocity of exiting the violent expiration (coughs) is around m/s, the droplets may travel four to five seats ahead, and the aerosol-cloud could go even further away ( figure b ). however, there is no lateral movement expected except the immediate passenger on either side. in contrast to the forward movement, there is a backward movement of droplets typically by one seat, but the aerosol movement may be more. this phenomenon illustrates that about five to ten people could get infected with the disease with an infected person onboard. nevertheless, the propensity of getting sick by exposure to a plume of aerosols produced by cough-jet is poorly understood, and the actual number of contracted cases may be far from recorded. the brownian motion followed by airflow jet movement governs the aerosol plume, after the dissipation of advective transport. such movement supports an agglomeration of viral-laden aerosols in fomites at passenger levels. it is, therefore, crucial to decide by all airlines that such suspicious fomites such as papers, magazines, pillows, and blankets be disposed of perhaps subjected to thermal destruction until the covid- pandemic recedes. figure c illustrates how the cough-jet trajectory travels with the patient equipped with a surgical mask. with the surgical mask worn, the droplets are meant to travel up to one-two seats forward, and one seat backward. such phenomena maybe because of the jet coming out from either side of the mask, as the mask is not tight enough on both sides. nevertheless, the aerosol cloud will travel far from two seats front and one seat behind by the brownian motion coupled with the airflow trajectories of the cabin. the streamlines of airflow are usually directed downward so that there will be a contribution of viral-laden aerosols back to the people on board. the illustration in figure d is more or less the same as that of c, with the exception that both droplets and aerosols do not travel far. with the n mask worn, an infected patient sheds droplets forward and backward by one seat and more than one seat for aerosols. the behavior of viral-laden aerosols resulted from a cough-jet has not yet been aerodynamically modeled with reasonable accuracy; hence, the actual level of impact that a single cough-jet envisages could not be simulated well. however, there exists evidence to showcase a profound risk of covid- being spread in an aircraft when a symptomatic or even asymptomatic patient is on board. further, the environmental factors such as moderately low relative humidity ( %), low temperature (< °c), and moderate ach (< per hour) would set the platform for the sars-cov- to sustain for extended periods within the cabin. strict guidelines for the minimization of such pandemic events are, therefore, paramount. international organization of motor vehicle manufacturers (oica) has estimated that over billion passenger cars travel on roads by worldwide, indicating that one out of seven people of the world has a passenger car. when the world is open back to normalcy by lifting the present state of lockdown, people will resort to traveling by passenger cars, and consequently, there will be a propensity of spreading the covid- unless precautions are taken. we, therefore, bring in a hypothesis to illustrate the best possible ways of preventing the covid- from spreading while traveling in a passenger car. a crucial attribute that supports the spread of covid- is the interior ventilation rate in the passenger vehicle, usually expressed in ach, which depends on the vehicular speed, ventilation setting and window positions (ott et al., ) . engelmann and his co-workers ( ) have estimated that with the air-conditioning (ac) system off, the ach for a stationary vehicle was in the range of . - . per hour. with the ac on, ach was between . - . per hour, and with the ac off and the fans on, it varied in the range of . - . per hour. park and others ( ) , with the windows closed and no mechanical ventilation, have reported the ach between . and . per hour, and with the ventilation set on recirculation, between . and . per hour. with the windows closed and the fan set on fresh air, the ach was between . and . per hour, and with windows open, but no mechanical ventilation, the ach ranged from . to . per hour (park et al., ) . offermann and others ( ) have measured the ach by letting the vehicle move with an average speed of km/hour and have found that with the window open and the ventilation system off, an ach of per hour, with the ventilation system on and the windows closed, per hour, and when the ventilation system was turned off, . per hour. following the study done by khatoon and kim ( ) , a typical pattern of velocity streamlines inside the vehicular cabin with a moderate level of ach assigned to a vehicle moving at a moderate speed under conditions of "ac on and windows closed" is shown in figure a . figure a illustrates that cooled air travels to the back seats and returns towards the front on either side at a lower level. under such circumstances, an infected person sitting in the back seat may cough and the resultant cough-jet in the form of droplets and a plume of aerosols (with an average speed of m/s; relative humidity < %; temperature < °c; ach < per hour) spreads towards the front seat, and the plume of aerosols may drop the advective transport phenomena with lower velocities and get carried away with existing velocity streamlines once again towards the back seats ( figure b ). such phenomena may expose all passengers in the vehicle, and the risk of contracting the disease seems to be high. two such cases have been reported in sri lanka, where an infected passenger had traveled sitting at the back seat in a rented car for a period not greater than one hour with ac on and windows closed, and the driver was subsequently reported to have got infected of the covid- . the other case was reported that a person had accompanied one of his siblings (an asymptomatic person) in his car with ac on and windows closed for more than minutes. such situations seem to be somewhat controlled when the infected person wears a surgical mask. however, the risk factor remains the same, as loose ends of the mask shed both droplets and aerosols, although the expiration from the front of the mask is substantially reduced (figure c ). conversely, when the infected passenger is equipped with an n respirator, under the same conditions, a minute payload of droplets and a faint cloud of aerosols may come out (figure d ). however, because of the circulation within the cabin, one cannot rule out that there is no element of risk. thus, a hypothesis could be built speculating that traveling in a passenger vehicle with people aboard under conditions of ac on and window closed, has a discernible risk factor of getting susceptible hosts infected, though masks are worn. when a passenger car moves at a certain speed with windows open, the velocity streamlines are generated from front and rear windows, and finally, sweeping the passengers aboard, they exit the cabin from the rear windows (figure a ). such transport-phenomena are simulated using computational fluid dynamics, but detailed information on the behavior of streamlines under different environmental settings is poorly investigated. in the case of passenger cars with windows open, different behaviors could be expected depending on the environmental settings prevailing in different geographical regions. in other words, the environmental settings for temperate climates such as east asia, europe, and north america (relative humidity < %; temperature < °c; ach > per hour) and tropical climates, including south east asia, africa, and south america (relative humidity > %; temperature > °c; ach > per hour) could be expected. the studies done on the sustenance of sars-cov- have manifested that there may be a better chance for the viral-laden cough-jets to sustain in temperate climates than tropical climates, as the daily mortality of covid- has been positively associated with diurnal temperature range, but negatively with the absolute humidity (ma et al., ). when the car moves at higher speeds (> km/h) with the same environmental settings, the droplets do not travel far and confined to a limited space (even not beyond the driver's seat), but the cloud of aerosol will drift far and finally exits from the rear windows. the explanations given in this paper restrict the analysis only for the case where the speed is less than km/h, as such speeds become the worse scenario for the sustenance of the sars-cov- virus. the cabin environment becomes much improved when the infected person wears a surgical mask while traveling (figure c ). there seems that only a minimal payload of droplets being shed from the front, but considerable load may come from either side of the mask, as the surgical mask is usually loosely fitted to the face. conversely, the aerosol cloud may still travel to the front area of the cabin and returns with the airflow stream coming from outside the vehicle. nevertheless, the cabin airflow streamlines drive such viral-laden plume out of the cabin in seconds. the cabin environment is further improved when the infected person wears an n respirator ( figure d ). still, one has to admit the fact that there is an element of risk for susceptible hosts to get infected. when two scenarios (scenario : ac on and windows closed; scenario : ac off and windows opened) are critically reviewed, one can speculate that the scenario will be better in controlling the sars-cov- virus; hence strongly recommended at least until the covid- pandemic ceases. for example, the index patient of covid- in sri lanka was a tour guide, and when he became symptomatic, he traveled to the hospital by his car driven by his son, with his wife sitting in the front seat. he made it a point to open all windows and sat behind until they reached the hospital. the traveling time was more than minutes, and no person in the car was infected with the covid- . this story epitomizes the rationale postulated above, and the relevant authorities of affected countries should come out with strict guidelines to get such best practices implemented for reduced morbidities and mortalities. conversely, two cases were reported in sri lanka, where drivers of rental cars got infected with scenario . besides, letting the car park under direct sunlight with windows open for at least minutes would be a better option to eradicate the potential payloads of the sars-cov- virus from the cabins of passenger cars. it would be imperative to explore the plausible factors of transmitting sars-cov- virus within indoor spaces, preferably makeshift hospitals, and healthcare, quarantine and isolation centers where accommodation facilities have large open spaces with many beds laid in a sequence. such a facility is, in this paper, described in respect of a healthcare center, but could be applicable for other indoor spaces mentioned above. it is a known fact that the sars diseases became epidemic and sometimes pandemic, forcing the authorities seek isolation facilities beyond their usual capacities available. such gestures invariably drive the authorities to build appropriate healthcare centers or convert other existing facilities in a short period. such spaces often become large floor areas whose ventilation facilities maybe poor in cleaning the viral-laden airborne plumes. the transmission of sars diseases in an epidemic or pandemic situation is usually -fold. the first being the non-nosocomial transmission by which suspected patients from outside will be brought into the healthcare center. in addition, with time, susceptible hosts residing at healthcare centers will contract the disease through nosocomial transmission unless the ventilation facilities (> ach or . l/s/ m , negative pressure difference > . pa, and the airflow difference > l/s) are adequate (who, ). the differentiation of both these transmission modes for a given situation is, however, a daunting task and extremely difficult (bi et al., ) . in a confined space of a healthcare center, appropriate management of non-nosocomial transmission should be implemented to control the onset of nosocomial transmission, where ventilation methods play a vital role. given the fact that inadequate ventilation prevails in a confined space, another classification indicates that -fold transmission types are distinguished; short-range (between individuals, generally less than -m apart) and longrange (within a room, between rooms or between distant locations, generally greater than -m distances) (tang et al., ) . expiration of cough-jets of an infected person composed of droplets and aerosols enters and mixes with air in the breathing zone of a susceptible host standing nearby (e.g., medical staff), which is capable of contracting the disease (short-range transmission) between individuals may interact to infect one another. in the meantime, cough-jet travels long distances depending on the airflow pattern of the space through the aerosol plume (long-range transmission) contracting people a couple of meters away from the infected person. the airflow in the confined space is often governed by a combination of differences in temperatures and humidity. figure (figure b ). such aerosol plume developed could follow the airflow trajectories, which are often altered by moving objects, opening and closing of doors and windows, and temperature and humidity variations. besides, a certain fraction of the viral-laden aerosols will diffuse towards lateral directions by brownian motion resulting in nosocomial transmission to many susceptible hosts in the same confined room (not shown in figure b ). these aerosol-generating plumes cause long-range transmission within the confined space, contracting many susceptible hosts far more than one could imagine. figure c shows the cough-jet trajectory with the infected patient wearing a surgical mask. with the surgical mask worn, the payload of droplets from the infected patient reduces drastically and restricted to a small distance. the neighboring people on either side may not be exposed to direct contamination, but they could contract the disease by touching fomitesladen viruses. however, viral-laden aerosols will travel forward and disappear via convective and diffusion processes. such transport phenomena may carry the disease-causing viral loads, promoting nosocomial infection. a similar scenario is observed with a patient wearing an n respirator, but to a lesser extent compared to that of a surgical mask (figure d reports that as of april , , in a naval complex in colombo, there have been more than sailors contracted with the covid- . the sailors have been on duty in cordoning off of potential areas of covid- pandemic. however, it has been brought to the notice that when they returned to the base, many of them have stayed in confined areas whose ventilation potential driven by mechanical fans was rather poor. this scenario has been a classic example of the nosocomial infection caused by poor ventilation that has promoted the viral-laden aerosol plume to linger for many hours inside the building. taking all case studies mentioned above into consideration, one cannot simply ignore that both droplet and aerosol laden transmissions of covid- are uncertain; hence administrative, clinical, and physical best management practices are paramount in implementing, especially in confined spaces. researchers have speculated that both droplets and aerosols generated from non-violent and violent expirations of sars-cov- -infected people may be responsible for the nonnosocomial and nosocomial transmission of covid- disease. however, more research work should be conducted to understand the behavior of viral-laden droplets and aerosols in different environmental settings, especially confined spaces so that the transmission of covid- pandemic in the built environment could be fully ascertained. the case studies found worldwide indicate that the behavior of the sars-cov- virus has been unprecedentedly unique with more survival and viable rates in the air and believed to linger in the air for an extended period. the challenge before many healthcare workers in combatting the disease would be a daunting task unless proper administrative, clinical, and physical measures are taken within the healthcare settings. inter-disciplinary research on the behavior of the sars-cov- virus needs to be conducted to prevent covid- disease from spreading worldwide. mahesh jayaweera: conceptualization, methodology, investigation, writing -original draft, visualization, supervision, project administration. hasini perera: conceptualization, methodology, resources, validation, formal analysis, investigation, data curation, writingoriginal draft. buddhika gunawardana: validation, resources, writing -review and editing. jagath manatunge: validation, resources, writing -review and editing. the authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. authors wish to acknowledge the assistance rendered by many in collating information on covid- case studies. this research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. bagshaw negative pressure of > . pa, an airflow having a difference between the exhaust to supply > cfm ( l/s), clean-to-dirty airflow, > ach for a new building, and > ach in existing buildings for an old building, and exhaust to the outside, or a hepa-filter if room air is recirculated the authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. coronavirus (sars-cov- ) and asseverated to be transmitted from human-to-human by multiple means, namely, by droplets, aerosols, and fomites (wang and du, ). it has been more than days that covid- , later declared as a pandemic and highly contagious, was first reported. as of may , , there have been more than . million confirmed cases and , deaths by the covid- disease worldwide (who, a). covid- infection triggers severe acute respiratory illness, with fever, cough, myalgia, and fatigue as common symptoms at the onset of illness judson and munster, ; . respiratory particles may often be distinguished to be droplets or aerosols based on the particle size and specifically in terms of the aerodynamic diameter . one could dispute that, unlike larger droplets, aerosols may pose a greater risk of the spread of the covid- disease among many susceptible hosts positioned far from the point of origin. nevertheless, it has been proven that viral disease outbreaks via aerosol transmission are not as severe as one would think, because of dilution and inactivation of viruses that linger for extended periods in the air . there has been no discernable evidence on the minimum infectious viral load for covid- pandemic, but many researchers speculate that a few hundreds of sars-cov- virus would be enough to cause the disease among susceptible hosts (beggs, ; smc, ). there have been numerous disagreements on the average particle size of droplets and aerosols . the world health organization (who) and centers for disease control and prevention (cdc) postulate that the particles of more than μm as droplets, and those less than μm as aerosols or droplet nuclei who, ) . brankston et al., ; tellier, ) . it is a well-known fact that covid- is transmitted by human-to-human contact; hence, contagious. one of the predominant mechanisms for covid- to be contagious is self- provinces, and about % of positive cases for covid- have been observed with the transmission through feces . further, they also highlighted the fact that covid- could be transmitted via fecal routes after they detected the live infectious agents of covid- in patients' stools . contrary to what has been stated above, the who, at early hours of manifestation of covid- , has denounced that there was besides, healthcare workers are unwittingly exposed to infectious agents through person-to- giving evidence of the airborne transmission . the sars-cov- is often said to be transmitted through droplets generated when a symptomatic person coughs, sneezes, talks, or exhales (morawska and cao, ) . some of these droplets are too heavy to remain in the air, and rather fall on nearby floors or surfaces. fomites collect droplets contaminated with sars-cov- , and touching of such surfaces by a susceptible host would get infected. however, some droplets, when ejected from an infected person, convert to aerosol particles (also known as bioaerosols) with relatively smaller aerodynamic diameters and, consequently, become airborne (morawska, ) . such virus- table . duguid ( ) has observed that % of particles were often smaller than μm, and the majority were between - μm. the findings corroborated that breathing and exhalation originated from the nose have shed up to a few hundreds of droplets of which some were aerosols. in contrast, talking, coughing, and sneezing have produced more aerosols than droplets (table ) . on the contrary to what duguid ( ) has presented, a study conducted by papineni and rosenthal ( ) with five healthy individuals has manifested that - % of particles from human expiratory activities were aerosols with the diameter being smaller than μm. the study also corroborated that the highest aerosol densities were generated during coughing and the lowest from nasal breathing, of which exhaled breath would be more responsible in by aerosol transmission (morawska, ) . the physicochemical processes affecting the fate of airborne aerosols constitute evaporation, interaction with other types of particles, transport, and removal from the air by deposition on solid surfaces (morawska, ) . particles in the air are often subjected to brownian motion, gravity, electrostatic forces, thermal gradients, electromagnetic radiation, turbulent diffusion, , ) . for droplets larger than μm, gravity becomes significant than brownian motion in deciding the fate of such particles (cox, ) . under the standard atmospheric conditions, droplets smaller than μm often evaporate before reaching the ground, and the evaporated droplet residues linger in the air for prolonged periods (morawska, ) . when the droplets contain infectious bioaerosols, such as viruses, bioaerosols will remain in the air, even after the liquid content evaporates (morawska, ) . approximately half of the initial volume, amounting to × − ml. exhaust ventilation, particle settling, die-off, and air disinfection methods are some prominent mechanisms by which the removal of viable airborne pathogens often takes place; each removal mechanism follows a first-order reduction rate . based on -hour viability of sars- cov- in the air (van doremalen et al., ) , prerequisites for the disease such as exposure, inhalation, and infection could occur minutes or a few hours later near and far from an aerosol source even in a stagnant environment (bourouiba, ) . and airflow patterns that govern the paths of movement (tang et al., ) . the stokes' law describes the resultant trajectory of the droplets subjected to the forces of gravity downwards and air friction upwards, which governs the droplet movement in the air . coughs and sneezes usually constitute a turbulent cloud of buoyant gas with suspended droplets of various sizes. the larger droplets follow a ballistic trajectory irrespective of flow in the gas phase, whereas the aerosols are buoyant to a varying degree within the turbulent gas cloud (bourouiba et al., ) . masks are believed to be not preventing aerosol transmission, and n respirators are recognized to be preventing aerosol and droplet transmission (derrick and gomersall, ; surgical mask (that filtered % of viral particles) was about three times better in controlling the viral transmission than that of a homemade mask made of a tee-shirt and cotton towel (davies et al., ) . davies and his co-workers ( ) in the meantime, it is imperative to explore situations where an infected patient coughs without any mask worn, and a susceptible host inhales the resultant plume of droplets and aerosols with different masks worn at a distance of m ( figure ). as shown in figure a , the host without a mask worn receives a considerable payload of viruses so that it is very aerodynamic modeling has been performed to get an insight into how the buoyant jet of coughing by an infected person of a respiratory illness spreads in the cabin of a flight (redrow et al., ; . the hypothesis on the most affected zones within the cabin is, therefore, highlighted below. would set the platform for the sars-cov- to sustain for extended periods within the cabin. strict guidelines for the minimization of such pandemic events are, therefore, paramount. (park et al., ) . offermann and others ( ) distinguished; short-range (between individuals, generally less than -m apart) and long- range (within a room, between rooms or between distant locations, generally greater than -m distances) (tang et al., ) . expiration of cough-jets of an infected person composed of droplets and aerosols enters and mixes with air in the breathing zone of a susceptible host standing nearby (e.g., medical staff), which is capable of contracting the disease (short-range transmission) between individuals may interact to infect one another. in the meantime, transmission to many susceptible hosts in the same confined room (not shown in figure b ). these aerosol-generating plumes cause long-range transmission within the confined space, contracting many susceptible hosts far more than one could imagine. figure c shows the cough-jet trajectory with the infected patient wearing a surgical mask. with the surgical mask worn, the payload of droplets from the infected patient reduces drastically and restricted to a small distance. the neighboring people on either side may not be exposed to direct contamination, but they could contract the disease by touching fomites- laden viruses. however, viral-laden aerosols will travel forward and disappear via convective and diffusion processes. such transport phenomena may carry the disease-causing viral loads, promoting nosocomial infection. a similar scenario is observed with a patient wearing an n respirator, but to a lesser extent compared to that of a surgical mask (figure d ). the tang, j.w., lai, f.y.l., wong, f., hon, k.l.e., . incidence of common respiratory viral turbulent gas clouds and respiratory pathogen emissions: potential implications for reducing transmission of covid- violent respiratory events: on coughing and sneezing transmission of influenza a in human beings active monitoring of persons exposed to patients with confirmed covid- -united states effects of air temperature and relative 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shelters in accidental releases of toxic materials hospital infection control practices advisory committee severe acute respiratory syndrome-related coronavirus-the species and its viruses, a statement of the coronavirus study group the role of particle size in aerosolised pathogen transmission: a review detection of airborne respiratory syncytial virus in a pediatric acute care clinic airborne micro-organisms: survival tests with four viruses virus survival as a seasonal factor in influenza and poliomyelitis aerosol technology: properties, behavior, and measurement of air borne particles clinical features of patients infected with novel coronavirus in wuhan severe acute respiratory syndrome and coronavirus survival characteristics of airborne human coronavirus e nosocomial transmission of emerging viruses via aerosolgenerating medical procedures assessment for the seasonality of covid- should focus on ultraviolet radiation and not 'warmer days'. ltte, v thermal comfort in the passenger compartment using a -d numerical analysis and comparison with fanger's comfort models. energies, , effects of humidity and other factors on the generation and sampling of a coronavirus aerosol influenza virus infectivity is retained in aerosols and droplets independent of relative humidity detection of airborne cytomegalovirus in hospital rooms of immuno-compromised patients aerosol susceptibility of influenza virus to uv-c light environmental transmission of sars at amoy gardens influenza and humidity -why a bit more damp may be good for you! droplet fate in indoor environments, or can we prevent the spread of infection? indoor air airborne transmission of sars-cov- : the world should face the reality sunlight-mediated inactivation of health-relevant microorganisms in water: a review of mechanisms and modeling approaches toward understanding the risk of secondary airborne infection: emission of respirable pathogens exposure to environmental tobacco smoke in an automobile 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transmission of infectious agents in healthcare settings medical issues associated with commercial flights exposure to light as a source of error in the estimation of the infectivity of virus suspensions stability of middle east respiratory syndrome coronavirus (mers-cov) under different environmental conditions influenza in tropical regions covid- may transmit through aerosol temperature significant change covid- transmission in cities detection of sars-cov- in different types of clinical specimens on air-borne infection: study ii. droplets and droplet nuclei prevention and control of nosocomial infections managing sars amidst uncertainty world health organization (who) infection prevention and control of epidemic-and pandemic-prone acute respiratory diseases in health care -who interim guidelines natural ventilation for infection control in healthcare settings infection prevention and control of epidemic and pandemic prone acute respiratory infections in healthcare -who guidelines 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procedures association between ambient temperature and covid- infection in cities from china sars-cov- viral load in upper respiratory specimens of infected patients active monitoring of persons exposed to patients with confirmed covid- -united states effects of air temperature and relative humidity on coronavirus survival on surfaces guidelines for environmental infection control in health-care facilities covid- ): how covid- spreads travelers from countries with widespread sustained (ongoing) transmission arriving in the united states a familial cluster of pneumonia associated with the novel coronavirus indicating person-to-person transmission: a study of a family cluster the effects of temperature and relative humidity on the viability of the sars coronavirus modeling ambient temperature and relative humidity sensitivity of respiratory droplets and their role in determining growth rate of covid- outbreaks makeshift hospitals for covid- patients: where health-care workers and patients need sufficient ventilation for more protection clinical characteristics and intrauterine vertical transmission potential of covid- infection in nine pregnant women: a retrospective review of medical records the influence of climatic conditions on the transmission dynamics of the a/h n influenza pandemic in chile physical aspects of bioaerosols particles inactivation of the coronavirus that induces severe acute respiratory syndrome, sars-cov testing the efficacy of homemade masks: would they protect in an influenza pandemic ozone and relative humidity in airliner cabins on polar routes: measurements and physical symptoms air quality and comfort in airliner cabins protecting healthcare staff from severe acute respiratory syndrome: filtration capacity of multiple surgical masks stability of sars coronavirus in human specimens and environment and its sensitivity to heating and uv irradiation the numbers and the sites of origin of the droplets expelled during expiratory activities the effectiveness of stationary automobiles as shelters in accidental releases of toxic materials hospital infection control practices advisory committee severe acute respiratory syndrome-related coronavirus-the species and its viruses, a statement of the coronavirus study group the role of particle size in aerosolised pathogen transmission: a review detection of airborne respiratory syncytial virus in a pediatric acute care clinic effect of ambient temperature on covid- infection rate. available at ssrn airborne micro-organisms: survival tests with four viruses virus survival as a seasonal factor in influenza and poliomyelitis aerosol technology: properties, behavior, and measurement of air borne particles severe acute respiratory syndrome and coronavirus sunlight-mediated inactivation of health-relevant microorganisms in water: a review of mechanisms and modeling approaches toward understanding the risk of secondary airborne infection: emission of respirable pathogens exposure to 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the estimation of the infectivity of virus suspensions effects of temperature on covid- transmission. medrxiv an initial investigation of the association between the sars outbreak and weather: with the view of the environmental temperature and its variation the effect of environmental parameters on the survival of airborne infectious agents correlation between weather and covid- pandemic in jakarta inactivation of viruses on surfaces by ultraviolet germicidal irradiation professional and home-made face masks reduce exposure to respiratory infections among the general population aerosol and surface stability of sars-cov- as compared with sars-cov stability of middle east respiratory syndrome coronavirus (mers-cov) under different environmental conditions influenza in tropical regions covid- may transmit through aerosol high temperature and high humidity reduce the transmission of covid- temperature significant change covid- transmission in cities cov- in different types of clinical specimens on air-borne infection: study ii. droplets and droplet nuclei prevention and control of nosocomial infections managing sars amidst uncertainty world health organization (who) infection prevention and control of epidemic-and pandemic-prone acute respiratory diseases in health care -who interim guidelines natural ventilation for infection control in health- care settings infection prevention and control of epidemic and pandemic prone acute respiratory infections in healthcare -who guidelines world health organization (who), a. coronavirus disease (covid- ) situation reports b. modes of transmission of virus causing covid- : implications for ipc precaution recommendations: scientific brief world health organization (who), c. report of the who-china joint mission on world health organization (who), d. infection prevention and control guidance for world health organization (who), e. management of ill travellers at points of entry- international airports, seaports and ground crossings-in the context of covid- outbreak temperature and humidity on the daily new cases and new deaths of covid- in countries. sci. total environ how far droplets can move in indoor environments--revisiting the wells evaporation-falling curve effects of cough-jet on airflow and contaminant transport in an airliner cabin section relationship between humidity and influenza a viability in droplets and implications for influenza's seasonality fecal specimen diagnosis novel coronavirus- infected pneumonia surgical masks as source of bacterial contamination during operative procedures association between ambient temperature and covid- infection in cities from china association between short-term exposure to air pollution and covid- infection: evidence from china sars-cov- viral load in upper respiratory specimens of infected patients key: cord- -ta hebbg authors: balachandar, s.; zaleski, s.; soldati, a.; ahmadi, g.; bourouiba, l. title: host-to-host airborne transmission as a multiphase flow problem for science-based social distance guidelines date: - - journal: nan doi: . /j.ijmultiphaseflow. . sha: doc_id: cord_uid: ta hebbg covid- pandemic has strikingly demonstrated how important it is to develop fundamental knowledge related to generation, transport and inhalation of pathogen-laden droplets and their subsequent possible fate as airborne particles, or aerosols, in the context of human to human transmission. it is also increasingly clear that airborne transmission is an important contributor to rapid spreading of the disease. in this paper, we discuss the processes of droplet generation by exhalation, their potential transformation into airborne particles by evaporation, transport over long distances by the exhaled puff and by ambient air turbulence, and final inhalation by the receiving host as interconnected multiphase flow processes. a simple model for the time evolution of droplet/aerosol concentration is presented based on a theoretical analysis of the relevant physical processes. the modeling framework along with detailed experiments and simulations can be used to study a wide variety of scenarios involving breathing, talking, coughing and sneezing and in a number of environmental conditions, as humid or dry atmosphere, confined or open environment. although a number of questions remain open on the physics of evaporation and coupling with persistence of the virus, it is clear that with a more reliable understanding of the underlying flow physics of virus transmission one can set the foundation for an improved methodology in designing case-specific social distancing and infection control guidelines. the covid- pandemic has made clear the fundamental role of airborne droplets and aerosols as potential virus carriers. the importance of studying the fluid dynamics of exhalations, starting from the formation of droplets in the respiratory tracts to their evolution and transport as a turbulent cloud, can now be recognized as the key step towards understanding sars-cov- transmission. respiratory droplets are formed and emitted at high speed during a sneeze or cough [ ] , and at a lower speed while talking or breathing. the virus-laden droplets are then initially transported as part of the coherent gas puff of buoyant fluid ejected by the infected host [ ] . the very large drops of o(mm) in size, which are visible to the naked eye, are minimally affected by the puff. they travel semi-ballistically with only minimal drag adjustment, but rapidly fall down due to gravitational pull. they can exit the puff either by overshooting or by falling out of the puff at the early stage of emission (fig. ). smaller droplets ( o( µm)) that remain suspended within the puff are advected forward. as the suspended droplets steadily evaporate within the cloud, the virus takes the form of potentially inhalable droplet nuclei when the evaporation of water is complete. meanwhile, the velocity of the turbulent puff continues to decay both due to entrainment and drag. once the puff slows down sufficiently, and its coherence is lost, the eventual spreading of the virus-laden droplet nuclei becomes dependent on the ambient air currents and turbulence. the isolated respiratory droplet emission framework was introduced by wells [ ] in the s and remains the framework used for guidelines by public health agencies, such as the who, cdc and others. however, it does not consider the role of the turbulent gas puff within which the droplets are embedded. regardless of their size and their initial velocity, the ejected droplets are subject to both gravitational settling and evaporation [ ] . although droplets of all sizes undergo continuous settling, droplets with settling speed smaller than the fluctuating velocity of the surrounding puff can remain trapped longer within the puff (fig. ) . furthermore, the water content of the droplets continuously decreases due to evaporation. when conditions are appropriate for near complete evaporation, the ejected droplets quickly become droplet nuclei of non-volatile biological material. the settling velocity of these droplet nuclei is sufficiently small that they can remain trapped as a cloud and get advected by ambient air currents and dispersed by ambient turbulence. based on the above discussion, we introduce the following terminology that will be consistently used in this paper: • puff: warm, moist air exhaled during breathing, talking, coughing or sneezing, which remains coherent and moves forward during early times after exhalation • cloud: the distribution of ejected droplets that remain suspended even after the puff has lost its coherence. the cloud is advected by the air currents and is dispersed by ambient turbulence • exited droplets: droplets that have either overshot the puff/cloud or settled down due to gravity • airborne (evaporating) droplets: droplets which have not completed evaporation and retained within the puff/cloud • (airborne) droplet nuclei: droplets that remain airborne within the puff/cloud and that have fully evaporated, which will also be termed aerosols. host-to-host transmission of virus-laden droplets and droplet nuclei generally occurs through direct and indirect routes [ , , ] . the direct route of transmission involves the larger droplets that may ballistically reach the recipient's mucosa. this route is currently thought to involve either the airborne route or drops that have settled on surfaces. the settled drops remain infectious, to be later picked up by the recipient, and are generally thought to be localized to the vicinity or at close range of the original infectious emitter. with increased awareness and modified physical distancing norms, it is possible to minimize the spreading of the virus by such direct route. the indirect route of transmission is one that does not necessarily involve a direct or close interaction between the infectious individual and the recipient or for the two to be synchronously present figure : image reproduction showing the semi-ballistic largest drops, visible to the naked eye, and on the order of mm, which can overshoot the puff at its early stage of emission [ , ] . the puff continues to propagate and entrain ambient air as it moves forward, carrying its payload of a continuum of drops [ ] , over distances up to meters for violent exhalations such as sneezes [ ] . in the same contaminated space at the same time. thus, the indirect route involves respiratory droplets and fully-evaporated droplet nuclei that are released to the surrounding by the infected individual, which remain airborne as the cloud carries them over longer distances [ , , , ] . the settling speeds of the airborne droplets and droplet nuclei are so small, that they remain afloat for longer times [ ] , while being carried by the background turbulent airflow over distances that can span the entire room or even multiple rooms within the building (o( − ) feet). a schematic of the two routes of transmission is shown in fig. and in this paper we will focus on the indirect airborne transmission. another factor of great importance is the possibility of updraft in the region of contamination, due to buoyancy of the virus-laden warm ejected air-mass. these slight updrafts can keep the virusladen droplets suspended in the air and enhance the inhalability of airborne droplets and droplet nuclei by recipients who are located farther away. the advection of airborne droplets and nuclei by the puff and subsequently as a cloud may represent transmission risk for times and distances much longer than otherwise previously estimated, and this is a cause of great concern [ , ] . note that if we ignore the motion of the puff of air carrying the droplets, as in the analysis of wells, the airborne droplets and nuclei would be subjected to such high drag that they could not propagate more than a few cm away from the exhaler, even under conditions of fast ejections, such as in a sneeze. this illustrates the importance of incorporating the correct multiphase flow physics in the modeling of respiratory emissions [ ] , which we shall discuss further here. it has been recently reported that the covid- virus lives in droplets and aerosols for many hours in laboratory experiments [ ] . at the receiving end, an increased concentration of virusladen airborne droplets and nuclei near the breathing zone increases the probability of them settling on the body or, more importantly, being inhaled. depending on its material and sealing properties, the use of a mask by the infected host can help reduce the number of virus-laden droplets ejected into the air. the use of a mask or other protective devices by the receiving host may reduce the probability of inhalation of the virus-laden airborne droplets and nuclei in a less effective way. the above description provides a clear sketch of the sequence of processes by which the virus is transferred host-to-host. this simplistic scenario, though pictorially evocative, is tremendously insufficient to provide science-based social distancing guidelines and recommendations. there is substantial variability (i) in the quantity and quality of contaminated droplets and aerosols generated by an infected person, (ii) in the manner by which the contaminated droplets and droplet nuclei remain afloat over longer distances and time, (iii) in the possibility of the contaminant being inhaled by a recipient and (iv) in the effectiveness of masks and other protection devices. violent exhalations, such as sneezing and coughing, yield many more virus-laden droplets and aerosols than breathing and talking [ , ] . all coughing and sneezing events are not alike -the formation of droplets by break up of mucus and saliva varies substantially between individuals. significant variation in initial droplet size and velocity distribution has been reported in [ , , , ] . the measured droplet size distribution, particularly for transient biological emissions such as respiratory exhalations, also depends on ambient temperature and humidity and on the methodology and instrumentation used to characterize the size distribution [ , , ] . furthermore, it is of importance to consider the volume of air, and the pathogen load, being inhaled during breathing by the receiving host. thus, there is great variability in how much of the virus-laden aerosols reach from the infected host to the receiving host. although less violent, it has been suggested that breathing can also be a significant source of contagion since it occurs at great regularity, and thus much more frequently [ , , , ] . furthermore, these works suggest different possible mechanisms of droplet generation in the lower respiratory tracts for these less violet periodic ejection events and as a result the ejected droplets and aerosols are typically much smaller. as a result the effectiveness of ordinary cotton and gauze masks have been questioned [ ] , leung, bae. though the general mathematical framework to be presented in this paper applies to all forms of exhalations, our particular focus of demonstration will be for more violent ejections in the form of coughing and sneezing. cdc guideline of social distancing of meters ( feet) is based on the disease transmission theory originally developed in s and later improved by others [ , , ] . the current recommendation of feet as the safe distance is somewhat outdated and based on the assumption that the direct route is the main mechanism of transmission. therefore, it can be improved in several ways: (i) by accurately accounting for the distance traveled by the puff and the droplets contained within it, while some continuously settling out of the puff, (ii) by accurately evaluating the evaporation of droplets and the subsequent advection and dispersal of droplet nuclei as a cloud [ ] , (iii) by incorporating the effect of adverse flow conditions that prevail under confined indoor environments including elevators, aircraft cabins, and public transit, or favorable conditions of open space with good breeze or cross ventilation, and (iv) by correctly assessing the effectiveness of masks and other protective devices [ ] . thus, mechanistic, evidence-based understanding of exhalation and dispersal of expelled respiratory droplets, and their subsequent fate as droplet nuclei in varying scenarios and environments is important. we must therefore revisit the safety guidelines and update them to modern understanding. in particular, a multi-layered guideline that differentiates between crowded class rooms, auditoriums, buses, elevators and aircraft cabins from open outdoor cafes is desired. only through a reliable understanding of the underlying flow physics of virus transmission, one can arrive at such nuanced guidance in designing case-specific social distancing guidelines. the objective of the paper is to aid in the development of a comprehensive scientific guideline for social distancing that (i) considers airborne transmission via state-of-the-art understanding of respiratory ejections and (ii) substantially improve upon the older models of [ , ] . towards this objective we present a coherent analytic and quantitative description of the droplet generation, transport, conversion to droplet nuclei, and eventual inhalation processes. we will examine the available quantitative relationships that describe the above processes and adapt them to the present problem. the key outcomes that we desire are (i) a simple universal description of the initial droplet size spectrum generated by sneezing, coughing, talking and breathing activities. such a description must recognize the current limitations of measurements of droplet size distribution under highly transient conditions of respiratory events. (ii) a first-order mathematical framework that describes the evolution of the cloud of respiratory droplets and their conversion to droplet nuclei, as a function of time, and (iii) a simple description of the inhalability of the aerosols along with the corresponding evaluation of the effectiveness of different masks based on existing data reported to date. the physical picture and the quantitative results to be presented can then be used to study a statistical sample of different scenarios and derive case-specific guidelines. we anticipate the present paper to spawn future research in the context of host-to-host airborne transmission. after presenting the mathematical framework in section , the three different stages of transmission, namely droplet generation, transport and inhalation will be independently analyzed in sections , and . these sections will consider the evolution of the puff of exhaled air and the droplets contained within. section will put together the different models of the puff and droplet evolution described in the previous sections, underline their simplifications, and demonstrate their ability to make useful predictions. finally, conclusions and future perspectives are offered in section . we wish to describe the three main stages involved in the host-to-host transmission of the virus: droplet generation during exhalation, airborne transport, and inhalation by the receiving host. in the generation stage, virus-laden drops are generated throughout the respiratory tract by the exhalation air flow, which carries them through the upper airway toward the mouth where they are ejected along with the turbulent puff of air from the lungs. the ejected puff of air can be characterized with the following four parameters: the volume q pe , the momentum m pe , and the buoyancy b pe of the ejected puff, along with the angle θ e to the horizontal at which the puff is initially ejected. the initial momentum and buoyancy of the puff are given by m pe = ρ pe q pe v pe and b pe = (ρ a − ρ pe )q pe g, where v pe is the initial velocity of ejected puff, ρ pe and ρ a are the initial density of the puff and the ambient, respectively, and g is the gravitational acceleration. the ejected droplets are characterized by their total number n e , size distribution n e (d), droplet velocity distribution v de (d) and droplet temperature distribution t de (d), where d is the diameter of the droplet. to simplify the theoretical formulation, here we assume the velocity and temperature of the ejected droplets to depend only on the diameter and show no other variation. as we shall see in section , this assumption is not very restrictive, since the velocity and temperature of the droplets that remain within the puff very quickly adjust to those of the puff. both the ejected puff of air and the detailed distribution of droplets depend on the nature of the exhalation event (i.e., breathing, talking, coughing or sneezing), and also on the individual. this is followed by the transport stage, where the initially ejected puff of air and droplets are transported away from the source. the volume of the puff of air increases due to entrainment of ambient air. the puff velocity decreases due to both entrainment of ambient air as well as drag. since the temperature and moisture content of the ejected puff of air is typically higher than the ambient, the puff is also subjected to a vertical buoyancy force, which alters its trajectory from a rectilinear motion. the exhaled puff is turbulent, and both the turbulent velocity fluctuations within the puff and the mean forward velocity of the puff decay over time. the time evolution of the puff during the transport stage can then be characterized by the following quantities: the volume q p (t), the momentum m p (t), buoyancy b p (t) of the ejected puff, and ρ p (t) is the density of air within the puff which changes over time due to entrainment and evaporation. the trajectory of the puff is defined in terms of the distance traveled s(t) and the angle to the horizontal θ(t) of its current trajectory. following the work of bourouiba et al. [ ] we have chosen to describe the puff trajectory in terms of s(t) and θ(t). this information can be converted to horizontal and vertical positions of the centroid of the puff as a function time. if we ignore the effects of thermal diffusion and ambient stratification between the puff and the surrounding air, then the buoyancy of the puff remains a constant as b p (t) = b pe . furthermore, as will be seen below, the buoyancy effects are quite weak in the early stages when the puff remains coherent, and thus, the puff to good approximation can be taken to travel along a straight line path, as long as other external flow effects are unimportant. to characterize the time evolution of the virus-laden droplets during the transport stage, we distinguish the droplets that remain within the puff, whose diameter is less than a cutoff (i.e., d < d exit ), from the droplets (i.e., d > d exit ) that escape out of the puff. as will be discussed subsequently in § , the cutoff droplet size d exit decreases with time. thus, the total number of droplets that remain within the puff can be estimated as n (t) = d exit n (d, t) dd. however, the size distribution of droplets at any later time, denoted as n (d, t), is not the same as that at ejection. due to evaporation, size distribution shifts to smaller diameters over time. we introduce the mapping d(d e , t), which gives the current diameter of a droplet initially ejected as a droplet of diameter d e . then, assuming well-mixed condition within the puff, the airborne droplet and nuclei concentration (number per volume) distribution can be expressed as where the inverse mapping d − gives the original ejected diameter of a droplet whose current size is d. the prefactor /q p (t) accounts for the decrease in concentration due to the enlargement of the puff over time. in this model, the airborne droplets and nuclei that remain within the coherent puff are assumed to be in equilibrium with the turbulent flow within the puff. under this assumption, the velocity v d (d, t) and temperature t d (d, t) of the droplets can be estimated with the equilibrium eulerian approximation [ , ] . when the puff's mean and fluctuating velocities fall below those of the ambient, the puff can be taken to lose its coherence. thus, the puff remains coherent and travels farther in a confined relatively quiescent environment, such as an elevator, class room or aircraft cabin, than in an open outdoor environment with cross-wind or in a room with strong ventilation. we define a transition time t tr , below which the puff is taken to be coherent and the above described puff-based transport model applies. for t > t tr , we take the aerosol transport and dilution to be dominated by ambient turbulent dispersion. accordingly, this late-time behavior of total number of airborne droplets and nuclei and their number density distribution are given by the theory of turbulent dispersion. it should be noted that the value of transition time will depend on both the puff properties as well as the level of ambient turbulence (see section . ) . we now consider the final inhalation stage. depending on the location of the recipient host relative to that of the infected host, the recipient may be subjected to either the puff that still remains coherent, carrying a relatively high concentration of virus-laden droplets or nuclei, or to the more dilute dispersion of droplet nuclei, or aerosols. these factors determine the number and size distribution of virus-laden airborne droplets and nuclei the recipient host will be subjected to. the inhalation cycle of the recipient, along with the use of masks and other protective devices, will then dictate the aerosols that reach sensitive areas of the respiratory tract where infection can occur. following the above outlined mathematical framework we will now consider the three stages of generation, transport and inhalation. knowing the droplet sizes, velocities and ejection angles resulting from an exhalation is the key first step in the development of a predictive ability for droplet dispersion and evolution. respiratory droplet size distributions have been the object of a large number of studies, as reviewed in [ ] , and among them, those of duguid [ ] and loudon & roberts [ ] have received particular scrutiny as a basis for studies of disease transmission by nicas, nazaroff & hubbard [ ] . there are substantial differences in the methodologies used for quantification of respiratory emission sprays. few studies have used common instrumentation that have enough overlap to reconstruct the full distribution of sizes. for example, there are important gaps in reporting the total volume or duration of air sampling, in addition there are issues in reporting the effective evaporation rates used to back-compute the initial distribution and in the documentation of assumptions about optical or shape properties of the droplets being sampled. in addition, sensitivity analyses are often missing regarding the role of orientation or calibration of sensing instruments with respect to highly variable emissions from human subjects. finally, regarding direct high-speed imaging methods [ , ] , the tools for precise quantification of complex unsteady fragmentation and atomization processes are only now being developed [ , , ] . there are far fewer studies on the velocities and angles of the droplets produced by atomizing flows. the studies of duguid and loudon & roberts have been performed by allowing the exhaled droplets to impact various sheets or slides, with different procedures being used for droplets smaller than µm. the size of the stains on the sheets was observed and the original droplet size was inferred from the size of the stains. to account for the difference between the droplet and the stain sizes an arbitrary factor is applied and droplets smaller than or microns are processed differently than larger droplets. the whole process makes the determination of the number of droplets smaller than microns less reliable. the data are replotted in fig. . many authors have attempted to fit the data with a log-normal probability distribution function. in that case, the number of droplets between diameter d and d + dd is n e (d) dd, and the frequency of ejected droplet size distribution is given by where dd is a relatively small diameter increment or bin width, b is a normalization constant,μ is the expected value of ln d, also called the geometric mean andσ is the standard deviation of ln d, also called the geometric standard deviation (gsd). on the other hand, there have also been numerous studies of the fragmentation of liquid masses in various physical configurations other than the exhalation of mucosalivary fluid [ , , , ] . these configurations include spray formation on wave crests [ ] , droplet impacts on solids and liquids [ ] , wave impacts on vertical or finite walls/surfaces [ , , ] , and jet atomization [ ] . these studies reveal a number of qualitative similarities between the various processes, which can be best described as a sequence of events. those events include a primary instability of sheared layers in high speed air flows [ ] , and then the nonlinear growth of the perturbation into thin liquid sheets. the sheets themselves may be destabilized by two routes, one involving the formation of taylor-culick end rims [ , ] , and their subsequent deformation into detaching droplets [ ] . the other route to the formation of droplets is the formation of holes in the thin sheets [ , , ] . the holes then expand and form free hanging ligaments, which fragment into droplets through the rayleigh-plateau instability [ ] . considering the apparent universality of the process, one may infer that a universal distribution of droplet sizes may exist. indeed, the log-normal distribution has often been fitted to experimental [ ] and numerical data on jet formation [ , ] , for droplet impacts on solid surfaces [ ] , and for wave impacts on solid walls [ ] . the log-normal distribution is frequently suggested for exhalations [ , ] . the fit of the numerical results of [ ] is shown in fig. . however, this apparent universality of the log-normal distribution is questionable for several reasons. first, many other distributions, such as exponential, poisson, weibull-rosin-rammler, beta, or families of gamma or compound gamma distributions [ , ] capture to some extent the complexity of atomization physics. second, the geometrical standard deviation (gsd) of the log-normal fits to the many numerical and experimental measurements is relatively small (of the order of . [ ] or . [ ] ), while the wide range of scales in fig. seems to indicate a much larger gsd. indeed nicas, nazaroff & roberts [ ] obtainσ − . one explanation for the smaller gsd in jet atomization studies, both numerical and experimental, is that the numerical or optical resolution is limited at the small scales. indeed, as grid resolution is increased, the observed gsd also increases [ ] . third, many authors [ , ] observe multimodal or bimodal distributions, that can be obtained for example by the superposition of several physical processes. this would arise in a very simple manner if the taylor-culick rim route produced drops of a markedly different size than the holes-infilm route. the non-newtonian nature of the fluid will also influence the instabilities and thereby the droplet generation process. other less violent processes could lead to the formation of small droplets such as the breakup of small films and menisci described in [ ] without going through the sequence of events described above. frequency n e (d) ( /microns) duguid cough data loudon and roberts cough data pareto b/d fit figure : frequency of droplet size distribution, replotted from duguid [ ] and loudon & roberts [ ] . the pareto distribution is also plotted. in order to elucidate this discrepancy, we take another look at the fit of the duguid data in fig. . we replot the data that was provided in table of duguid. since the data are given as counts n i in bins defined by the interval (d i , d i+ ), we approximate n e (d) at collocation points fig. , since if plotted in the variables x = ln d and y = ln[dn e (d)] the distribution ( ) appears as a parabola. when one attempts to fit a parabola between and µm, one obtains a log-normal distribution withσ = . andμ = ln( ) (for diameters in microns). however, the data above µm are completely outside this distribution. if instead the whole range from to µm is fit to a log-normal distribution, one obtains a very wide log-normal or alternatively a pareto distribution of power in figs roberts data. it is especially clear from fig. that if one does not trust either data at d < µm then both data sets are well described by the pareto distribution. this, however, does not eliminate the possibility that more data with more statistical power could show deviations from pareto, in particular, as multimodal distributions. nevertheless, the multimodal deviation from the pareto distribution is difficult to characterize and will not be pursued in what follows for the sake of simplicity. it is clear that the pareto distribution cannot be valid at diameters that are either too large or too small. the equivalent diameter of the total mass of liquid being atomized is an obvious upper bound, but it is also very unlikely that droplets with d > h where h is the initial film thickness will be observed. it is reasonable to put this film thickness on the scale of mm, which corresponds to the upper bound on diameters in the data of figs. and . the lower bound on droplet diameter is much harder to determine. exhalations are highly transient, or unsteady, processes involving complex multiscale geometry [ ] , and thread breakup is a fractal multiscale process with satellite droplets [ , ] . going down in scale, the fractal process repeats itself as long as continuum mechanics remains valid, to around nm. this would not be relevant for viral disease propagation as a lot of the relevant viruses have sizes ranging from o( − nm), with an estimated size for sars-cov- ranging from - nm, for example. if the smallest length scale is the thickness at which the thin liquid sheets will break, then experimental observations in water [ ] suggest a scale of o( ) nm. other fluids, including biological fluids or biologically contaminated fluids such as those investigated in [ , , ] may yield different length scales. based on the above considerations, we take a histogram of droplet sizes that reads where d is set to o( nm) and d to o( mm) for simplicity. the total volume of the droplets is fig. . the fit is adequate only up to µm. as a result, only a fraction of the reliable data fits the log-normal. the pareto distribution is a reasonable capture of the data in the to µm range. in the log-log coordinates, the log-normal distribution appears as a parabola while the pareto distribution is a straight line. since d is four orders of magnitude smaller than d , the total number of droplets is well approximated by and the cumulative number of droplets f (x) = n e (d ≤ d ≤ x), i.e., the number of droplets with diameter smaller than x, is very well approximated by so that f ( d )/n e = % of the droplets are of size less than d µm. in other words, a numerical majority of the droplets are near the lower diameter bound. on the other hand, a majority of the volume of fluid is in the larger droplet diameters. the distribution of velocities and ejection angles has been investigated in the atomization experiments of [ ] , which follow approximately the geometry of a high speed stream peeling by a gas layer. these experiments were qualitatively reproduced in the numerical simulations of [ ] . to cite ref. [ ] , "most of the ejection angles are in the range • to • , however, it occurs occasionally that the drops are ejected with angles as high as • ". on the other hand, there are to our knowledge no experimental data on the velocity of droplets, as they are formed in an atomizing jet, that could be used directly to estimate the ejection speed of droplets in exhalation. there are however numerical studies [ , ] in the limit of very large reynolds and weber numbers. the group velocity of waves formed on a liquid layer below a gas stream has been estimated by dimotakis [ ] as where ρ d is droplet density. in [ , ] it was shown that this was also the vertical velocity of the interface perturbation. it is thus likely that this velocity plays a role at the end of the first instability stage of atomization. after this stage, droplets are detached and immersed in a gas stream of initial ejection velocity v pe . since the density ratio ρ p /ρ d is o( − ), we expect the initial velocity of the ejected droplets at the point of their formation to be small. as we show below, it is interesting to note that the large reynolds number limit may apply at the initial injection stage to a wide range of droplets in the spectrum of sizes found above. indeed the ejection reynolds number of a droplet ejected at a velocity v de in a surrounding air flow of velocity v pe is where ν a is the kinematic viscosity of the ejected puff of air (here taken to be the same as that of the ambient air). the largest reynolds number is obtained for the upper bound of d = mm. for example, if the droplet's initial velocity is set to v de ≈ , and the air flow velocity in some experiments [ ] is as high as m/s, we can estimate the largest ejection reynolds number to be re e ≈ and the reynolds number will stay above unity for droplets down to micron size. but as the puff of air and the droplets move forward, the droplet reynolds number rapidly decreases for the following reasons: (i) as will be seen in section . the puff velocity decreases due to entrainment and drag, (ii) as will be seen in section . . the droplet diameter will decrease rapidly due to evaporation, (iii) as will be seen in section . . the time scale τ v on which the droplet accelerates to the surrounding fluid velocity of the puff is quite small, and (iv) very large droplets quickly fall out of the puff and do not form part of airborne droplets. thus, it can be established that droplets smaller than µm quickly equilibrate with the puff within the first few cm after exhalation. this section will consider the evolution of the puff of hot moist air with the droplets after their initial ejection. first in section . we will present a simple modified model for the evolution of the puff of exhaled air, evaluating the effects of drag and the inertia of the droplets within it. this will enable us, in section . to discuss the evolution of the droplet size spectrum, velocity and temperature distributions, with simple first order models. additionally, section . will discuss the effect of non-volatiles on the droplet evolution and the formation of a fully evaporated droplet nuclei or aerosol particle. late-time turbulent dispersion of the virus-laden droplet nuclei, when the puff of air within which they are contained stops being a coherent entity, is then addressed in section . . for the puff model, we follow the approach of bourouiba et al. [ ] , but include the added effects of drag and the mass of the injected droplets. in addition, a perturbation approach is pursued to obtain a simple solution with all the added effects included. fig. shows the evolution of the puff along with quantities that define the puff [ ] . we define t to be the time elapsed from exhalation and s(t) to be the distance traveled by the puff since exhalation. for analytical considerations we define the virtual origin to be at a distance s e from the real source in the backward direction and t e to be the time it takes for the puff to travel from the virtual origin to the real source. we define t = t + t e to be time from the virtual origin and s = s + s e to the distance traveled from the virtual origin -their introduction simplifies the analysis. from the theory of jets, plumes, puffs and thermals [ ] the volume of the puff exhaled grows by entrainment. bourouiba et al. [ ] defined the puff to be spheroidal in shape with the transverse dimension to evolve in a self-similar manner as r (t ) = αs (t ), where α is related to entrainment coefficient. the volume of the puff is then q p (t ) = ηr (t ) = ηα s (t ) and the projected, or cross-sectional, area of the puff a(t ) = βr (t ) = βα s (t ), where the constants η and β depend on the shape of the spheroid. for a spherical puff η = π/ and β = π. as defined earlier, the ejected puff at the real source (i.e., at t = t e ) is characterized by the volume q pe = ηα s e , momentum m pe = ρ pe q pe v pe , buoyancy b pe = q pe (ρ a − ρ pe )g and ejection angle θ e . from the assumption of self-similar growth, we obtain the virtual origin to be defined as where the constant c depends on the drag coefficient of the puff and will be defined below. if we assume a spherical puff with an entrainment factor α = . [ ] , the distance s e depends only on the ejected volume. experimental measurements suggest q pe to vary over the range . to . m . accordingly, s e can vary from . to . m. similar estimates of t e can be obtained for a spherical puff: as q pe varies from . to . m and as the ejected velocity varies from to m/s the value of t e varies over the range . to . s. the horizontal and vertical momentum balances in dimensional terms are in the above c d is the drag coefficient of the puff and m d is the momentum of droplets within the puff. while the puff velocity decreases rapidly over time, the velocity of the larger droplets will change slowly. note that in the analysis to follow, we take the velocity of those droplets that remain within the puff to be the same as the puff velocity. figure : evolution of a typical cloud of respiratory multiphase turbulent droplet-laden air following breathing, talking, coughing and sneezing activities. image adapted from [ ] . we use s e and t e as the length and time scales to define nondimensional quantities:s = s /s e andt = t /t e . with this definition the virtual origin becomest = ands = and the real source becomest = ands = . in terms of non-dimensional quantities the governing momentum equations can be rewritten as there are three nondimensional parameters: mass ratio of the initial ejected droplets to the initial air puff: r m = ρ d q de /(ρ p q pe ); the scaled drag coefficient: c = c d β/( ηα); and the buoyancy parameter: a = b pe t e /(ρ pe q pe s e ). in the above equations, r m is defined in terms of the mass of the initial ejected droplets. this is an approximation since some of the droplets exit the puff over time. even though the droplet mass decreases due to evaporation, the associated momentum is not lost from the system since it remains within the puff. in any case, soon it will be shown that the value of r m is small and the role of ejected droplets on the momentum balance is negligible. it should also be noted that under boussinesq approximation the small difference in density between the puff and that the ambient is important only in the buoyancy term. for all other purposes, the two will be taken to be the same and as a result the time variation of puff density is not of importance (i.e., ρ p = ρ pe = ρ a ). the importance of inertia of the ejected droplets, drag on the puff and buoyancy effects can now be evaluated in terms of the magnitude of the nondimensional parameters. typical experimental measurements of breathing, talking, coughing and sneezing indicate that the value of r m is smaller than . and often much smaller. furthermore, as droplets fall out continuously [ ] from the turbulent puff, this ratio changes over time. here we will obtain an upper bound on the inertial effect of injected droplets by taking the value of r m to be . . the drag coefficient of a spherical puff of air is also typically small -again as an upper bound we take c d = . , which yields c = . for a spherical puff. the value of the buoyancy parameter a depends on the density difference between the ejected puff of air and the ambient, which in turn depends on the temperature difference. for the entire range of ejected volumes and velocities, the value of a comes to be smaller than . , for temperature differences of the order of ten to twenty degrees between the exhaled puff and the ambient. since all three parameters r m , c and a can be considered as small perturbations, the governing equations can be readily solved in their absence to obtain the following classical expressions for the nondimensional puff location and puff velocity: with the inclusion of the drag term the governing equations become nonlinear. nevertheless, they allow a simple exact solution which can be expressed as thus, as to be expected, the forward propagation of the puff slows down with increasing nondimensional drag parameter c. for small values of c the above can be expanded in taylor series as a comparison of the exact solution with the above asymptotic expansion shows its adequacy for small values of c. for small non-zero values of r m , c and a, the governing equations can be solved using regular perturbation theory. the result can be expressed as and the above expression is accurate to o(c , r m , a ). although the effect of buoyancy is to curve the trajectory of the puff, the leading order effect of buoyancy is to only alter the speed of rectilinear motion. also, as expected, the effect of non-zero r m is to add to the total inertia and thereby slow down the motion of the puff. on the other hand, the effect of buoyancy is to slow down if the initial ejection is angled down (i.e., if θ e < ) and to speed up if the ejection is angled up, provided the ejected puff is warmer than the ambient. the time evolution of the puff as predicted by the above analytical expression is shown in fig. . note that the point of ejection is given byt = ,s = , and the initial non-dimensional velocitỹ v(t = ) = / . the results for four different combinations of c and r m are shown. the buoyancy parameter has very little effect on the results and, therefore, is not shown. it should be noted that at late stages when the puff velocity slows down the effect of buoyancy can start to play a role as indicated in experiments and simulations. it can be seen that the effect of inertia of the ejected droplets, even with the upper bound of holding their mass constant at the initial value, has negligible effect. only the drag on the puff has a significant effect in reducing the distance traveled by the puff. it can then be taken that the puff evolution to good accuracy can be represented by ( ) . over a time span of nondimensional units the puff has traveled about . s e and the velocity has dropped to about % of the initial velocity. by nondimensional units the puff has traveled about . s e and the velocity has dropped to about . % of the initial velocity. the ejected droplets are made of a complex fluid that is essentially a mixture of oral fluids, including secretions from both the major and minor salivary glands. in addition, it is added up with several constituents of non-salivary origin, such as gingival crevicular fluid, exhalted bronchial and nasal secretions, serum and blood derivatives from oral wounds, bacteria and bacterial products, viruses and fungi, desquamated epithelial cells, other cellular components, and food debris [ ] . therefore, it is not easy to determine precisely the transport properties of the droplet fluid. although surface tension is measured similar to that of water, viscosity can be one or two orders of magnitude larger [ ] making drops less coalescence prone [ , ] . in the present context, viscosity and surface tension might be of importance, because they can influence droplet size distribution specifically by controlling coalescence and breakage. these processes are important only during the ejection stage, and once droplets are in the range below µm, coalescence and break up processes are impeded. due to the dilute dispersed nature of the flow droplet-droplet interaction can be ignored. the ejected swarm of droplets is characterized by its initial size spectrum as given in ( ). the time evolution of the spectrum of droplets that remain within the puff in terms of droplet size, velocity and temperature is the object of interest in this section. the evolution of the ejected droplets depends on the following four important parameters: the time scale τ v on which the droplet velocity relaxes to the puff fluid velocity (in the absence of other forcings), the time scale τ t on which the droplet temperature relaxes to the puff fluid temperature, the settling velocity w of the droplet within the puff fluid, and the reynolds number re based on settling velocity. these quantities are given by [ , , ] where ρ ≈ is the droplet-to-air density ratio, c r ≈ . is the droplet-to-air specific heat ratio, g is the acceleration due to gravity, ν p and κ p are the kinematic viscosity and thermal diffusivity of the puff. in the above, Φ = + . re . and n u = + . re / p r / are the finite reynolds number drag and heat transfer correction factors, where the later is the well-known ranz-marshall nusselt or sherwood number correlation. both corrections simplify in the stokes regime for drops smaller than about µm. here we take the prandtl number of air to be p r = . . in the stokes limit, the velocity and thermal time scales, and the settling velocity of the droplet increase as d , while reynolds number scales as d . the value of these four parameters for varying droplet sizes is presented in fig. , where it is clear that the effect of finite re becomes important only for droplets larger than µm. for smaller droplets τ v , τ t (s), w (m/s), and re . the size of the droplets under investigation is sufficiently small, and the swarm is dilute to prevent their coalescence. furthermore, the droplet weber number w e = ρ p w d/σ can be estimated to be quite small even for droplets of size µm, where σ is the surface tension of the droplet and the relative velocity will be shown in the next section to be well approximated by the settling velocity. therefore, secondary breakup of droplets within the puff can be ignored and the only way in which droplets change their size is via evaporation. according to the analysis of langmuir [ ] , the rate of mass loss due to evaporation of a small sphere depends on the diffusion of the vapor layer away from the sphere surface, and under reasonable hypotheses [ , , , ] , it can be expressed as : where, m is the mass of a droplet of diameter d, d is the diffusion coefficient of the vapor, ρ p is the density of puff air and is the spalding mass number, where y d is the mass fraction of water vapor at the droplet surface and y p is the mass fraction of water vapor in the surrounding puff. under the assumption that n u and b m are nearly constant for small droplets, the above equation can be integrated [ ] to obtain the following law (mapping) for the evolution of the droplet: where d e is the initial droplet diameter at ejection and k = dn u ln( + b m )/ρ has units of m /s and thus represent an effective evaporative diffusivity. it is important to observe that ( ) would predict a loss of mass per unit area tending to infinity as the diameter of the drop tends to zero. this implies that the droplet diameter goes to zero in a finite time and we establish the result which for any time t yields a critical value of droplet diameter, and all droplets that were smaller, or equal, at exhalation (i.e., d e ≤ d e,evap ) would have fully evaporated by t. the only parameter is k . assuming n u = and d = . × − m /s, even for very small values of b m , we obtain the evaporation time for a µm droplet to be less than a second. however, it appears that smaller than a certain critical size, the loss of mass due to evaporation slows down [ ] . this could partly be due to the presence of non-volatiles and other particulate matter within the droplet, whose effects were ignored in the above analysis, and will be addressed in section . . it seems that ( ) can give reliable predictions for droplet diameter down to a few µm with much slower evaporation rates for smaller sizes. irrespective of whether water completely evaporates leaving only the non-volatile droplet nuclei, or the droplet evaporation slows down, the important consequence on the evolution of the droplet size distribution is that it is narrower and potentially centered around micron size. we now consider the motion of the ejected droplets, while they rapidly evaporate. the equation of motion of the droplet is newton's law where e e e z is the unit vector along the vertical direction, m p is the mass of puff displaced by the droplet, v v v d and v v v p are the vector velocity of the droplet and the surrounding puff. provided the droplet time scale τ v is smaller than the time scale of surrounding flow, which is the case for droplets of diameter smaller than µm, the above ode can be perturbatively solved to obtain the following leading order solution [ , , ] according to the above equation, the equilibrium eulerian velocity of the droplet depends on the local fluid velocity plus the still fluid settling velocity w of the droplet plus the third term that arises due to the inertia of the droplet. though at ejection the droplet speed is smaller than the surrounding gas velocity, as argued in section . , the droplets quickly accelerate to approach the puff velocity. in fact, since the puff is decelerating (i.e., |dv v v p /dt| < ), the droplet velocity will soon be larger than the local fluid velocity. as long as the droplet stays within the puff, the velocity and acceleration of the surrounding fluid can be approximated by those of the puff as |v v v p | = ds/dt and |dv v v p /dt| = d s/dt . this allows evaluation of the relative importance of the third term (inertial slip velocity) in terms of the puff motion, which is given in ( ) as [ ] this ratio takes its largest value at the initial time of injection and then decays as /t. using the range of possible values of t e given earlier, this ratio is small for a wide range of initial droplet sizes. we thus confirm that for the most part droplet inertia can be ignored in its motion, and the droplet velocity can be taken to be simply the sum of local fluid velocity and the still fluid settling velocity of the droplet. while the effect of buoyancy on the puff was shown to be small, the same cannot be said of the droplets. the vertical motion of a droplet with respect to the surrounding puff, due to its higher density, is dependent only on the fall velocity w , which scales as d , which in turn decreases as given in ( ) due to evaporation. the droplet's gravitational settling velocity can be integrated over time to obtain the distance over which it falls as a function of time. we now set this fall distance (left hand side) equal to the puff radius (right hand side) to obtain where we have set the droplet diameter at exhalation to be d e,exit , indicating the fact that a droplet of initial diameter equal to d e,exit has fallen by a distance equal to the puff size at time t. thus all larger droplets of size d e > d e,exit have fallen out of the puff by t and we have been referring to these as the exited droplets. it should be pointed out that in the above simple analysis the vertical motion of the particle ignored the vertical component of fluid velocity both from turbulent fluctuations and from the entrainment process. the two critical initial droplet diameters, d e,evap and d e,exit are plotted in fig. a as a function of t. the only other key parameter of importance is k , whose value is varied from − to − m /s. in evaluating d e,exit using ( ), apart from the property values of water and air, we have used the nominal values of α = . , s e = . m and t e = . s (as an example). the solid lines correspond to d e,exit , which decreases with increasing t and for each value of k , there exists a minimum d e below which there is no solution to ( ) since the droplet fully evaporates before falling out of the puff. the dotted lines correspond to d e,evap , which increases with t. the intersection of the two curves is marked by the solid square, which corresponds to the limiting time t lim (k ), beyond which the puff contains only fully-evaporated droplet nuclei containing the viruses. correspondingly we can define a limiting droplet diameter d e,lim (k ). given sufficient time, all initially ejected larger droplets (i.e., d e > d e,lim ) would have fallen out of the puff and all smaller droplets (i.e., d e ≤ d e,lim ) would have evaporated to become droplet nuclei. at times smaller than the limiting time (i.e., for t < t lim ) we have the interesting situation of some droplets falling out of the puff (exited droplets), some still remaining as partially evaporated airborne droplets, and some fully-evaporated to become droplet nuclei. this scenario is depicted in fig. a with an example of t = . s for k = − m /s plotted as a dashed line. there can be significant presence of non-volatile material such as mucus, bacteria and bacterial products, viruses and fungi, and food debris in the ejected droplets [ ] . however, the fraction of ejected droplet volume q de that is made up of these non-volatiles varies substantially from person to person. the presence of non-volatiles alters the analysis of the previous sections in two significant ways. first, each ejected droplet, as it evaporates, will reach a final size that is dictated by the amount of non-volatiles that were initially in it. the larger the droplet size at initial ejection, the larger will be its final size after evaporation, since it contains a larger amount of non-volatiles. if ψ is the volume fraction of non-volatiles in the initial droplet, the final diameter of the droplet nuclei after complete evaporation of volatile matter (i.e., water) will be this size depends on the initial droplet size and composition. note that even a small, for example %, non-volatile composition results in d dr being around % of the initial ejected droplet size. it has also been noted that the evaporation of water can be partial, depending on local conditions in the cloud or environment. we simply assume the fraction ψ to also account for any residual water retained within the droplet nuclei. the second important effect of non-volatile is to reduce the rate of evaporation. as evaporation occurs at the droplet surface, a fraction of the surface will be occupied by the non-volatiles reducing the rate of evaporation. for small values of ψ, the effect of non-volatiles is quite small only at the beginning. the effect of non-volatiles will increase over time, since the volume fraction of nonvolatiles increases as the volatile matter evaporates. because of this ever decreasing evaporation rate, it may take longer for a droplet to decrease from its ejection diameter of d e to its final droplet nuclei diameter of d dr , than what is predicted by ( ) . it should be noted that intermittency of turbulence and heterogeneity of vapor concentration and droplet distribution within the puff will influence the evaporation rate [ , , ] . nevertheless, for simplicity, and for the purposes of the present first order mathematical framework, we use the d -law given in ( ) , but with a smaller value of effective k to account for the effect of non-volatiles and turbulence intermittency. this approximation is likely to be quite accurate in describing the early evolution of the droplet. only at late stages as the droplet approaches its final diameter d dr , the d -law will be in significant error. applying the analysis of the previous sections, taking into account the presence of non-volatiles, we separate the two different time regimes of t ≤ t lim and t ≥ t lim . in the case when t ≤ t lim , we have three types of droplets: (i) exited droplets whose initial size at injection is greater than d e,exit , (ii) droplets of size at ejection smaller than d e,evap that have completely evaporated to become droplet nuclei of size d dr and (iii) intermediate size airborne droplets that are within the puff and still undergoing evaporation. we assume an equation of the form ( ) to approximately apply even in the presence of non-volatiles. with this balance between fall distance of a droplet and the puff radius we obtain the following expression the corresponding limiting diameter of complete evaporation can be obtained from setting d = d e,evap ψ / and d e = d e,evap in ( ) as while the above two estimates are in terms of the droplet diameter at injection, their current diameter at t can be expressed as form the above expressions, we define t lim to be the time when d e,exit = d e,evap , which in terms of current droplet diameter becomes d exit = d evap . beyond this limiting time (i.e., for t > t lim ) the droplets can be separated into only two types: (i) exited droplets whose initial size at injection greater than d e,exit = d e,evap , and (ii) droplets of size at ejection smaller that have become droplet nuclei. the variation of t lim and d e,lim as a function of k is presented in fig. b . it is clear that as k varies over a wide range, t lim ranges from . s to s, and correspondingly d e,lim varies from to µm. we now put together all the above arguments to present a predictive model of the droplet concentration within the puff. the initial condition for the size distribution is set by the ejection process discussed in section , and the simple pareto distribution given in ( ) provides an accurate description. based on the analysis of the previous sections, we separate the two different time regimes of t ≤ t lim and t ≥ t lim . in the case when t ≤ t lim the droplet/aerosol concentration (or the number per unit volume of the puff) can be expressed as where we have recognized the fact that equation ( ) is the mapping d between the current droplet size and its size at injection. due to the turbulent nature of the puff, the distribution of airborne droplets and nuclei is taken to be uniform within the puff. quantities such ass, d evap and d exit are as they have been defined above and the pre-factor /q(t) accounts for the expansion of the puff volume. in the case of t ≥ t lim , the droplet number density spectrum becomes and only droplet nuclei remain within the puff. here, the size of the largest droplet nuclei within the puff is related to its initial unevaporated droplet size as d lim = d e,lim ψ / , and the plot of d e,lim as a function of k for a specific example case of puff and droplet ejection was shown in fig. b . in this subsection we will briefly consider droplet temperature, since it plays a role in determining saturation vapor pressure and the value of k . following pirhadi et al. [ ] we write the thermal equation of the droplet as where c pw is the specific heat of water, k p is the thermal conductivity of the puff air, l is the latent heat of vaporization, t d and t p are the temperatures of the droplet and the surrounding puff. the first term on the right accounts for convective heat transfer from the surrounding air and the second term accounts for heat needed for phase change during evaporation. it can be readily established that the major portion of heat required for droplet evaporation must come from the surrounding air through convective heat transfer. the equilibrium eulerian approach [ ] can again be used to obtain the asymptotic solution of the above thermal equation and the droplet temperature can be explicitly written as where τ t is the thermal time scale of the droplet that was introduced earlier. the second term on the right is negative and thus contributes to the droplet temperature being lower than the surrounding puff. simple calculation with typical values shows that the contribution of the third term is quite small and can be ignored. as a result, the temperature difference between the droplet and the surrounding is largely controlled by the evaporation rate dm/dt, which decreases over time. again, using the properties of water and air, and typical values for n u and b m , we can evaluate the temperature difference t p − t d to be typically a few degrees. thus, the evaporating droplets need to be only a few degrees cooler than the surrounding puff for evaporation to continue. when the puff equilibrates with the surrounding and its velocity falls below the ambient turbulent velocity fluctuation, the subsequent dynamics of the droplet cloud is governed by turbulent dispersion. this late-time evolution of the droplet cloud depends on many factors that characterize the surrounding air. this is where the difference between a small enclosed environment such as an elevator or an aircraft cabin or an open field matters, along with factors such as cross breeze and ventilation. a universal analysis of the late-time evolution of the droplet nuclei cloud is thus not possible, due to problem-specific details. the purpose of this brief discussion is to establish a simple scaling relation to guide when the puff evolution model presented in the above sections gives way to advection and dispersion by ambient turbulence. it should again be emphasized that the temperature difference between the puff fluid containing the droplet nuclei cloud and the ambient air may induce buoyancy effects, which for model simplicity will be taken into account as part of turbulent dispersion. we adopt the classical scaling analysis of richardson [ ] , according to which the radius of a droplet cloud, in the inertial range, will increase as the / power of time as given by where c is a constant, is the dissipation rate, which will be taken to be a constant property of ambient turbulence, and t is the time shift required to match the cloud size at the transition time between the above simple late time model and the puff model. in the above, the subscript lt stands for the late-time behavior of the radius of the droplet-laden cloud. we now make a simple proposal that there exists a transition time t tr , below which the rate of expansion of the puff as given by the puff model is larger than dr lt /dt computed from the above expression. during this early time, ambient dispersion effects can be ignored in favor of the puff model. but for t > t tr droplet-laden cloud's ambient dispersion becomes the dominant effect. the constants t and t tr can be obtained by satisfying the two conditions: (i) the size of the droplet-laden cloud given by ( ) at t tr matches the puff radius at that time given by αs e ((t tr + t e )/t e ) /( +c) , and (ii) the rate of expansion of the droplet-laden cloud by turbulent dispersion matches the rate of puff growth given by the puff model. this latter condition can be expressed as from these two simple conditions, we obtain the final expression for the transition time as given a puff, characterized by its initial ejection length and time scales s e and t e , and the ambient level of turbulence characterized by , the value of transition time can be estimated. if we take entrainment coefficient α = . , the constant c = , and typical values of s e = . m and t e = . s, we can estimate t tr = . s for a dissipation rate of c = − m /s . the transition time t tr increases (or decreases) slowly with decreasing (or increasing) dissipation rate. thus, the early phase of droplet evaporation described by the puff model is valid for o( ) s, before being taken over by ambient turbulent dispersion. however, it must be stressed that the scaling relation of richardson is likely an over-estimation of ambient dispersion, as there are experimental and computational evidences that suggest that the power-law exponent in ( ) is lower than [ ] . but it must be remarked that even with corresponding changes to late-time turbulent dispersion, the impact on transition time can be estimated to be not very large. also, it must be cautioned that according to classical turbulent dispersion theory, during this late-time dispersal, the concentration of virus-laden droplet nuclei within the cloud will not be uniform, but will tend to decay from the central region to the periphery. nevertheless, for sake of simplicity here we assume ( ) to apply and we take the droplet nuclei distribution to be uniform. according to above simple hypothesis, the effect of late-time turbulent dispersion on the number density spectrum is primarily due to the expansion of the could, while the total number of droplet nuclei within the cloud remains the same. thus, the expressions ( ) and ( ) still apply. however, the expression for the volume of the cloud must be appropriately modified as the location of the center of the expanding cloud of droplets is still given by the puff trajectory s(t), which has considerably slowed down during late-time dispersal. the strength of the above model is in its theoretical foundation and analytical simplicity. but, the validity of the approximations and simplifications must be verified in applications to specific scenarios being considered. for example, considering variability in composition, turbulence intermittency, initial conditions of emissions and the state of the ambient, direct observations show that the transition between puff dominated and ambient flow dominated fate of respiratory droplets vary from o( - s) [ ] . this section will mainly survey the existing literature on issues pertaining to what fraction of the droplets and aerosols at any location gets inhaled by the recipient host, and how this is modified by the use of masks. these effects modeled as inhalation (aspiration) and filtration efficiencies will then be incorporated into the puff-cloud model. the pulmonary ventilation (breathing) has a cyclic variation that varies markedly with age and metabolic activities. the intensity of breathing (minute ventilation) is expressed in l/min of inhaled and exhaled air. for the rest condition, the ventilation rate is about - l/min and increases to about - l/min for mild activities. during exercise, ventilation increases significantly depending on age and metabolic needs of the activity. in the majority of earlier studies on airflow and particle transport and deposition in human airways, the transient nature of breathing was ignored for simplification and to reduce the computational cost. haubermann et al. [ ] performed experiments on a nasal cast and found that particle deposition for constant airflow is higher than those for cyclic breathing. shi et al. [ ] performed simulations on nanoparticle depositions in the nasal cavity under cyclic airflow and found that the effects of transient flow are important. grgic et al. [ ] and horschler et al. [ ] performed experimental and numerical studies, respectively, on flow and particle deposition in a human mouth-throat model, and the human nasal cavity. particle deposition in a nasal cavity under cyclic breathing condition was investigated by bahmanzadeh et al. [ ] , naseri et al. [ ] , and kiasadegh et al. [ ] , where the unsteady lagrangian particle tracking was used. they found there are differences in the predicted local deposition for unsteady and equivalent steady flow simulations. in many of these studies, a sinusoidal variation for the volume of air inhaled is used. that is here q max is the maximum flow rate, and t = s is the period of breathing cycle for an adult during rest or mild activity. the period of breathing also changes with age and the level of activity. haghnegahdar et al. [ ] investigated the transport, deposition, and the immune system response of the low-strain influenza a virus iav laden droplets. they noted that the shape of the cyclic breathing is subject dependent and also changes with nose and mouth breathing. they provided an eight-term fourier series for a more accurate description of the breathing cycle. the hygroscopic growth of droplets was also included in their study. analysis of aspiration of particles through the human nose was studied by ogden and birkett [ ] and armbruster and breuer [ ] . accordingly, the aspiration efficiency η a is defined as the ratio of the concentration of inhaled particles to the ambient concentration. using the results of earlier studies and also his works, vincent [ ] proposed a correlation for evaluating the inhalability of particles. that is, the aspiration efficiency η a of particles smaller than µm is given as, η a (d) = . [ + exp(− . d)] for d < µm . ( ) figure : influence of thermal plume on aspiration efficiency [ ] . here, d is the aerodynamic diameter of the particles in micron. while the above correlation provides the general trend that larger particles are more difficult to inhale, it has a number of limitations. it was developed for mouth-breathing with the head oriented towards the airflow direction with speeds in the range of m/s to m/s. the experimental investigation of aerosol inhalability was reported by hsu and swift [ ] , su and vincent [ , ] , aitken et al. [ ] , and kennedy and hinds [ ] . dai et al. [ ] performed in-vivo measurements of inhalability of large aerosol particles in calm air and fitted their data to several correlations. for calm air condition, they suggested, where d must be in microns. computational modeling of inhalability of aerosol particles were reported by many researchers [ , , , , , ] . interpersonal exposure was studied by [ , ] . the influence of thermal plume was studied by salmanzadeh et al. [ ] . naseri et al. [ ] performed a series of computational modeling and analyzed the influence of the thermal plume on particle aspiration efficiency when the body temperature is higher or lower than the ambient. their results are reproduced in figure . here the case that the body temperature t b = . • c and the ambient temperature t a = . • c (upward thermal plume) and the case that t b = . • c and t a = . • c (downward thermal plume) are compared with the isothermal case studied by dai et al. [ ] . it is seen that when the body is warmer than the surrounding, the aspiration ratio increases. when the ambient air is at a higher temperature than the body, the inhalability decreases compared to the isothermal case. in light of the results of the previous section, it can be concluded that at a distance of o( ) m the ejected mostly water droplets have sufficiently reduced in size that these o( ) µm aerosols have near perfect inhalability. using a respiratory face mask is a practical approach against exposure to airborne viruses and other pollutants. among the available facepiece respirators, n , and surgical masks are considered figure : filtration efficiency of different respiratory masks under normal breathing conditions [ , ] . to be highly effective [ , ] . n mask has a filtration efficiency of more than % in the absence of face leakage [ , ] . surgical masks are used extensively in the hospital and operating rooms [ ] . nevertheless, there have been concerns regarding their effective filtration of airborne bacteria and viruses [ , , ] . there is often discomfort in wearing respiratory masks for extended durations that increases the risk of spread of infection. the breathing resistance of a mask is directly related to the pressure drop of the filtering material. the efficiency of respiratory masks varies with several factors, including the intensity and frequency of breathing as well as the particle size [ ] . the filtration efficiencies of different masks under normal breathing conditions, as reported by zhang et al. [ ] and feng et al. [ ] , in the absence of leakage, are shown in figure . as an example, the measured filtration efficiency of the surgical mask can be fit as where droplet nuclei diameter d must be in microns. it is seen that the filtration efficiencies of different masks vary significantly, with n having the best performance, which is followed by the surgical mask. it is also seen that all masks could capture large particles. the n , surgical, and procedure masks remove aerosols larger than a couple of microns. cotton and gauze masks capture a major fraction of particles larger than µm. the capture efficiency of all masks also shows an increasing trend as particle size becomes smaller than nm due to the effect of the brownian motion of nanoparticles. figure also shows that the filtration efficiencies of all respiratory masks drop for the particle sizes in the range of nm to about µm. this is because, in this size range, both the inertia impaction and the brownian diffusion effect are small, and the mask capture efficiency reduces. based on these results, and the earlier finding that most ejected droplets within the cloud reduce their size substantially and could become sub-micron-sized aerosol particles by about o( − ) m distance, it can be stated that only professional masks such as n , surgical, and procedure masks provide reliable reduction in the inhaled particles. hence, it is important for healthcare workers to have access to high-grade respirators upon entering a room or space with infectious patients [ ] . another importance of mask is that it will eliminate the momentum of expelled puff during sneezing, coughing, speaking, and breathing, and reduce the distance that the droplet cloud would transport. therefore, wearing a mask will reduce the chance for transmission of infectious viruses. it should be emphasized that the concentration that a receiving host will inhale (φ inhaled ) depends on the local concentration in the breathing zone adjusted by the aspiration efficiency given by equations ( ) and ( ) (or plotted in figure ). when the receiving host wears a mask, an additional important correction is needed by multiplying by a factor ( − η f ), where η f is the filtration efficiency plotted in figure . that is, where φ(d, t) is the droplet nuclei concentration at the breathing zone given in ( ) or ( ) . it is seen that the concentration of inhaled droplets larger than microns significantly decreases when the mask is used. but the exposure to smaller droplets, particularly, in the size range of nm to µm varies with the kind of mask used. the object of this section is to put together the different models of the puff and droplet evolution described in the previous sections, underline their simplifications, and demonstrate their ability to make useful predictions. such results under varying scenarios can then be potentially used for science-based policy making, such as establishing multi-layered social distancing guidelines and other safety measures. in particular, we aim at modeling the evolution of the puff and the concentration of airborne droplets and nuclei that remain within the cloud so that the probability of potential transmission can be estimated. as discussed in section . , the virus-laden droplets exhaled by an infected host will undergo a number of transformations before reaching the next potential host. to prevent transmission, current safety measures impose a safety distance of two meters. furthermore, cloth masks are widely used by the public and their effectiveness has been shown to be questionable for droplets and aerosols of size about a micron. the adequacy of these common recommendations and practices can be evaluated by investigating the concentration of airborne droplets and nuclei at distances larger than one meter and the probability of them being around a micron in diameter, since such an outcome will substantially increase the chances of transmission. in the following we will examine two effects: the presence of small quantities of non-volatile matter in the ejected drops that remain as droplet nuclei after evaporation, and the adequacy of the log-normal or pareto distribution to quantify the number of droplets in the lower diameter classes. first, in section . , we will consider predictions based on a currently used model, where the droplets are allowed to fully evaporate. then, in section . we will consider improved predictions based on the present model, where the effect of non-volatiles and the motion of the puff are accurately modeled. let us consider the situation of speaking or coughing, whose initial puff volume and momentum are such that they yield s e . m and t e . s. under this specific condition, as shown in figure the puff travels about m in about s . for this simple example scenario, we will examine our ability to predict airborne droplet and nuclei concentration, as an important step towards estimating the potential for airborne transmission in situations commonly encountered. in most of the countries, current guidelines are based on the work by xie et al. [ ] , who revisited previous guidelines by [ ] with improved evaporation and settling models. they identified the possibility that, due to evaporation, the droplets quickly become vanishingly small before reaching a significant distance and thus may represent a minor danger for transmission due to their minimal virus loading. this scenario is shown in figure , where we present the evolution of the drop size figure : evolution of the drop size distribution spectra according to the currently used evaporation models [ , ] . spectrum while droplets are transported by the ejected puff. the initial droplet size distribution is taken to be that measured by duguid [ ] modeled with a log-normal distribution, which in the monte-carlo approach is randomly sampled with one million droplets divided into one thousand diameter classes. each droplet is then followed while evaporating and falling. the evaporation model is taken to be ( ) with the effective diffusion coefficient estimated as k · − m /s. this value is computed under the assumption that drops are made of either pure water or a saline solution [ ] and that air has about % humidity. therefore, this is an environment unfavorable to evaporation and consequently drop size reduction happens relatively slowly. however, from the figure it is clear that, even in this extreme case, after few tens of centimeters, and within a second, all droplets have evaporated down to a size below µm. this is in line with the predictions of xie et al. [ ] . naturally, if the air is dryer, the effective evaporation coefficient will be larger (even as large as k − m /s) and the droplet size spectrum will evolve even faster, leaving virtually all droplets to be smaller than µm in the puff. in the model, we set the minimum diameter that all drops can achieve equal to µm (shown by the single point indicated in the figure) so to emphasize this effect of the model. recall that intermittency of turbulence with the puff can create clusters of droplets and concentration of vapor and thereby significantly alter the evaporation rate [ , , ] . hence, our estimate of evaporation time is a lower bound, as governed by the d -law ( ). as discussed in section . there is current consensus that droplets ejected during sneezing or coughing contain, in addition to water, other biological and particulate non-volatile matter. specifically, viruses themselves are of size almost . µm. here we will examine the evolution of droplet size distribution in the presence of non-volatile matter. it will be clear in the following, that in this case, even a small amount of non-volatile matter plays an important role with the evaporation coefficient being a minor factor in deciding how fast the final state is reached. in figure , we show the final distribution of droplets under two scenarios, where the initially ejected droplets contain . % and . % of non-volatile matter. in figure a , the initial drop size distribution is modeled as a log-normal distribution (i.e., as in fig. ), whereas in figure b , the initial drop size distribution is modeled according to the pareto distribution with initial droplet size varying between and µm. this range is smaller than that suggested earlier in section . however, drops that are larger than µm fall out of the cloud and therefore are not important for airborne transmission and droplets initially smaller than µm have much smaller viral load. here "final droplet size distribution" indicates the number of droplets that remain within the puff after all the larger droplets have fallen out and all others have completed their evaporation to become droplet nuclei. this final number of droplet nuclei as a function of size does not vary with time or distance. the size distribution is computed here as in figure , with a random sampling from the initial log-normal or pareto distribution. as before, these computations used an evaporation coefficient of k = − m /s. however, there are two important differences: each droplet is allowed to fall vertically according to its time-dependent settling velocity, w , which decreases over time as the droplet evaporates. integration of the fall velocity over time provides the distance traveled by the droplet relative to the puff. droplets whose fall distance exceeds the size of the puff are removed from consideration. second, each droplet that remains within the puff evaporates to its limiting droplet nuclei size that is dictated by the initial amount of non-volatile matter contained within the droplet. for ψ = . % non-volatile matter, the final aerosol size cannot decrease below % of the initial droplet diameter, whereas for . % of non-volatile matter, the final droplet size cannot decrease below % of the initial diameter. from fig. , it is clear that when evaporation is complete, the drop size distribution rigidly shifts towards smaller diameters, with a cut-off upper diameter due to the settling of large drops (these cut-offs are the upper limits of the blue and red curves). essentially, it is clear that the initial number of viruses that were in droplets of size smaller than d e,exit still remain within the cloud almost unchanged, representing a more dangerous source of transmission than predicted by the conventional assumption of near-full evaporation. again, it is important to note that the final droplet size distribution is established rapidly even with the somewhat lower effective evaporation diffusivity of k = − m /s, and when not accounting for the effect of localized moisture of the cloud in further reducing the rate. figure also illustrates the important difference in the drop size distribution. the pareto distribution will predict a much larger number of drops in the micron and sub-micron range, possibly the most dangerous for both aspiration efficiency and filtration inefficiency. in this section we will demonstrate the efficacy of the simple model presented in ( ) and ( ) for the prediction of droplet/aerosol concentration. in contrast to the monte-carlo approach of the previous subsection, where the evolution of each droplet was accurately integrated, here we will use the analytical prediction along with its simplifying assumptions. the cases considered are identical to those presented in figure for ψ = . % and k = − m /s. the initial droplet size distributions considered are again log-normal and pareto distributions. in this case, however, we underline that the quantity of importance in airborne transmission is not the total number of droplet nuclei, but rather their concentration in the proximity of a susceptible host. accordingly, we plot in figure airborne droplet and nuclei concentration (per liter) of volume as a function of droplet size. these results are without taking into account the aspiration and filtration efficiencies given in ( ) . here the area under the curve between any two diameters yields the number of droplets within this size range per liter of volume within the cloud. at the early times of t = . and . s, we see that larger droplets above a certain size have fallen out of the cloud, while droplet nuclei smaller than d evap have fully evaporated and their distribution is a rigidly-shifted version of the original distribution. the distribution of intermediate size airborne droplets reflects the fact that they are still undergoing evaporation. unlike in figure , the concentration continues to fall even after t lim . s when the number and size of droplets within the cloud have reached their limiting value. this is simply due to the fact that the volume of the puff continues to increase and this continuously dilutes the aerosol concentration. most importantly, the results of the simple model presented in ( ) and ( ) are in excellent agreement with those obtained from monte-carlo simulation. the increasing size of the contaminated cloud with time can be predicted with ( ) and the centroid is given by the scaling law ( ) . as the final step, we include the effect of aspiration and filtration efficiencies to compute the concentration of droplet nuclei that get into the receiving host. in computing φ inhaled using ( ), we take the droplet/nuclei concentration at the location of the receiving host to be that computed and presented in figure . we consider the receiving host to be using a surgical mask, whose efficiency was shown in figure and given in ( ) . the aspiration efficiency of the receiving host is taken to that given in ( ) . the results are presented in figure , where the figure includes the initial log-normal and pareto distributions (green lines). it is clear that due to filtration efficiency of the surgical mask no droplet nuclei of size greater than µm gets into the receiving host. for smaller droplet nuclei, the inhaled concentration is substantially lower due to both the aspiration and the filtration efficiencies. clearly, the inhaled concentration will be higher and the size range will be wider, and will approach those shown in figure , with the use of cotton or gauze masks. figure : droplet/aerosol concentration evolution as predicted by the analytical model presented in ( ) and ( ) . left frame shows the evolution starting from the log-normal distribution. right frame shows the evolution starting from the pareto distribution. both cases use k = − m s. the primary goal of this paper is to provide a unified theoretical framework that accounts for all the physical processes of importance, from the ejection of droplets by breathing, talking, coughing and sneezing to the inhalation of resulting aerosols by the receiving host. these processes include: (i) forward advection of the exhaled droplets with the puff of air initially ejected; (ii) growth of the puff by entrainment of ambient air and its deceleration due to drag; (iii) gravitational settling of some of the droplets out of the puff; (iv) modeling of droplets evaporation, assuming that the d law prevails; (v) presence of non-volatile compounds which form the droplet nuclei left behind after evaporation; (vi) late-time dispersal of the droplet nuclei-laden cloud due to ambient air turbulent dispersion. despite the complex nature of the physical processes involved, the theoretical framework results in a simple model for the airborne droplet and nuclei concentration within the cloud as a function of droplet diameter and time, which is summarized in equations ( ), ( ) and ( ) . this framework can be used to calculate the concentration of virus-laden nuclei at the location of any receiving host as a function of time. as additional processes, the paper also considers (vii) efficiency of aspiration of the droplet nuclei by the receiving host; and (viii) effectiveness of different kinds of masks in filtering the nuclei of varying size. it must be emphasized that the theoretical framework has been designed to be simple and therefore involves a number of simplifying assumptions. hence, it must be considered as the starting point. by relaxing the approximations and by adding additional physical processes of relevance, more complex theoretical models can be developed. one of the primary advantages of such a simple theoretical framework is that varying scenarios can be considered quite easily: these figure : droplet nuclei concentration inhaled by the infected host wearing a surgical mask as predicted by the analytical model presented in ( ) and ( ) with the aspiration and filtration efficiencies given in ( ) and ( ) . the left and right frames show the results of initial log-normal and pareto distributions. both cases use k = − m s. different scenarios include varying initial puff volume, puff velocity, number of droplets ejected, their size distribution, non-volatile content, ambient temperature, humidity, and ambient turbulence. the present theoretical framework can be, and perhaps must be, improved in several significant ways in order for it to become an important tool for reliable prediction of transmission. (i) accurate quantification of the initially ejected droplets still remains a major challenge. further high-quality experimental measurements and high-fidelity simulations [ ] are required, especially mimicking the actual processes of breathing, talking, coughing and sneezing, to fully understand the entire range of droplet sizes produced during the exhalation process. (ii) as demonstrated above, the rate at which an ejected droplet evaporates plays an important role in determining how fast they reach their fully-evaporated state. it is thus important to calculate more precisely the evaporation rate of non-volatile-containing realistic droplets resulting from human exhalation. the precise value of evaporation rate may not be important when droplets evaporate fast, since all droplets remaining within the puff would have completed their evaporation. but under slow evaporation conditions, accurate evaluation of evaporation is important. 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size distribution of secondary ejected droplets by crown splashing of droplets impinging on a solid wall how far droplets can move in indoor environmentsrevisiting the wells evaporation-falling curve investigation of the flow-field in the upper respiratory system when wearing n filtering facepiece respirator airflow resistance and bio-filtering performance of carbon nanotube filters and current facepiece respirators key: cord- -okxzqzl authors: gulec, fatih; atakan, baris title: a molecular communication perspective on airborne pathogen transmission and reception via droplets generated by coughing and sneezing date: - - journal: nan doi: nan sha: doc_id: cord_uid: okxzqzl infectious diseases spread via pathogens such as viruses and bacteria. airborne pathogen transmission via droplets is an important mode for infectious diseases. in this paper, the spreading mechanism of infectious diseases by airborne pathogen transmission between two humans is modeled with a molecular communication perspective. an end-to-end system model which considers the pathogen-laden cough/sneeze droplets as the input and the infection state of the human as the output is proposed. this model uses the gravity, initial velocity and buoyancy for the propagation of droplets and a receiver model which considers the central part of the human face as the reception interface is proposed. furthermore, the probability of infection for an uninfected human is derived by modeling the number of propagating droplets as a random process. the numerical results reveal that exposure time and sex of the human affect the probability of infection. in addition, the social distance for a horizontal cough should be at least . m and the safe coughing angle of a coughing human to infect less people should be less than - $^circ$. abstract-infectious diseases spread via pathogens such as viruses and bacteria. airborne pathogen transmission via droplets is an important mode for infectious diseases. in this paper, the spreading mechanism of infectious diseases by airborne pathogen transmission between two humans is modeled with a molecular communication perspective. an end-to-end system model which considers the pathogen-laden cough/sneeze droplets as the input and the infection state of the human as the output is proposed. this model uses the gravity, initial velocity and buoyancy for the propagation of droplets and a receiver model which considers the central part of the human face as the reception interface is proposed. furthermore, the probability of infection for an uninfected human is derived by modeling the number of propagating droplets as a random process. the numerical results reveal that exposure time and sex of the human affect the probability of infection. in addition, the social distance for a horizontal cough should be at least . m and the safe coughing angle of a coughing human to infect less people should be less than - • . index terms-airborne pathogen transmission, molecular communication, expiratory droplet reception, social distance. m olecular communication (mc) is an emerging research area which employs chemical signals for information transfer. originally, mc is proposed as the communication method of the nanomachines mimicking the biological cells in microscale in a nanonetwork [ ] . mc can also be helpful for practical applications in macroscale [ ] . the pioneering experimental study in macroscale mc is about establishing a communication link using an electrical sprayer, an alcohol sensor and alcohol molecules as the transmitter (tx), receiver (rx) and messenger molecules, respectively [ ] . for this experimental setup, several channel models are proposed in [ ] - [ ] and its data rate is improved via multiple input multiple output (mimo) technique in [ ] . furthermore, it is shown that mc can be used in macroscale environments where there is significant attenuation for electromagnetic wave-based communication [ ] , [ ] . in [ ] , an experimental platform consisting of pumps, pipes and a ph meter is proposed. this platform encodes the information symbols according to the ph level, as also used in a macroscale fluidic platform explained in [ ] . magnetic nanoparticles which are sensed by a susceptometer (as a rx) are employed to encode information symbols in [ ] . in [ ] , a platform in which a mass spectrometer (as a rx) and an odor generator (as a tx) communicate is developed. [ ] proposes a platform with a chemical vapor transmitter and photoionization detectors. moreover, laser induced florescence technique is implemented as an experimental platform for macroscale mc [ ] . all of the aforementioned macroscale platforms are generally proposed to develop more efficient mc methods. however, macroscale mc can also be employed to solve practical problems such as finding the distance to a source or the location of the source. for the test-bed given in [ ] , statistical distance estimation methods are proposed in [ ] by using the features extracted from molecular signals with the proposed feature extraction algorithm. for a long range underwater scenario it is theoretically shown that a molecular tx can be localized with a mobile search robot [ ] . the localization of a passive molecular tx is proposed by using a clustered localization algorithm for the proposed sensor network-based platform [ ] . in [ ] , the distance is estimated by considering liquid droplets as information carriers. the experimental study in [ ] shows that encoding information in droplets is possible. hence, mc can be employed as a tool to model the biological phenomena which consider droplets such as the transmission and reception of pathogens (viruses, bacteria, etc.) which cause contagious diseases via droplets. this concept is first proposed in [ ] which consider the infectious human as a blind tx emitting pathogen-laden droplets and sensors as the rx for outdoor environments. this study is improved in [ ] by taking silicon nanowire field effect transistor-based biosensors into account to model pathogen detection for airborne pathogen transmission. airborne transmission and self-inoculation (direct contact) are two modes of infectious disease transmission via pathogens [ ] . droplets can be classified as large droplets and droplet nuclei (aerosols) which have sizes of larger and smaller than µm, respectively [ ] . all expiratory activities such as coughing, sneezing, breathing and speaking can generate large droplets and aerosols. while large droplets can be effective in short-range, aerosols can spread pathogens to longer distances due to their interactions with air. airborne transmission via droplets is a significant infection mechanism for pathogens such as influenza virus [ ] , severe acute respiratory syndrome (sars) virus [ ] and new sars coronavirus- (sars-cov- ) which causes coronavirus disease (covid- ) [ ] . by the time this paper is written, the global pandemic of covid- still continues and there is no cure for covid- . it is essential to emphasize that this study is related with the covid- outbreak, since one of the main mechanisms of this disease is airborne transmission. in this paper, we investigate airborne pathogen transmission and reception mechanisms between humans with a mc perspective for indoor environments. this mc perspective leads us to use and adapt the well-known communication engineering techniques to model the spread of the infectious diseases between humans. the infectious human which emit a cloud consisting of pathogen-laden droplets and air by coughing/sneezing is considered as the tx and the uninfected human is defined as the rx unlike the studies in [ ] , [ ] where the rx is a biosensor. furthermore, the effect of gravity and buoyancy is taken into account for the indoor propagation of the cloud, which is not considered in [ ] . the propagation of the cloud is modeled by modifying the deterministic model in [ ] in a probabilistic way. the cloud travels under the influence of initial velocity, buoyancy and gravity. the number of droplets in this cloud is modeled as a random process. a receiver model which takes the central part of human face as the interface with pathogens into account is proposed. the propagation and reception models are employed for the proposed end-to-end system model in order to give the infection state of the rx as the system output. the contributions of this paper can be summarized as follows: • mc perspective is proposed to model the airborne pathogen transmission and reception mechanisms by humans. • the interaction of pathogen-laden droplets and the uninfected human is examined by proposing a rx model. hence, an end-to-end system model is proposed which combines the channel and receiver models. • a probabilistic approach which enables the derivation of the probability of infection for an uninfected human is employed. furthermore, the proposed model is evaluated by numerical results to understand the effects of physical parameters for different indoor scenarios. our key findings for a coughing tx is given as follows: • increased exposure time to pathogens increases the probability of infection. • for a horizontal cough, the social distance should be at least . m. • it is safer to cough with an initial angle less than - • to infect less people. • male humans are more susceptible to airborne infection due to their larger faces for some situations. the rest of the paper is organized as follows. in section ii, the proposed end-to-end system model is presented. section iii provides the derivation of the probability of infection. numerical results are given in section iv and the paper is concluded in section v. this section provides a detailed explanation of the proposed end-to-end system model for droplet-based mc between two humans via sneezing/coughing in four steps. as given in fig. , this model incorporates the airborne pathogen-laden droplet transmission with the reception of these droplets by the human that is considered as the rx. fig. also shows that the endto-end system impulse response is defined as the infection state which is the output of the end-to-end system, since a sneeze/cough can be considered as an impulsive input signal. transmitted droplets via sneezing/coughing are modeled as a cloud which is a mixture of air and droplets. the propagation of the cloud is defined as a two-phase flow where the first and second phase represent the liquid phase of droplets and the gas phase of the air, respectively [ ] . as the first step of the endto-end system model, the trajectory of the cloud is derived. in this study, the model given in [ ] for the propagation of the cloud is adopted and modified. in the second step, we derive an end-to-end system model with a probabilistic approach instead of the deterministic approach in [ ] . the third step details the rx model which includes signal reconstruction, integration, quantization and detection parts. in the last step, the algorithm for the implementation of the system model is given. in our scenario, the tx emits the cloud with an initial velocity on the x-axis by sneezing or coughing. due to the warmer air in the mouth (with density ρ f at • c) with respect to ambient air (with density ρ a at • c), where ρ f < ρ a [ ] , the emitted cloud is subject to buoyancy on y-axis. as illustrated in fig. , buoyancy, gravity and initial velocity of the cloud affect the trajectory of the cloud. therefore, the trajectory is defined with the curvilinear s-axis and θ which shows the angle between the s and x axes. in order to find the position of the cloud in -d space, it is essential to derive the time-dependent density of the cloud (ρ c (t)). at the initial state (t = ), the initial cloud mass (m c ( )) can be represented by the addition of the initial droplet mass (m d ( )) and initial air mass in the cloud (m a ( )) as given by [ ] where v (t) is the cloud volume, ρ d is the droplet density, ρ f is the air density in the mouth. the volume of droplets in the cloud (v d (t)) consists of different sized droplets with diameter d k and can be defined in terms of the volume fraction here, k is the number of the different droplet sizes, φ k ( ) = n k ( )v k /v ( ), n k (t) and v k is the number and volume of the spherical droplets of diameter d k , respectively. n k (t) changes during the propagation of the cloud due to the settling of droplets to the ground as explained in section ii-b. by substituting v d ( ) into ( ) and solving for ρ c ( ), the initial density of the cloud is derived as as the cloud moves, it entrains the ambient air with density ρ a and its volume becomes is the acquired air volume. since the initial volume fraction of the air in the mouth with density ρ f is relatively small in the moving cloud ( − ) [ ] , it is assumed as after the emission of droplets, ρ c (t) can be derived via the conservation of mass [ ] . hence, the mass of droplets at the time instance t (m d (t)) is equal to the initial mass of droplets (m d ( )) and droplet mass can be expressed by the difference of cloud mass and air mass according to ( ) as given by cloud mass at time t − air mass at time t = initial cloud mass − initial air mass ( ) via the substitution of ( ) into ( ) and some algebraic manipulation, the cloud density is derived as as illustrated in fig. , there are two acting forces on the cloud which stem from the gravity and buoyancy on y-axis. since ρ f < ρ a , the buoyant force (b(t)) affects the movement of the cloud upwards. the net buoyant force acting on the cloud (f b (t)) on y-axis is given by the difference of b(t) and the gravitational force (g(t)) as given by [ ] where g is the gravitational acceleration. on x-axis, the movement of the cloud is driven by the momentum (i) which is defined as the multiplication of the mass and velocity [ ] . the momentum is not effective on y-axis and also there is not any acting force on the cloud for z−axis. i is defined on s-axis and is decomposed into two components on x (i x = |i| cos(θ)) and y axes (i y = |i| sin(θ)). since the force can be represented as the derivative of the momentum [ ] and there is not any acting force on the x-axis during the propagation, the net force (f x ) on x-axis is given by furthermore, the net force on y-axis, i.e., f b (t) is given by since the initial buoyancy is conserved [ ] , we have f b (t) = f where f is the net initial buoyant force. with the initial conditions which are |i( )| = i , θ( ) = θ , i x ( ) = i cos(θ ) and i y ( ) = i sin(θ ), i x and i y can be given as the solutions of ( ) and ( ) as since there is not any acting force on z-axis, the momentum can be expressed as |i| = i x + i y . due to its definition, the momentum can be written as [ ] where we can express the cloud velocity (v c (t)) as the displacement on s-axis (s(t)) in an infinitesimal time interval, i.e., v c (t) = ds(t)/dt. the cloud volume is defined as v (t) = ηr(t) where η = π/ for a spherical cloud. furthermore, the radius of the cloud (r(t)) is linearly related with the distance such that r(t) = α e s(t) where α e is the entrainment coefficient and is empirically determined [ ] . hence, ( ) can be rewritten as here, ( ) and ( ) are substituted into ( ) as given by remembering that , the denominator part of ( ) is simplified as for convenience, θ is chosen as in [ ] . however, θ = is also considered in order to observe the effect of the initial cough/sneeze angle in our study. in addition to this, the initial conditions which are s( ) = and t( ) = are taken into account in the integration of ( ) to obtain the quartic equation as given by ( ) . since the discriminant of the quartic equation ( ) is less than zero for physically meaningful parameter values, two of the roots are complex and one of the roots is a real and negative number. therefore, there is only one possible positive real root which is used as the solution. however, this solution is a very long expression to write in this paper and ( ) is solved numerically as detailed later in this section. in order to determine the trajectory of the cloud, θ needs to be derived. via the substitution of i x = |i| cos(θ) and i y = |i| sin(θ) into ( ), two expressions are obtained. then, by solving these two expressions for |i| and equating them gives the equation below which can be solved for θ as given by after the emission of droplets, some of the droplets settle to the ground due to gravity and their interaction with the air [ ] , [ ] . therefore, the number of droplets decreases during the propagation due to the settling of droplets. in addition, since the movement of each droplet in the cloud is independent of each other at each time instance, the number of droplets in the cloud (n (t) = k k= n k (t)) can be modeled as a poisson process with an intensity function λ(t). due to the large number of emitted droplets, n (t) can be approximated as a gaussian random process with the same mean and variance, i.e., n (t) ∼ n (λ(t), λ(t)) [ ] . here, λ(t) which is the mean number of droplets in the cloud can be derived by using the flow rate of the droplets [ ] . moreover, it is assumed that the droplets are homogeneously distributed within the cloud. the flow rate of the droplets (j), which is the derivative of the number of droplets and gives the number of droplets flowing through a surface in unit time (number of droplets/s), is defined as [ ] whereρ c (t) = λ(t)/v (t) and a is the cross-sectional area that droplets are flowing through. since droplets settle through the lower half of the cloud due to the observations in [ ] , a in ( ) is substituted with a(t)/ where a(t) is the surface area of the cloud. hence, ( ) becomes where v s is the settling velocity of droplets and (−) sign represents the decrease in the number of droplets due to the settling. for a spherical cloud, when the substitutions a(t) = πr(t) , v (t) = πr(t) / and r(t) = α e s(t) are made into ( ), the rate of change of the mean number of droplets in the cloud is given by since the solution of ( ) is very long and makes the solution of ( ) very complicated, the trajectory and number of droplets can be found numerically for each time instance. furthermore, the number of droplets can be different for each droplet size. thus, ( ) is manipulated to derive the change of the mean number of droplets at each time instance (∆λ) as given by where ∆t is the time step, the subscripts i and k show the corresponding variables at t = t i for the droplets of diameter d k . at each time step, t i is increased by ∆t and the mean number of droplets of diameter d k in the cloud is increased via λ k,i+ = λ k,i +∆λ. for each time step and droplet size, the number of droplets in the cloud becomes a gaussian random variable as a sample of the gaussian random process n (t), i.e., n k,i ∼ n (λ k,i , λ k,i ). settling velocities of droplets during the propagation are defined according to the flow regimes which are newton's (turbulent) flow, intermediate flow and stokes (laminar) flow regimes [ ] . these regimes are determined according to reynolds number (re) which is a dimensionless coefficient showing the flow type of the fluid as defined by [ ] ( ) shows that re k,i depends on the changing cloud velocity and droplet diameter at each time step. the settling velocities according to the aforementioned flow regimes are derived in the appendix. the result of these derivations are given by [ ] v s k,i = airborne pathogen transmission via droplets is infectious, since emitted pathogen-laden droplets can be sensed by nose, mouth and eyes [ ] , [ ] . hence, the human face is where the sensing of the infectious pathogens mostly occurs. even if the pathogens are not directly received via the facial sensory organs, it is possible to become infected by directly touching the face and sensory organs consecutively. with this motivation, the cross-sectional area of the central part of the human face is considered as the rx cross-section as shown in fig. . moreover, a receiver model is proposed for the reception of droplets as shown in fig. . as the first step of the reception, the droplets in the vicinity of the rx is sensed by the human, which is defined as the signal reconstruction. different signal reconstruction models for a sensor in macroscale and a nanomachine in microscale are proposed in [ ] and [ ] , respectively. as given in fig. , the rx is assumed to be the cross-section of the human face. in order to determine a circular cross-section area (a r ) for the rx by encompassing the eyes, mouth and nose, a right-angled triangle whose sides are biocular (biectocanthus) breadth (β bb ), sellion-stomion length (β ss ) and the diameter of the receiver cross-section ( r r ) as the hypotenuse side is formed as depicted in fig. . here, β bb is the length of the line connecting the outer end points of the left and right eyes (eyelid junctions) and β ss is the vertical distance between the eye and mouth [ ] . hence, the radius of the cross-sectional area of the rx (r r ) is given as r r = ( β bb + β ss )/ . when the cloud is transmitted via sneezing/coughing, there are three cases for the interaction of the rx and the cloud of droplets with diameter d k whose centers are at the positions for the i th time step (x r ,y r ,z r ) and (x k,i ,y k,i ,z k,i ), respectively. the relation between the -d cartesian coordinates and curvilinear s-axis is detailed in the next subsection. in the first case, the cloud and rx do not coincide and there is no reception. the other two cases include the reception of droplets. as illustrated in fig. , when the cloud and rx coincide, the reception of droplets is related with the cross-sectional area of the cloud at x k,i = x r (a cs k,i ), a r and their intersection area (a rc k,i ). the second case occurs when the intersection area is less than or equal to the cross-sectional area of the rx, i.e., a rc k,i < a r . in the last case, the cloud encompasses the rx, i.e., for the case shown in fig. , a rc k,i can be derived by calculating the intersection area of two circles as given by ( ) [ ] where the distance between the centers of a rc k,i and a r (d rc k,i ) is defined as given below. the received number of droplets can be derived by multiplying the time step (∆t) with the flow rate of the droplets (j in number of droplets/s) at each time step. since the rx senses the droplets proportional to a rc k,i , the received signal after the signal reconstruction step for the aforementioned cases at each time step by recalling ( ) is expressed as where a rc k,i = πr rc k,i , a r = πr r , η = π/ and the volume is ηr k,i for the spherical cloud. as the time elapses, the cumulative exposure to the pathogen-laden droplets at the rx can be modeled by the cumulative sum (integration) of droplets with respect to time subsequent to the signal reconstruction step as given in fig. . afterwards, the signal is quantized, since the rate of the change in the mean number of droplets may not be an integer. the number of droplets after the cumulative sum is rounded to the nearest integer in the quantization step. the received signal after the quantization step is given by here, the mean received number of droplets after the quantization step for the k th droplet diameter at the i th time step (n r k,i ) is defined as where . shows the floor function which maps a variable to the integer less than or equal to this variable. the addition with within the floor function in ( ) quantization by rounding the number of received droplets to the nearest integer. subsequent to quantization, the infection state of the human needs to be determined as the output of the system as shown by figs. and . therefore, the detection is essential according to a threshold value (γ) as the last step of the reception. physically, γ corresponds to the quantity of pathogen-laden droplets that suffice to make a human infected. furthermore, γ depends on the immune system of a human. thus, detection via the threshold γ enables to quantify the strength of the human immune system and to handle the determination of the infection state as a detection problem. hence, the infection state (or the received symbol) can be expressed by binary hypothesis testing which is given as where the hypotheses h and h are defined as the situations of no infection as the received symbol and infection as the received symbol , respectively. here, the received symbol sequence with m samples is represented as h = [h , h , ..., h m ] which also gives the end-to-end system response. in this part, the way to obtain the output of the end-to-end system model by employing the derivations made up to here is clarified in the proposed algorithm . before the procedure starts, the initial parameters such as the number of droplet sizes (k), total simulation time (t s ), initial number of droplets for each droplet size (n ( ,..k), ), initial momentum (i ), initial net buoyant force (f ), initial velocity of the cloud (v c ), rx dimensions (β bb , β ss ) and initial positions of the tx and rx are taken as the input. in the algorithm, the propagation, changing number of droplets in the cloud and their interaction with the rx are handled separately at each time step for each droplet size d k . as the first step of the algorithm, the trajectory of the spherical cloud is calculated for each time step, i.e., the distance on the s-axis and θ values for t = t i are calculated by ( ) and ( ) . then, the updated position of the cloud on the s-axis is utilized to find its step length (∆s). as shown in fig. , ∆s can be employed to express the step lengths on x (∆x) and y axes (∆y) as given by ∆x = ∆s cos(θ k,i ), ∆y = ∆s sin(θ k,i ), where ∆x and ∆y values are used to update the cloud position on the corresponding axis. since there is not any acting force on z-axis, the center of the cloud maintains its position on this axis. however, the cloud expands on x, y and z axes linearly due to the relation r k,i = α e s k,i as given in section ii-a. algorithm algorithm of the end-to-end system model : input: k, t s , ∆t, v c , i , f , ρ a , ρ d , ρ f , µ a , α e , g, d ( ,...,k) , n ( ,...,k), , θ , β bb , β ss , initial positions of the tx and rx, : t = : ∆t : t s : for k = : : k do : for i = : : length(t) do : step : trajectory : calculate s k,i by the real positive root of ( ) x k,i = x k,i− + ∆x; y k,i = y k,i− + ∆y : step : number of droplets in the cloud : v c k,i = ∆s/∆t : calculate v s k,i according to re k,i by ( )-( ) : calculate ∆λ by ( ) : step : reception : if (x r − r k,i ) < x k,i < (x r + r k,i )) then : calculaten r k,i by ( ) : ( ) in the second step of algorithm , the mean number of droplets in the propagating cloud is calculated. to this end, the cloud velocity (v c k,i ) at the corresponding time step is calculated by the displacement on s-axis. then, settling velocity (v s k,i ) is determined by ( )-( ) according to re k,i which is calculated by using v c k,i and droplet size. v s k,i is exploited to calculate the change in the mean number of droplets (∆λ) and thus, the mean number of droplets is updated according to this change. here, the flow type of the cloud found by employing the velocity of droplets affects the number of droplets in the cloud. the third step of algorithm describes the reception via the interaction of the cloud with the rx. when the cloud comes to a sufficient distance to interact with the rx, the radius of the cloud's circular cross-section (r cs k,i ) is determined by the geometrical relation with the the radius of the cloud and the positions of the tx and rx on the x-axis as given by which allows us to calculate the circular area of the cloud's cross-section (a cs k,i ). during the reception, the case that a cs k,i ≤ a r can also be represented in terms of radii of the circles and the distance between them such that (r cs k,i − r r ) < d rc k,i < (r cs k,i + r r ). in addition, the case for the cloud encompassing the rx (a cs k,i > a r = a rc k,i ) can be expressed as d rc k,i < (r cs k,i − r r ). using these conditions, the mean number of droplets given in ( )- ( ) is calculated. then, the detection is made according to the threshold γ in order to determine the infection state. next, the probability of infection is derived by using the end-to-end system model. the probabilistic approach which is considered in the system model enables the derivation of the probability of infection of a human exposed to a sneeze or cough. to this end, it is essential to derive the probability density function (pdf) of the received number of droplets before the detection. as given in section ii-b, the number of droplets in the cloud is a gaussian random variable for the droplet diameter of d k and i th time step, i.e., n k,i ∼ n (λ k,i , λ k,i ). hence, its pdf (f n (n k,i )) is given by since the received number of droplets before the detection (n ri ) is a function of n k,i as given in ( )- ( ) , its pdf (f n r (n ri )) is given in ( )-( ). the probability of infection corresponds to the situation where n ri > γ as given by the solution for ( ) can be derived for the pdf given in ( )- where Ω and Ω are defined as the derived probability of infection and the system model given in the previous section can be employed to analyze the dynamics of the pathogen transmission as given with the numerical results in the next section. in this section, numerical results using the algorithmic endto-end system model and derived probability of infection are given. the values of the experimental parameters are given in table i . except the simulation parameters such as ∆t, t s and the positions of the tx and rx, this table includes measured values which are obtained by empirical studies [ ] , [ ] , [ ] - [ ] . furthermore, the initial number of droplets according to their diameters for a cough is given in table ii . for sneezing, there are not sufficient empirical data in the literature to obtain the parameter values given in table i such as α e and initial velocity [ ] . therefore, although our proposed model is applicable to a sneezing scenario, we only consider a coughing scenario for two static humans where one of them is the tx and the other is rx. for the results in figs. - , the dimensions of the rx are applied by using the average values of male and female humans. namely, β bb and β ss are obtained by calculating the average of the female and male values given in table i . the trajectories of the cloud with respect to rx in -d and -d, respectively. due to initial momentum of coughing and net buoyant force, the cloud propagates in the horizontal and vertical directions, respectively. as also observed in these trajectories, the -d cloud can encompass (or intersect with) the rx and the rx is exposed to droplets during the passage of the cloud. fig. (c) shows the interaction of a human who can be infected with a disease-spreading human by quantifying the number of droplets received from the cloud. the number of droplets are given by their mean and their variations (vertical bars) due to the gaussian distribution. these variations are calculated as three times the standard deviation ( . % confidence interval) for each sample. as observed in fig. (c) , the number of droplets in cloud decreases, since large-sized droplets settle due to the gravity. as mentioned in section ii, the rx gets infected, when the received number of droplets is above γ as plotted in fig. (c) . this figure shows the importance of the exposure time which is the interval of the changing zone in the received signal. if the rx is exposed to the cloud less, it is possible not to be infected, since the received number of droplets can be below the threshold. this interaction is also clarified in fig. by showing the relation of total the infection probability with the distance of the rx to the tx for different propagation time instances. actually, this figure reveals that if the rx is exposed to the cloud for a longer period, the rx is more likely to be infected. different scenarios can be analyzed by employing the infection state, which is the output of the end-to-end system model, for various x r , γ, θ values and male/female receivers. in fig. (a) , the threshold is set to zero to determine the safe zone where there is no possibility of infection. this safe zone starts at x r = . m which also shows the minimum social distance. fig. (c) shows that initial coughing angle affects the infection state severely. for θ values between and − degrees, it is more likely to infect someone due to the buoyant forces affecting the propagation of the cough cloud. therefore, it is safer to cough with an initial angle θ ≤ − • which is depicted as safe coughing angle in fig. (c) . coughing with θ ≥ • may not be safe, since small droplets (aerosols) can suspend in the air and settle eventually due to gravity or drift due to the indoor air currents in the long term. in figs. (a) and (c), the results are indistinguishable for male and female receivers. however, fig. (b) shows that the infection states of female and male humans can be affected differently for the same γ values. actually, this figure reveals that female humans are less likely to get infected, even if their immune system's strength are the same with male humans due to the slight difference in the face dimensions. in this paper, an algorithmic end-to-end system model is proposed for droplet-based communication via coughing/sneezing between two static humans for an indoor sce-nario. the tx emits a cloud which is a mixture of droplets and air and it propagates under the influence of the initial momentum, gravity and buoyancy. a receiver model which defines the central part of the human face as the rx crosssection is proposed for the reception of droplets to give an output of infection state of the rx. the transmitted and received number of droplets are modeled as random processes which lead us to derive the probability of infection. numerical results show that the safe zone for the rx starts at . m for a horizontally coughing tx. it is also revealed that the initial coughing angle of the tx, the distance between the tx and rx and the detection threshold which actually corresponds to the strength of the human immune system are significant parameters to model the airborne pathogen transmission. furthermore, the reception of pathogens can be affected by the sex of the human. as the future work, we plan to extend our study for channel parameter estimation and modeling end-to-end communication for mobile txs and rxs. appendix for a settling droplet, the downwards net force for a spherical droplet at the i th time step with the diameter d k is given as k,i (ρ d −ρ a )g ( ) furthermore, an upward drag force acts in the opposite direction of gravity due to the interaction of the droplet with the air. this upward drag force is given as [ ] f upi = where c d is the drag coefficient. for the settling condition, these upward and downward forces are in equilibrium. hence, we can obtain the settling velocity by equating these two forces and pulling out v s as given by v s k,i = d k,i g(ρ d − ρ a ) ρ d c d . here, c d changes according to re as given by [ ] c when the drag coefficients in ( )-( ) and re in ( ) are substituted into ( ), the settling velocities in ( )-( ) can be obtained. molecular communications and nanonetworks: from nature to practical systems a comprehensive survey of recent advancements in molecular communication tabletop molecular communication: text messages through chemical signals channel and noise models for nonlinear molecular communication systems a universal channel model for molecular communication systems with metal-oxide detectors a fluid dynamics approach to channel modeling in macroscale molecular communication molecular mimo: from theory to prototype a molecular communication link for monitoring in confined environments molecular versus electromagnetic wave propagation loss in macro-scale environments a novel experimental platform for in-vessel multi-chemical molecular communications an experimental platform for macro-scale fluidic medium molecular communication experimental molecular communication testbed based on magnetic nanoparticles in duct flow parameter analysis in macro-scale molecular communications using advectiondiffusion high speed chemical vapor communication using photoionization detectors in turbulent flow mutual information and noise distributions of molecular signals using laser induced fluorescence distance estimation methods for a practical macroscale molecular communication system long range and long duration underwater localization using molecular messaging localization of a passive molecular transmitter with a sensor network fluid dynamics-based distance estimation algorithm for macroscale molecular communication information encoding in droplet-based microfluidic systems: first practical study communication through breath: aerosol transmission modeling of viral aerosol transmission and detection violent expiratory events: on coughing and sneezing airborne spread of expiratory droplet nuclei between the occupants of indoor environments: a review routes of influenza transmission the severe acute respiratory syndrome reducing transmission of sars-cov- fundamentals of fluid mechanics the size and the duration of air-carriage of respiratory droplets and droplet-nuclei turbulent gravitational convection from maintained and instantaneous sources investigation on optimal spray properties for ground based agricultural applications using deposition and retention models probability, random variables, and stochastic processes. tata mcgraw-hill education the metrics of material and metal ecology: harmonizing the resource, technology and environmental cycles signal reconstruction in diffusion-based molecular communication head and face anthropometry of adult us civilians circle-circle intersection study on transport characteristics of saliva droplets produced by coughing in a calm indoor environment toward understanding the risk of secondary airborne infection: emission of respirable pathogens revised formula for the density of moist air a schlieren optical study of the human cough with and without wearing masks for aerosol infection control he is currently pursuing the ph.d. degree in zmir institute of technology, zmir, turkey as a research/teaching assistant under the supervision of assoc. prof. dr. bar atakan. his research interests include micro and macroscale molecular communications and molecular networks key: cord- -qav yb p authors: li, xiangdong; shang, yidan; yan, yihuan; yang, lin; tu, jiyuan title: modelling of evaporation of cough droplets in inhomogeneous humidity fields using the multi-component eulerian-lagrangian approach date: - - journal: build environ doi: . /j.buildenv. . . sha: doc_id: cord_uid: qav yb p this study employed a multi-component eulerian-lagrangian approach to model the evaporation and dispersion of cough droplets in quiescent air. the approach is featured with a continuity equation being explicitly solved for water vapor, which allows comprehensively considering the effects of inhomogeneous humidity field on droplets evaporation and movement. the computational fluid dynamics (cfd) computations based on the approach achieved a satisfactory agreement with the theoretical models reported in the literature. the results demonstrated that the evaporation-generated vapor and super-saturated wet air exhaled from the respiratory tracks forms a “vapor plume” in front of the respiratory track opening, which, despite the short life time, significantly impedes the evaporation of the droplets captured in it. the study also revealed that due to the droplet size reduction induced by evaporation, both the number density of airborne droplets and mass concentration of inhalable pathogens remarkably increased, which can result in a higher risk of infection. parametric studies were finally conducted to evaluate the factors affecting droplet evaporation. summary: the study demonstrated the importance of considering inhomogeneous humidity field when modelling the evaporation and dispersion of cough droplets. the multi-component eulerian-lagrangian model presented in this study provides a comprehensive approach to address different influential factors in a wide parametric range, which will enhance the assessment of the health risks associated with droplet exposure. transmissible respiratory diseases such as influenza, tuberculosis (tb) and severe acute respiratory syndromes (sars) are serious threats to the public health due to their high morbidity and mortality. the survey by palache et al. [ ] estimated that the influenza a virus (iav) alone causes around million infection cases globally every year, resulting in , to , annual deaths. since the airborne routes play a key role in spreading respiratory pathogens from person to person, an enhanced understanding of pathogen transmission via aerosolized sputum and saliva droplets is vital to the public health measures aiming at reducing infection risks. droplets generated from human respiratory activities are distributed in a wide size range. according to the experimental measurements by gralton et al. [ ] , the droplets generated from human coughing, sneezing and talking are mostly between nm and μm. the diameter is a critical parameter determining the fate of the droplets because droplets larger than μm would quickly settle while those smaller than μm could become airborne and have the chance to be inhaled [ ] . for airborne droplets, their movement could be dominated by the inertial and gravitational effects or the airflow, depending on the droplet size and air velocity [ ] . in addition, studies on particle deposition in human airways [ ] have proven that particles larger than μm tend to impact onto the surface of upper airways while those smaller than μm are more likely to penetrate deeper into the lower airways and pulmonary region. some investigators [ , ] hence recommended μm as a cut-off diameter to delineate upper and lower respiratory tract infections. apparently, appropriate characterization of droplet size is of great importance to the assessment of health risks based on droplet trajectories [ ] , and to the analyses of individual health hazards associated with particulate exposure. respiratory droplets are composed of water and a small amount of non-volatile compounds including sodium chloride, carbohydrate, lipids, protein and microorganisms [ , ] . after being expelled, water in the droplets would gradually evaporate and finally leave behind the non-volatile components to form solid droplet nuclei. the equilibrium diameter of a completely desiccated droplet nucleus d d,e is correlated to its initial diameter d d, by ref. [ ] . a common estimation of the droplet density and initial concentration of non-volatile compounds is ρ nv = kg/m and c nv = . % [ ] , which results in an equilibrium diameter of d d,e = . d d, . this means that as water evaporates, some free-falling large droplets could become airborne [ ] , leading to an elevated number density of inhalable droplets in the breathing zone and an increased probability of infection [ , ] . the evaporation of droplets is driven by the equilibrium vapor pressure on the droplet surface relative to the partial pressure of water vapor in the ambient air [ ] . this process is strongly controlled by the droplets specific area and ambient conditions including the air temperature, humidity and turbulence. the calculation by wei and li [ ] revealed that a droplet with an initial diameter of μm needed only . s to reach its equilibrium diameter in dry air ( % relative humidity, rh) while a -μm droplet required over s to complete the same process in % rh air. given that the size of a droplet significantly determines its movement and fate, plus the fact that the viability of viruses within the droplet is affected by the moisture content and temperature [ , ] , an effective modelling of the time-dependent droplet size is crucial to the assessment of health risks associated with droplets exposure, for both the public and individual interests. despite the importance of droplets in transmitting respiratory disease has long been recognized, the theoretical models and experimental data on respiratory droplets are still very scarce, particularly in terms of the evaporation and dispersion. the classic wells evaporation-falling curve ( ) [ ] was widely used to estimate the droplet size as a function of time. however, xie et al. [ ] suspected that the curve was plotted based on experimental results through extrapolation using various inappropriate assumptions. in recent years, a couple of mathematic models [ , , , ] were developed in which the effects of respiratory jets, air turbulence, droplet salinity and ambient humidity were partially considered. however, most of these models simply ignored the inhomogeneous humidity field induced by the evaporating droplets and the supersaturated water vapor exhaled from the respiratory tracts. although some theoretical models, such as that of chao and wan [ ] , employed a transportable scalar to model the concentration diffusion of water vapor in air, the effects of inhomogeneous water vapor concentration on droplet evaporation were not fully addressed. in fact, the inhomogeneous vapor concentration, particularly in the immediate vicinity of the droplets, may have a strong effect on the droplet trajectories through changing the time-size relationship. in addition, the transport characteristics of water vapor in the air may be subjected to many factors including the air pressure and temperature, as well as the vapor concentration itself [ ] . a transportable scalar may be inappropriate to model the transport behaviours. this is particularly true when the local vapor concentration is high. in order that droplet evaporation and transport could be modelled in a systematic way, the diffusion of water vapor in the air needs to be modelled mechanistically. in this study, the multi-component eulerian-lagrangian approach was employed to realize a mechanistic modelling. compared with the existing models reported in the literature, the approach is unique as a continuity equation was explicitly solved for the water vapor. although droplets can be expelled through various respiratory activities such as breathing, coughing, sneezing and talking, only cough was considered in this study as it is a common symptom of most respiratory infections and the major source of pathogen-carrying droplets in indoor air [ ] . other important factors including the exhaled humidity, expelled droplets amount, ambient humidity and temperature were also discussed. in the multi-component eulerian model, the wet air is treated as an ideal mixture composed of dry air and water vapor. all the thermodynamic properties of the mixture are calculated by where, the subscripts m, a and v denote the air-vapor mixture, dry air and water vapor, respectively. φ represents a property parameter (φ = ρ, μ, λ, c p , etc) and f is the mass fraction (f a + f v = ). to capture the transport characteristics of water vapor through the air, continuity equations for the dry air and water vapor are solved separately where, ⇀ u m is the mass-averaged mixture velocity. s v is the mass source of water vapor due to droplets evaporation. d k is the kinematic diffusivity of water vapor in the air. since air and water vapor are mixed at the molecular level, it's safe to assume they share the same local velocity, pressure and temperature, which allows solving only one momentum and energy equation for the mixture m m m m m m m md ( ) where, s buoy is the momentum source due to buoyancy, ⇀ f md is the interfacial forces acting on the droplet interfaces, ∇p is the pressure gradient, h m is the mixture enthalpy, t m is the mixture temperature and q md is the interphase heat transfer rate across the droplet interfaces. for a unit control volume containing n droplets, the interfacial heat transfer rate between the phases is calculated by where, d d is the droplet diameter, t d is the droplet temperature and h md is the interfacial heat transfer coefficient estimated according to ranz and marshall [ ] . where, re d and pr m are the droplet reynolds number and the mixture prandtl number, respectively. the movement of droplets is tracked using the lagrangian approach. for micron-sized droplets with a density much higher than that of the carrying fluid, the interfacial forces depending on the density ratio are negligibly small [ ] . therefore, only the buoyancy force ⇀ f and buoy drag force ⇀ f d are considered and the equation of droplet motion is defined by where, ⇀ u d is the droplet velocity. the turbulent dispersion of droplets was modelled in this study by adding a turbulence fluctuating component, which is correlated to the turbulence kinetic energy k and a normally distributed random number Φ, onto the mixture velocity. the expelled saliva/phlegm droplets are assumed to be composed of . % water and . % non-volatile solid compounds, according to nicas et al. [ ] . the evaporation of water is controlled by the equilibrium vapor pressure at the droplet surface relative to the ambient pressure. when the effects of non-volatile compounds were ignored, the equilibrium vapor pressure at the droplet surfaces is calculated using the antoine equation where, p scale is the pressure scale. a, b and c are the antoine constants. when p scale = . bar, the constants take values of a = . , b = . and c = − . according to bridgeman and aldrich [ ] . for droplets suspended in common indoor air, their evaporation is subject to the diffusion mechanism and the mass transfer rate is calculated by where, d dyn is the dynamic diffusivity of water vapor in the continuum. sh is the sherwood number [ ] . m v and m m are the molecular weights of the vapor and the mixture, respectively. x v,s is the equilibrium mole fraction of water vapor at the droplet surface and x v,m is the local mole fraction of water vapor in the mixture, which can be represented by the partial pressures of water vapor at the droplet surface p e,v and in the mixture p v , respectively. when the temperature gradient inside a droplet is ignored, the temperature decrease of the droplet due to the latent heat of phase change is expressed by a chamber representing a cuboid space in front of a coughing person was assumed, as shown in fig. . the chamber was created big enough ( m-length × m-width × m-height) so that the airflow was free from the effects of the no-slip chamber walls. no ventilation was designed in order to create a quasi-quiescent environment. droplets were injected through a nozzle which was located . m above the floor. the diameter of the nozzle was cm representing a coughing human mouth opening. the other end of the chamber opposite to the nozzle was open to the atmosphere, allowing taking into account the ambient conditions such as the air temperature and humidity. non-rebounding boundary conditions were specified at all the solid chamber walls, which acted as a sink term of droplet mass when the droplets hit the walls. due to the symmetric distribution of the airflow field, only half of the chamber was built as the computational domain with the central plane (y = m) being set as a symmetric plane (fig. ) . the domain was then discretized using structured hexahedral grids with very fine mesh applied in the near-wall regions. mesh independence was achieved at , mesh elements because a further increase to , mesh elements only produced a negligible change (less than . %) in the predicted air velocity and vapor concentration profiles along a randomly selected line. the number of droplet trajectories was also analysed. it was found that when the trajectory number was larger than , , the predicted vapor concentration field was free from the number. the model equations were discretized based on a finite-volume method and solved using the commercial cfd code cfx- , together with the rng k-ε model for the air turbulence because of its successful depiction of indoor airflows [ ] . the evaporation of droplets falling freely in quiescent air was firstly simulated for model validation. during the computations, two single droplet seizes ( and μm) and very small droplet mass flow rates ( . × − kg/s for the -μm droplets and . × − kg/s for the -μm droplets, respectively) were used in order to match the computational conditions of wei and li [ ] , who assumed single droplets were released one after another with a time interval of . s. computations were conducted with a constant temperature of °c and different air humidity (rh = % and %) conditions, respectively. the predicted time-dependent droplet diameter (solid lines) was compared against the theoretical calculations (dot points) by wei and li [ ] and redrow et al. [ ] , as shown in fig. . satisfactory agreement was obtained between the numerical results of this study and the data reported in the literature, for the both initial droplet size and air relative humidity. the figures also reveal that the evaporation of droplets is sensitive to the both parameters considered here. firstly, the evaporation rate is strongly affected by the droplet size. smaller droplets evaporate much faster than larger droplets because of the enlarged specific surface area for heat and mass transfer. secondly, the relative humidity of air plays an important role. when the relative humidity increased from % to %, the time required for the droplets to reach their equilibrium diameters tremendously increased from . s to . s ( % increment) for the -μm droplets and from . s to . s ( % increment) for the -μm droplets. it was noted that the above validation computations were conducted with very small droplet mass flow rates ( . × − kg/s and . × − kg/s, respectively). with such small mass flow rates, it was safe to ignore the effects of inhomogeneous humidity field [ ] . however, coughing is featured with an instantaneous pulse airflow carrying water vapor and droplets coming from the respiratory tracts. due to the supersaturated wet air ( % water vapor) and droplets evaporation, the respiratory droplets are factually dispersed in a heterogenous humidity field, particularly in the region close to the respiratory tract openings (mouth and nostrils). apart from that, many other factors including the mass of exhaled droplets, the ambient temperature and humidity could have significant effects on the process of droplet evaporation, resulting in different time-size correlation and droplet dispersion trajectories. in this section, parametric studies were performed to evaluate the effects of each individual factor. in order to capture the dynamic characteristics of cough and droplets evaporation, transient simulations were conducted. a pulse air jet representing a single cough was applied at the nozzle according to the experimental data of gupta et al. [ ] . the pulse air jet had a time duration of . s and a peak flow rate of . l/s at t = . s (fig. (a) ), which generated a peak air velocity of . m/s at the nozzle. droplets were injected into the domain with the same instantaneous velocity of the pulse airflow. given that the droplets expelled by human cough are dispersed in a wide size range, the number and mass probability density distributions of droplets between and μm (fig. (b) ), which were measured mm in front of the mouth opening by chao et al. [ ] , were employed to specify the droplet injection conditions. it was noticed from fig. (b) that over % of the droplets expelled by a human cough are smaller than μm. however, these small droplets only account for around . % of the expelled liquid mass. for the purpose of comparison, a baseline computation (case ) was firstly conducted without considering the inhomogeneous humidity field, namely, f v = and eq. ( ) being not solved. then, the evaporation-generated water vapor and exhaled water vapor ( % mass concentration [ ] ) was progressively added to case (case and ) . finally, computations were also conducted to parametrically evaluate the effects of the expelled droplet mass (case - ) and ambient temperature (case , - ) and humidity (case , and ). the boundary conditions of each computational case are listed in table . during the computations, very small-time steps ( . s) were used in the beginning in order to capture the instantaneous cough jet ( . s). the time steps then gradually increased up to . s. the total droplet tracking time was s, which took around h to run a single simulation on a workstation with cpu cores ( . g hz intel ® xeon ® ) and gb ram. the effects of locally elevated water vapor concentration on the evaporation and dispersion of droplets were analysed through comparing the results yielded from case , and . the predicted transient air velocity vectors and water vapor concentration contours in a small rectangular area ( m-length × . m-height) next to the nozzle are shown in fig. (case ) . the results revealed that the cough created a strong pulse air jet, which, however, quickly faded away in the quiescent air. the maximum air velocity decreased from . m/s at t = . s s down to . m/s at t = . s, . m/s at t = . s and further down to . m/s at t = . s. the cough also remarkably elevated the local air humidity due to the exhaled wet air, creating an instantaneous "vapor plume" in which the vapor concentration is significantly higher than that in the bulk air. fig. shows that the vapor plume, analogous to the air jet, also quickly dissipated so that at t = . s no significant gradients of vapor concentration can be observed. however, despite its short life, the vapor plume was found to have a significant effect on the evaporation and dispersion characteristics of droplets, particularly on those of the small droplets. shown in fig. are the droplet trajectories predicted without and with vapor transport (case and ) , respectively. the results show that the diameter of μm acted as a critical size for droplet movement as droplets smaller than μm were steadily suspended in the air and dispersed by the air turbulence, while the movement of droplets larger than μm was jointly controlled by the gravitational and inertial effects. as shown in fig. , droplets larger than μm were free falling and quickly settled onto the floor following smooth trajectories analogous to parabolic curves. the locally elevated air humidity seemed to have no noticeable effects on the trajectories of these large droplets. thus, the diameter of μm can be treated as a cut-off size to delineate airborne and free-falling droplets, which is in accordance with the recommendation of weber and stilianakis [ ] . however, for the airborne droplets with diameter smaller than μm, the inclusion of vapor transport in the computational model could result in different predictions of evaporation and dispersion. as shown in fig. , when the inhomogeneous humidity field was considered, the airborne droplets were predicted to travel faster and further than predicted without water vapor transport. when the transport equation of water vapor (eq. ( )) was included, the airborne droplets were predicted to have travelled up to . m at the end of the cough (t = . s), which was % larger than the maximum travelling distance ( . m) predicted without vapor transport. although the airborne droplets soon lost their momentum due to the decreasing air velocity, the predicted particle travelling distance was still % larger at t = . s when the inhomogeneous humidity was considered. referring to fig. , it seems that the locally elevated air humidity is beneficial for maintaining the droplets' momentum and inertia. it was noted the "droplet plume" in fig. had a comparable size to that of the "vapor plume" in fig. . this means that the airborne droplets were completely located in humid air in the following few seconds after a cough, which can certainly hinder their evaporation. fig. shows the size variation of the -μm droplets after expulsion. when the inhomogeneous humidity field was ignored (case ), the droplet median evaporation time was only . s. the evaporation rates of all the droplets were predicted to be similar, so that the time-dependent droplet sizes were distributed in a narrow area near their average value. in addition, the curves of the average and median sizes were almost overlapping with each other, meaning that the droplets were predicted to evaporate at the same speed. however, when the inhomogeneous humidity field induced by droplets evaporation was considered (case ), the median evaporation time was significantly prolonged ( . s). the time-dependent droplet sizes were predicted to be dispersed in a much wider range, suggesting different evaporating rates of the droplets despite the same initial diameter. as shown in fig. (b) , some droplets only needed . s to completely evaporate while some others spent as much as . s to accomplish the same process. because of this, the average droplet size was predicted to decrease significantly slower than the median size. finally, the inclusion of the exhaled humidity further decreased the predicted droplets evaporation rate (fig. (c) ), particularly the droplet median evaporation time was significantly prolonged. the effects of inhomogeneous humidity field on the time-dependent median size and temperature of two selected groups of droplets ( -μm and -μm) are shown in fig. . when the evaporation-induced humidity was considered, the time required for % of the -μm droplets to completely evaporate increased from . s to . s ( % increment), which further increased to . s when the exhaled vapor was added ( % additional increment). comparatively, the time-dependent size of the -μm droplets was not significantly affected by the inhomogeneous humidity field, probably because the travelling speed of this group of droplets was larger than that of vapor dispersion (refer to figs. and ) , so that they were travelling outside the vapor plume and their evaporation was not affected by the locally elevated water vapor concentration. fig. clearly demonstrates that the comprehensive consideration of the inhomogeneous humidity field is critical to an effective modelling of droplet evaporation and dispersion. therefore, both the exhaled water vapor and evaporation-generated water vapor were included in the following computational cases. the effects of exhaled droplets amount were also investigated (case - ). although the experimental data on how much salivary or phlegmy droplets can be expelled by a single cough is still unavailable in the open literature, it is reasonable to estimate that this amount could be as high as hundreds of milligrams according to the high-speed ccd images (fig. ) of bourouiba et al. [ ] . therefore, computations were conducted with three different droplet masses ( , and mg) corresponding to mild, moderate and severe coughs, respectively. fig. shows the contour maps and droplet trajectories predicted with different droplet masses. only the trajectories of airborne droplets (smaller than μm) were shown in the figure to improve the illustration clarity. the results firstly revealed that the increased droplet yes yes yes yes yes yes yes yes yes mass noticeably enlarged the size of the high-humidity area and the maximum vapor concentration in the domain. at t = . s when the exhaled humidity had fully dispersed, the evaporation of the droplets was still significantly elevating the local humidity. as shown in fig. (a), the maximum local mass concentration of water vapor reached . % when the droplet mass was mg (case ). if the droplet mass could increase up to mg, the maximum local vapor mass concentration could reach as high as . %, which was the saturated water vapor concentration in the air at the given temperature and pressure conditions ( °c and . kpa). the increased droplet mass also changed the droplet trajectories. as shown in fig. (b) , the gravitational settlement of droplets became more significant. particularly, when the mass flow rate of droplets increased to mg, the droplets presented a remarkably changed distribution pattern, which will certainly result in different risk assessments if the assessments were based on droplet trajectories [ ] . the time-dependent sizes of the representative droplets ( -μm and -μm) are shown in fig. . the results demonstrated that the increased droplet mass significantly prolonged the median evaporation time of the -μm droplets. the time required for % of the -μm droplets to completely evaporate was . , . and . s, respectively, when the exhaled droplet mass was , and mg. however, the -μm droplets seemed unaffected by the droplet mass. computations were also conducted with different ambient conditions. the ambient temperature and humidity ranges were - c°and rh - % (case , - ), respectively. such a wide parametric range was selected to cover the worst-scenario conditions. the time-dependent sizes of the representative droplets predicted with different ambient temperature and humidity are shown in figs. and , respectively. the results demonstrated that the evaporation of droplets, particularly airborne droplets, is sensitive to the both ambient parameters. at a relative humidity of %, the increasing ambient temperature can observably accelerate the droplet evaporation (fig. ) . when the ambient temperature increased from c°to c°, the median evaporation time of the -μm droplets decreased from . s down to . s ( % decrease). although under all the selected ambient temperatures, the -μm droplets did not fully evaporate as they settled quickly onto the floor, their final median size decreased to , , and μm, respectively, when hitting the floor (fig. ) , fig. . droplets expulsion by a human cough [ ] . indicating significant evaporation. the ambient humidity also has a strong effect on the rate of droplet evaporation. as shown in fig. , when the ambient relative humidity decreased from % to %, not only the median evaporation time of the -μm droplets significantly dropped from . s down to . s, but also % of the -μm droplets were completely evaporated within s and became steadily airborne. however, the -μm droplets only slightly evaporated in the rh % air, so that their median diameter was still μm when hitting the floor, which was only . % smaller than their initial size. according to figs. and , it seems that the ambient humidity plays a more important role in affecting the rate of droplet evaporation than the ambient temperature does. the computational results shew that due to the evaporation-induced size reduction, some large free-falling droplets (larger than μm) could become airborne (smaller than μm) and hence improve the number density of inhalable droplets in the domain (fig. ) . some of these new airborne droplets and nuclei could be entrained into the breathing zone by uprising airflows such as the human thermal plume. due to the large mass of pathogens carried in these type of new airborne droplets/nuclei, the possibility of infection can be significantly increased. similarly, some small airborne droplets could further shrink in size, becoming smaller than μm and increasing the probability of lower respiratory tracts infections [ ] . fig. shows the time-dependent number fraction of airborne droplets/nuclei (smaller than μm). the mass fraction of inhalable pathogen, which is defined as the pathogen carried by the airborne droplets/nuclei, is also shown in the figure. it was demonstrated that although the airborne droplets took a predominant number proportion ( . ) of the exhaled droplets, they only accounted for a very small mass fraction ( . × − ) of the total mass of expelled pathogen. when the ambient relative humidity was medium ( fig. (a) , rh %), although the total number fraction of inhalable droplets/nuclei and total mass fraction of inhalable pathogen did not change till s after the cough, the number fraction of small droplets/nuclei (smaller than μm) increased from . to . while the mass fraction of the inhalable pathogens carried by them significantly increased from . × − to . × − , which was an astonishing -fold increase. when the ambient air had a low relative humidity (rh %), the evaporation of droplet was significantly accelerated. as shown in fig. (b) , at time t = s, . % of the exhaled droplets had become airborne, among which % were smaller than μm. correspondingly, the mass fraction of inhalable pathogens sharply increased to . × − with . × − being carried by the droplets/nuclei smaller than μm. compared with the . × − mass fraction yielded from the medium ( %) relative humidity (case ), the . × − mass fraction predicted with the low ( %) relative humidity (case ) was more than times larger. given that the morbidity of many respiratory diseases is strongly related to the exposure dose [ ] , it is expected that the elevated mass concentration of the inhalable pathogen in the air could increase the probability of infection, particularly increase the risk of lower respiratory tract infections. this may also give a useful clue to the mystery why influenza always breaks out in winters [ , ] because of the lower relative humidity in winters. a multi-component eulerian-lagrangian model was presented in this study to model the evaporation and dispersion of cough droplets in quasi-quiescent air. the model features a water vapor transport equation which is capable of taking into account the inhomogeneous humidity field. a number of computations with various cough and environmental conditions were conducted to evaluate the critical parameters affecting the evaporation and dispersion of cough droplets. the conclusions arising from this study are as follows: ) the inhomogeneous humidity field induced by vapor exhalation and droplet evaporation has a strong effect on the characteristics of droplet evaporation and dispersion. when the transport of evaporation-induced water vapor and exhaled water vapor was progressively included in the computational model, the predicted median evaporation time of the -μm droplets significantly increased. it was demonstrated that the exhaled water vapor can form a "vapor plume" in front of the respiratory tract opening. despite its short life time (only a few seconds), the vapor plume is big enough to contain all the airborne droplets and significantly impedes their evaporation. consequently, the airborne droplets were predicted to travel faster when the inhomogeneous humidity diffusion was included. comparatively, the evaporation of droplets larger than μm is insensitive to the vapor plume, probably because their travelling speed is larger than the dispersion speed of the vapor plume so that they are mostly located outside the vapor plume. ) the mass of exhaled liquid and the ambient temperature and humidity all have their effects on the droplet evaporation rate and dispersion pattern. comparatively, the ambient humidity plays a critical role. ) evaporation causes the droplet sizes to decrease, making some freefalling droplets become airborne and some airborne droplets become small enough to penetrate into the lower airways. consequently, both the number density of airborne droplets/nuclei and the mass concentration of inhalable pathogens can be significantly increased, resulting in higher infection risks, particularly higher infection risks of the lower respiratory tracts. seasonal influenza vaccine dose distribution in countries ( - ): little progress in estimated global vaccination coverage the role of particle size in aerosolised pathogen transmission: a review inactivation of influenza a viruses in the environment and modes of transmission: a critical review numerical investigation of micron particle inhalation by standing thermal manikins in horizontal airflows detailed predictions of particle aspiration affected by respiratory inhalation and airflow effect of human movement on airborne disease transmission in an airplane cabin: study using numerical modeling and quantitative risk analysis modeling the evaporation and dispersion of airborne sputum droplets expelled from a human cough toward understanding the risk of secondary airborne infection: emission of respirable pathogens evaporation and dispersion of respiratory droplets from coughing numerical investigation of particle transport and inhalation using standing thermal manikins review of aerosol transmission of influenza a virus a probabilistic transmission dynamic model to assess indoor airborne infection risks enhanced spread of expiratory droplets by turbulence in a cough jet influenza and humidity -why a bit more damp may be good for you! on air-borne infection -study ii droplets and droplet nuclei how far droplets can move in indoor environments -revisiting the wells evaporation-falling curve a study of the dispersion of expiratory aerosols in unidirectional downward and ceiling-return type airflows using a multiphase approach transport of water vapor through the atmospheric boundary layer a -deepak, adarsh flow dynamics and characterization of a cough evaporation from drops particle inhalation and deposition in a human nasal cavity from the external surrounding environment vapor pressure tables for water evaluation of various categories of turbulence models for predicting air distribution in an airliner cabin characterization of expiration air jets and droplet size distributions immediately at the mouth opening a hydrogen peroxide sensor for exhaled breath measurement violent expiratory events: on coughing and sneezing evaluation of airborne disease infection risks in an airliner cabin using the lagrangian-based wells-riley approach particulate air-pollution as a predictor of mortality in a prospective-study of us adults dynamics of airborne influenza a viruses indoors and dependence on humidity the financial supports provided by the railway manufacturing crc of australia (project id: r . . ), natural science foundation of china (grant no. ) and australian research council (project id: dp ) are gratefully acknowledged. key: cord- -ohkki ke authors: verma, siddhartha; dhanak, manhar; frankenfield, john title: visualizing the effectiveness of face masks in obstructing respiratory jets date: - - journal: phys fluids ( ) doi: . / . sha: doc_id: cord_uid: ohkki ke the use of face masks in public settings has been widely recommended by public health officials during the current covid- pandemic. the masks help mitigate the risk of cross-infection via respiratory droplets; however, there are no specific guidelines on mask materials and designs that are most effective in minimizing droplet dispersal. while there have been prior studies on the performance of medical-grade masks, there are insufficient data on cloth-based coverings, which are being used by a vast majority of the general public. we use qualitative visualizations of emulated coughs and sneezes to examine how material- and design-choices impact the extent to which droplet-laden respiratory jets are blocked. loosely folded face masks and bandana-style coverings provide minimal stopping-capability for the smallest aerosolized respiratory droplets. well-fitted homemade masks with multiple layers of quilting fabric, and off-the-shelf cone style masks, proved to be the most effective in reducing droplet dispersal. these masks were able to curtail the speed and range of the respiratory jets significantly, albeit with some leakage through the mask material and from small gaps along the edges. importantly, uncovered emulated coughs were able to travel notably farther than the currently recommended -ft distancing guideline. we outline the procedure for setting up simple visualization experiments using easily available materials, which may help healthcare professionals, medical researchers, and manufacturers in assessing the effectiveness of face masks and other personal protective equipment qualitatively. infectious respiratory illnesses can exact a heavy socioeconomic toll on the most vulnerable members of our society, as has become evident from the current covid- pandemic. , the disease has overwhelmed healthcare infrastructure worldwide, and its high contagion rate and relatively long incubation period , have made it difficult to trace and isolate infected individuals. current estimates indicate that about % of infected individuals do not display overt symptoms and may contribute to the significant spread of the disease without their knowledge. in an effort to contain the unabated community spread of the disease, public health officials have recommended the implementation of various preventative measures, including social-distancing and the use of face masks in public settings. the rationale behind the recommendation for using masks or other face coverings is to reduce the risk of cross-infection via the transmission of respiratory droplets from infected to healthy individuals. , the pathogen responsible for covid- is found primarily in respiratory droplets that are expelled by infected individuals during coughing, sneezing, or even talking and breathing. [ ] [ ] [ ] [ ] [ ] [ ] apart from covid- , respiratory droplets are also the primary means of transmission for various other viral and bacterial illnesses, such as the common cold, influenza, tuberculosis, sars (severe acute respiratory syndrome), and mers (middle east respiratory syndrome), to name a few. [ ] [ ] [ ] [ ] these pathogens are enveloped within respiratory droplets, which may land on healthy individuals and result in direct transmission, or on inanimate objects, which can lead to infection when a healthy individual comes in contact with them. , , , in another mode of transmission, the droplets or their evaporated contents may remain suspended in the air for long periods of time if they are sufficiently small. this can lead to airborne several studies have investigated respiratory droplets produced by both healthy and infected individuals when performing various activities. the transport characteristics of these droplets can vary significantly depending on their diameter. [ ] [ ] [ ] [ ] [ ] [ ] the reported droplet diameters vary widely among studies available in the literature and usually lie within the range μm- μm, with a mean diameter of ∼ μm. the larger droplets (diameter > μm) are observed to follow ballistic trajectories under the effects of gravity and aerodynamic drag. , intermediate-sized droplets , , may get carried over considerable distances within a multiphase turbulent cloud. [ ] [ ] [ ] the smallest droplets and particles (diameter < μm- μm) may remain suspended in the air indefinitely, until they are carried away by a light breeze or ventilation airflow. , after being expelled into the ambient environment, the respiratory droplets experience varying degrees of evaporation depending on their size, ambient humidity, and temperature. the smallest droplets may undergo complete evaporation, leaving behind a dried-out spherical mass consisting of the particulate contents (e.g., pathogens), which are referred to as "droplet nuclei." these desiccated nuclei, in combination with the smallest droplets, are potent transmission sources on account of two factors: ( ) they can remain suspended in the air for hours after the infected individual has left the area, potentially infecting unsuspecting individuals who come into contact with them and ( ) they can penetrate deep into the airways of individuals who breathe them in, which increases the likelihood of infection even for low pathogen loads. at present, the role of droplet nuclei in the transmission of covid- is not known with certainty and the matter is the subject of ongoing studies. [ ] [ ] [ ] in addition to generating microscopic droplets, the action of sneezing can expel sheet-like layers of respiratory fluids, which may break apart into smaller droplets through a series of instabilities. the majority of the fluid contained within the sheet falls to the ground quickly within a short distance. regardless of their size, all droplets and nuclei expelled by infected individuals are potential carriers of pathogens. various studies have investigated the effectiveness of medical-grade face masks and other personal protective equipment (ppe) in reducing the possibility of cross-infection via these droplets. , , [ ] [ ] [ ] [ ] [ ] [ ] [ ] notably, such respiratory barriers do not prove to be completely effective against extremely fine aerosolized particles, droplets, and nuclei. the main issue tends to be air leakage, which can result in aerosolized pathogens being dispersed and suspended in the ambient environment for long periods of time after a coughing/sneezing event has occurred. a few studies have considered the filtration efficiency of homemade masks made with different types of fabric; - however, there is no broad consensus regarding their effectiveness in minimizing disease transmission. , nonetheless, the evidence suggests that masks and other face coverings are effective in stopping larger droplets, which, although fewer in number compared to the smaller droplets and nuclei, constitute a large fraction of the total volume of the ejected respiratory fluid. while detailed quantitative measurements are necessary for the comprehensive characterization of ppe, qualitative visualizations can be invaluable for rapid iteration in early design stages, as well as for demonstrating the proper use of such equipment. thus, one of the aims of this letter is to describe a simple setup for visualization experiments, which can be assembled using easily available materials. such setups may be helpful to healthcare professionals, medical researchers, and industrial manufacturers, for assessing the effectiveness of face masks and other protective equipment qualitatively. testing designs quickly and early on can prove to be crucial, especially in the current pandemic scenario where one of the central objectives is to reduce the severity of the anticipated resurgence of infections in the upcoming months. the visualization setup used in the current study is shown in fig. and consists of a hollow manikin head which was padded on the inside to approximate the internal shape and volume of the nasal-and buccal-cavities in an adult. in case a more realistic representation is required, such a setup could include d-printed or silicone models of the internal airways. the manikin was mounted at a height of ∼ ft and in. to emulate respiratory jets expelled by an average human male. the circular opening representing the mouth is . in. in diameter. the pressure impulse that emulates a cough or a sneeze may be delivered via a manual pump, as shown in fig. , or via other sources such as an air compressor or a pressurized air canister. the air capacity of the pump is ml, which is comparable to the lower end of the total volume expelled during a cough. we note that the setup here emulates a simplified representation of an actual cough, which is an extremely complex and dynamic problem. we use a recreational fog/smoke machine to generate tracer particles for visualizing the expelled respiratory jets, using a liquid mixture of distilled water ( parts) and glycerin ( part). both the pressure-and smoke-sources were connected to the manikin using clear vinyl tubing and npt fittings wherever necessary. the resulting "fog" or "smoke" is visible in the right panel of fig. and is composed of microscopic droplets of the vaporized liquid mixture. these are comparable in size to the smallest droplets expelled in a cough jet (∼ μm- μm). we estimate that the fog droplets are less than μm in diameter, based on stokes' law and our observation that they could remain suspended for up to min in completely still air with no perceptible settling. the laser source used to generate the visualization sheet is an off-the-shelf mw green laser pointer with nm wavelength. a plane vertical sheet is created by passing the laser beam we first present visualization results from an emulation of an uncovered heavy cough. the spatial and temporal evolution of the resulting jet is shown in fig. . the aerosolized microscopic droplets visible in the laser sheet act as tracer particles, revealing a twodimensional cross section of the conical turbulent jet. these tracers depict the fate of the smallest ejected droplets and any resulting nuclei that may form. we observed high variability in droplet dispersal patterns from one experimental run to another, which was caused by otherwise imperceptible changes in the ambient airflow. this highlights the importance of designing ventilation systems that specifically aim to minimize the possibility of cross-infection in a confined setting. , [ ] [ ] [ ] despite high variability, we consistently observed jets that traveled farther than the -ft minimum distance proposed by the u.s. centers for disease control and prevention (cdc's). in the images shown in fig. , the ejected tracers were observed to travel up to ft within ∼ s. moreover, the tracer droplets remained suspended midair for up to min in the quiescent environment. these observations, in combination with other recent studies, , suggest that current social-distancing guidelines may need to be updated to account for the aerosol-based transmission of pathogens. we note that although the unobstructed turbulent jets were observed to travel up to ft, a large majority of the ejected droplets will fall to the ground by this point. importantly, both the number and concentration of the droplets will decrease with increasing distance, which is the fundamental rationale behind socialdistancing. we now discuss dispersal patterns observed when the mouth opening was blocked using three different types of face masks. for these results, we focus on masks that are readily accessible to the general public, which do not draw away from the supply of medical-grade masks and respirators for healthcare workers. figure shows the impact of using a folded cotton handkerchief mask on the expelled respiratory jet. the folded mask was constructed by following the instructions recommended by the u.s. surgeon general. it is evident that while the forward motion of the jet is impeded significantly, there is notable leakage of tracer droplets through the mask material. we also observe a small amount of tracers escaping from the top edge of the mask, where gaps exist between the nose and the cloth material. these droplets remained suspended in the air until they were dispersed by ambient disturbances. in addition to the folded handkerchief mask discussed here, we tested a single-layer bandana-style covering (not shown) which proved to be substantially less effective in stopping the jet and the tracer droplets. we now examine a homemade mask that was stitched using two-layers of cotton quilting fabric consisting of threads/in. the mask's impact on droplet dispersal is shown in fig. . we observe that the mask is able to arrest the forward motion of the tracer droplets almost completely. there is minimal forward leakage through the material, and most of the tracer-escape happens from the gap between the nose and the mask along the top edge. the forward distance covered by the leaked jet is less than in. in this case. the final mask design that we tested was a non-sterile conestyle mask that is available in most pharmacies. the corresponding droplet-dispersal visualizations are shown in fig. , which indicate that the flow is impeded significantly compared to figs. and . however, there is noticeable leakage from gaps along the top edge. the forward distance covered by the leaked jet is ∼ in. from the mouth opening, which is farther than the distance for the stitched mask in fig. . a summary of the various scenarios examined in this study is provided in table i , along with details about the mask material and the average distances traveled by the respiratory jets. we observe that a single-layer bandana-style covering can reduce the range of the expelled jet to some extent, compared to an uncovered cough. importantly, both the material and construction techniques have a notable impact on the masks' stopping-capability. the stitched mask made of quilting cotton was observed to be the most effective, followed by the commercial mask, the folded handkerchief, and, finally, the bandana. importantly, our observations suggest that a higher thread count by itself is not sufficient to guarantee better stoppingcapability; the bandana covering, which has the highest thread count among all the cloth masks tested, turned out to be the least effective. we note that it is likely that healthcare professionals trained properly in the use of high-quality fitted masks will not experience leakage to the extent that we have observed in this study. however, leakage remains a likely issue for members of the general public who often rely on loose-fitting homemade masks. additionally, the masks may get saturated after prolonged use, which might also influence their filtration capability. we reiterate that although the non-medical masks tested in this study experienced varying degrees of flow leakage, they are likely to be effective in stopping larger respiratory droplets. in addition to providing an initial indication of the effectiveness of protective equipment, the visuals used in this study can help convey to the general public the rationale behind social-distancing guidelines and recommendations for using face masks. promoting widespread awareness of effective preventative measures is crucial, given the high likelihood of a resurgence of covid- infections in the fall and winter. the data that support 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rooms dispersion of exhaled droplet nuclei in a two-bed hospital ward with three different ventilation systems role of ventilation in airborne transmission of infectious agents in the built environment-a multidisciplinary systematic review on coughing and airborne droplet transmission to humans how to make your own face covering key: cord- -tyhtdawb authors: zhao, l.; qi, y.; luzzatto-fegiz, p.; cui, y.; zhu, y. title: covid- : effects of weather conditions on the propagation of respiratory droplets date: - - journal: nan doi: . / . . . sha: doc_id: cord_uid: tyhtdawb as the number of confirmed cases of coronavirus disease (covid- ) continues to increase, there has been a rising concern regarding the effect of weather conditions, especially over the upcoming summer, on the transmission of this disease. in this study, we assess the transmission of covid- under different weather conditions by investigating the propagation of infectious respiratory droplets. a comprehensive mathematical model is established to explore their evaporation, heat transfer and kinematics under different temperature, humidity and ventilation conditions. the transmitting pathway of covid- through respiratory droplets is divided into short-range droplet contacts and long-range aerosol exposure. we show that the effect of weather conditions is not monotonic: low temperature and high humidity facilitate droplet contact transmission, while high temperature and low humidity promote the formation of aerosol particles and accumulation of particles with a diameter of . m or less (pm . ). our model suggests that the ft of social distance recommended by the center for disease control and prevention (cdc) may be insufficient in certain environmental conditions, as the droplet spreading distance can be as long as m ( . ft) in cold and humid weather. the results of this study suggest that the current pandemic may not ebb in the summer of the northern hemisphere without proper intervention, as there is an increasing chance of aerosol transmission. we also emphasize that the meticulous design of building ventilation systems is critical in containing both the droplet contact infections and aerosol exposures. abstract: as the number of confirmed cases of coronavirus disease (covid- ) continues to increase, there has been a rising concern regarding the effect of weather conditions, especially over the upcoming summer, on the transmission of this disease. in this study, we assess the transmission of covid- under different weather conditions by investigating the propagation of infectious respiratory droplets. a comprehensive mathematical model is established to explore their evaporation, heat transfer and kinematics under different temperature, humidity and ventilation conditions. the transmitting pathway of covid- through respiratory droplets is divided into short-range droplet contacts and long-range aerosol exposure. we show that the effect of weather conditions is not monotonic: low temperature and high humidity facilitate droplet contact transmission, while high temperature and low humidity promote the formation of aerosol particles and accumulation of particles with a diameter of . μm or less (pm . ). our model suggests that the ft of social distance recommended by the center for disease control and prevention (cdc) may be insufficient in certain environmental conditions, as the droplet spreading distance can be as long as m ( . ft) in cold and humid weather. the results of this study suggest that the current pandemic may not ebb in the summer of the northern hemisphere without proper intervention, as there is an increasing chance of aerosol transmission. we also emphasize that the meticulous design of building ventilation systems is critical in containing both the droplet contact infections and aerosol exposures. coronavirus disease (covid- ) is an ongoing global pandemic with more than million confirmed cases and over . million deaths as of may th,( ) within six months since the first case was identified. the disease is caused by the severe acute respiratory syndrome coronavirus (sars-cov- ). ( ) ( ) ( ) ( ) one major challenge for the effective containment and mitigation of the virus before vaccines are available is its high transmissibility. ( ) ( ) ( ) ( ) the basic reproduction number r , which measures the average secondary infections caused by one infectious case, for covid- has a mean value of . and may rise to as high as . without proper public health interventions,( - ) a sobering value compared to r = . - . for influenza and r = - for the severe acute respiratory syndrome (sars). ( , ) therefore, a detailed and quantitative understanding of the transmission mechanisms of sars-cov- under realistic circumstances is of paramount importance, particularly as many countries start to ease their mobility restrictions. among known transmitting pathways of sars-cov- , transmission via respiratory droplets is believed to be a primary mode, based on previous studies on sars ( ) and influenza ( ) . as many as , respiratory droplets can be generated by sneezing, coughing and even normal talking, with initial speeds ranging from a few meters per second up to more than a hundred meters per second. ( ) ( ) ( ) these respiratory droplets are expelled from our upper respiratory tracts (urts) and serve as potential pathogen carriers. ( ) extensive studies have been conducted to investigate the formation, ( , ) spreading, ( ) ( ) ( ) ) and infectivity ( , ) of respiratory droplets. models to predict the infection probability under different circumstances have been developed as well. ( ) ( ) ( ) these past studies suggest that both aerodynamics and the heat and mass exchange process with the environment can determine the mode and the effectiveness of virus propagation during the travel of respiratory droplets. while large droplets usually settle onto a surface within a limited distance due to gravity, smaller droplets evaporate rapidly to form aerosol particles that are able to carry the virus and float in air for hours. ( , ) under certain weather conditions, how far can the virus carriers travel on average? what fraction of droplets will turn into aerosol particles? what role do the hvac and air conditioning systems play in virus propagation? quantitative answers to these practical questions can provide urgently needed guidance to both policy makers and the general public, e.g. on social distancing rules. in fact, there have already been intensive ongoing debates about the potential impact of weather conditions on the covid- pandemic. environmental parameters, such as temperature and humidity, can profoundly affect the survival and transmission of the virus, as well as the immune function and social behaviors of the hosts.( - ) as a result, the spreading of sars and influenza have shown strong dependence on seasonality: sars vanished in the summer of and the massive infection of influenza mostly happens in wintertime. however, whether covid-reproductive number r for chinese cities and argued that high temperature and high humidity reduced the transmission of covid- . ( ) in contrast, another research by kissler et al ( ) assumed similar seasonality of covid- with human coronavirus oc (hcov-oc ) and hcov-hku . they highlighted potentially recurrent seasonal outbreaks of covid- until in spite of the immunity gained from vaccination. it is clear that a comprehensive study on the interactions between weather conditions and the propagation of sars-cov- -containing respiratory droplets can help resolve some of the controversies. this study investigates the influence of weather conditions including temperature, humidity and wind velocity, on the transmission of sars-cov- -containing respiratory droplets. we integrate aerodynamics, evaporation, heat transfer and kinematic theories into a mathematical model to predict the spreading capabilities of covid- in different weather conditions. we expanded the modeling framework developed by wells,( ) kukkonen et al ( ) and xie et al( ) by discussing brownian motion, considering residual salt and incorporating kinematic analysis of aerosol particles. as shown in figure , the transmission of covid- through respiratory droplets is categorized into two modes: droplet contact and exposure to aerosol particles. we first focus on the effect of temperature and relative humidity on these two modes of disease transmission. our results suggest that high temperature and low humidity promote the formation of aerosol particles, while low temperature and high humidity promote droplet contact transmission. although social distancing has been proven effective in slowing down covid- transmission, the feet of physical distance recommended by the centers for disease control and prevention (cdc) turns out to be insufficient in eliminating all possible droplet contacts. in some extremely cool and humid weather conditions, the droplet spreading distance may reach as far as m ( . feet). we suggest that the current pandemic may not ebb over the summer without continuous and proper public health intervention, because ( ) in hot and dry weather, respiratory droplets more easily evaporate into aerosol particles capable of long-range transmission; ( ) infectious pm . that can infiltrate deeply into our lung has a longer suspension time in hot and dry weather; ( ) many public spaces implement air-conditioning systems that can still operate at temperature and humidity setpoints that favor droplet transport. our results also demonstrate that ventilation has both favorable and adverse consequences. on one hand, ventilation to outdoor air can effectively dilute the accumulation of infectious aerosol particles; on the other hand, improper design of ventilation systems may void the effort of social distancing by expanding the traveling all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted may , . . https://doi.org/ . / . . . doi: medrxiv preprint distance of pathogen-carrying droplets and aerosols. last but not least, we emphasize that the effect of weather on covid- transmission is not monotonic. to curb the spread of this disease and avoid possible resurgent waves of infections, we advise that flexible public health measures should be taken depending on detailed environmental conditions. after being exhaled by a patient, respiratory droplets with various sizes will travel and simultaneously evaporate in the ambient environment. small-sized droplets dry immediately to form a cloud of aerosol particles. these particles will suspend in the air for a significant amount of time. largesized droplets can reach a limited distance and fall to the ground due to gravity. we define lmax as the maximum horizontal distance that droplets can travel before they either become dry aerosol particles or descend below the level of another person's hands, i.e., h/ from the ground, where h is the height of another person. to understand the evolution of respiratory droplets, we first examine a single respiratory droplet expelled from the urt of a patient. upon being released, the droplet begins to exchange heat and mass with the environment while moving under various forces (gravity fg, buoyancy fb and air drag fd in figure ). as described earlier, respiratory droplets will evolve into two categories depending on their initial diameter d : ) aerosol particles made up of residues (salts, pathogens, enzymes, cells, and surfactants) after the dehydration of small droplets. here we name those solid particles originating from small droplets as aerosol particles to distinguish from the airborne aerosol defined by the world health organization (who),( ) which employed a straight all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted may , . . https://doi.org/ . / . . . doi: medrxiv preprint μm cut-off. generally, the aerosol particles in this study range from μm to μm and share similar dynamic behaviors and impact on human respiratory systems. likewise, such viruscarrying aerosol particles can lead to airborne transmission of covid- once being inhaled ( , ) . because of their long suspension time in air, they have the potential of achieving long-range infection( ) generally wearing a face mask can effectively lower the chance of transmission via aerosol particles. ) large droplets that transmit the disease by contact. the infection range of these droplets is limited to a relatively short distance, because they are more sensitive to gravity and can settle on a surface before drying. if these droplets happen to land on the upper body of another person, viruses can easily enter their urts by face-touching and eye-rubbing. this type of virus transmission can be prevented by practicing social distancing. we define a critical distance lmax as the maximum horizontal distance that all respiratory droplets can travel before they either shrink to suspending aerosol particles or descend to the level of another person's hands (h/ from the ground, where h is the person's height). beyond lmax, an individual will be completely clear of falling droplets (category ), but can still be exposed to long-range aerosol particles (category ), as shown in figure . the general modeling framework can be briefly summarized as: ( ) the evaporation is a mass transport process dominated by the difference in the vapor pressure between the droplet surface and the ambient environment; ( ) the temperature of the droplet is solved by considering heat transfer between the droplet and the environment via evaporation, radiation and convection; ( ) gravity, buoyancy and drag contribute to the displacement of droplets/aerosol particles; ( ) all thermophysical properties of the droplet and air are dependent on temperature and humidity. to improve upon previous models, ( , , ) we further analyzed the effect of brownian motion, considered the effect of residue salts in respiratory droplets on the terminal particle size, and incorporated a kinematic analysis on aerosol particle transport and deposition. we find that the brownian motion becomes significant only for droplets with diameters smaller than . μm. the expected fluctuations of a μm particle caused by brownian motion is limited to . m in the life of a droplet. therefore, we eventually neglected the brownian force in formulating the kinematic equation. after complete evaporation of the droplets, the analysis on the residue aerosol particle was continued by solving its transport and deposition using kinematic equations. detailed model formulations, including evaporation model, heat transfer model, kinematic analysis, and validations of our model can be found in the supporting information. all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted may , . . https://doi.org/ . / . . . doi: medrxiv preprint key parameters considered in the model include the distribution of initial droplet size d , initial velocity v , environmental temperature t ∞ , relative humidity rh, air velocity vair, whose values are given here. the initial velocity v of droplets was taken as . m/s for speaking. ( ) we also calculated the sneezing mode (v = m/s) and the results are shown in the supporting information. for the subsequent sections, we choose to focus on speaking mode to mimic a real social distancing situation where people keep a reasonable physical distance and only sneeze/cough into a tissue or their elbow. the probability distribution of initial droplet diameter d is from a previous experimental work by duguid.( ) , listed in the supporting information. the initial temperature t of exhaled droplets was set to be ℃. ( ) for the environment, we used an average vair = . m/s in horizontal direction as the wind speed for an indoor environment, ( ) and varied the wind speed from - m/s when analyzing the effect of ventilation and wind. in order to explore the effects of weather conditions, environmental temperature t ∞ and relative humidity rh were varied from - ℃ and - . , respectively. figure s (a) shows that the droplet diameter shrinks over time and that droplets smaller than μm evaporate within s. figure s (b) demonstrates that all the droplets cool to the wet bulb temperature twb in less than second due to the latent heat required by evaporation. the trajectory of a droplet is analyzed in terms of the vertical distance lz (figure (a)) and horizontal distance lx (figure (b)) that the droplet can travel before it either completely dries or descends to the level of another person's hand (h/ ). here we set h to be the average height of american adults ( . m). figure (a) shows that droplets with diameter smaller than . μm can completely dehydrate into aerosol particles and therefore only descend a vertical distance less than h/ . droplets larger than . μm fall below the level of hands (h/ ). they are less likely to transmit the disease and we do not consider them dangerous. therefore, we used a plain cut-off of lz = h/ for all droplets falling below that. a critical droplet diameter dc can be defined by identifying the initial diameter below which droplets can fully evaporate before descending to the hands. figure (b) reveals that the maximum of lx occurs at d = dc as well. as shown in figure (c), for d<dc, lx increases with respect to d because a larger droplet takes longer time to fully all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted may , . . https://doi.org/ . / . . . doi: medrxiv preprint evaporate and thus travels further; as d exceeds dc, the droplet falls more quickly due to gravity resulting in a smaller lx. figure . for droplet contact transmission, we plotted lmax as defined previously, under different temperature and humidity conditions ( figure a ). it is shown that droplets can travel a longer distance in humid but cool environments, and therefore such environments require a longer social distance to completely eliminate droplet contact. in extremely cold and humid scenarios it can require as far as m. on the other hand, respiratory droplets in hot and dry environments experience a faster mass loss as evaporation has been dramatically intensified. as those droplets sharply decrease in size, the horizontal traveling distance is reduced due to the growing damping effect of air. as a result, a less strict social distancing rule may potentially be applied on a really dry summer day, although at this point we have not examined the transmission via aerosol particles. we highlight that in most regions of figure (a), lmax exceeds . m, i.e., the feet of physical distance recommended by cdc. therefore, current social distancing guidelines all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted may , . . https://doi.org/ . / . . . doi: medrxiv preprint a quick remark regarding droplet-based transmission is that, if we consider a relaxed standard that only blocks % of viruses carried by respiratory droplets (excluding viruses carried by aerosol particles), this distance occurs at . m based on our model ( figure s ). here we assumed a constant concentration of the virus in the droplets and the number of viruses is consequently proportional to the initial mass of respiratory droplets.( ) interestingly, we find that this relaxed social distancing standard does not show an apparent dependence on the weather conditions (see supporting information). therefore, . m may serve as a relaxed weatherindependent criterion that can eliminate the majority of viruses from directly landing on another person. caution is still required as this relaxed rule does not block transmission via aerosol particles and is evaluated for speaking mode with an air velocity of . m/s. the distance increases for an increased air velocity, the effect of which is discussed in a later section. to further evaluate the potential risk of transmission of covid- via aerosol particles, a mode that may be equally important, ( ) we estimate the number of aerosolized particles, and elucidate the impact of environmental temperature and relative humidity. on the contrary to the trend observed for lmax, figure (b) predicts an increasing aerosolization rate φa for hot and dry environments. φa is defined as the percentage of respiratory droplets that completely dehydrate before settling below the level of hands (h/ ), and characterizes the amount of infectious aerosol particles that can be produced by speaking. the terminal sizes of these aerosol particles are in the range of μm to μm based on our model (figure c and figure s ). such small particles can potentially suspend in air for hours ( , ) before settling ( figure s ) and tend to accumulate in public areas such as schools, offices, hotels, and hospitals. in particular, the increasing number of superspreading events that occurred at indoor environments evidenced the possibility of covid- transmitting efficiently via aerosol particles. therefore, the long-range infection induced by aerosol particles deserves more attention in the coming summer, especially in dry weather, since the resistivity of sars-cov- in these warm and dry environment is still not fully understood.( , the effectiveness of aerosol-based disease transmission is also linked to the ability of aerosol particles to infiltrate respiratory tracts, which has a strong particle size dependence. generally, small particles are able to infiltrate lower in the respiratory tract to establish infections, as they can travel with inhaled air current and avoid impaction within the nasal region.( ) in all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted may , . . https://doi.org/ . / . . . doi: medrxiv preprint particular, studies have shown that pm . (particles less than . μm in diameter) can penetrate deeply into our lungs, ( ) which makes them potentially more dangerous than larger aerosol particles. here we calculated the terminal size of an aerosol particle after dehydration by approximating it to the volume of sodium chloride originally dissolved in the aqueous solution. we assumed the respiratory droplet as a physiological saline solution ( . % weight fraction), ( ) when the composition of respiratory fluids is undoubtedly more complicated and can vary with respect to the site of origin, breathing pattern and health conditions of the host. we calculate the average diameter of aerosol particles floating in air under different weather conditions. figure (c) demonstrates that aerosol particles have average diameters between - μm, and the maximum diameters are generally smaller than μm, indicative of their strong ability to penetrate into the human respiratory system. the average particle diameter is increased for hot and dry weather, because more large droplets can completely evaporate due to enhanced evaporation (figure b ). since pm . has been associated with a higher possibility of reaching the lung, we then discuss the transport and deposition of aerosol particles classified within pm . under different weather conditions. we first computed the size-dependent suspension time ts from the following equation: where ve is the falling velocity of the aerosol particle by assuming gravity is entirely balanced by buoyancy and air drag, vt is the downward velocity of the aerosol particle at the time of drying out. if we neglect the brownian motion, the time constant of the micro-sized droplet/particle can be written as (see supporting information for details): where ⍴d is the density of the droplet, r is the droplet radius and μa is the dynamic viscosity of air. for respiratory droplets with diameters smaller than μm, the time constant is less than . s, indicative of a strong damping effect of air. while large aerosol particles can suspend in air for at least minutes, small aerosol suspends substantially longer ( figure s (b) ), which agrees with previous literature. ( ) we further calculated the steady-state total mass md of pm . produced by a patient in an enclosed and unventilated space. md is taken as the mass of pm . when new all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted may , . . https://doi.org/ . / . . . doi: medrxiv preprint aerosol particles produced from speaking is balanced by their deposition onto the ground. figure (d) presents the values of md in different environmental conditions. there is slightly more pm . suspended in air in a hot and dry environment than in a cold and humid environment. this is mainly due to the increased suspension time in hot and dry environments as a result of the corresponding thermophysical properties of the air. by combining figure (b) and (d) , the hot and dry weather not only increases the percentage of respiratory droplets turning into aerosols, but also facilitates the accumulation of pm . in an enclosed space. these facts raise a growing concern of aerosol transmission of covid- in the coming summer, especially when the humidity is low. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. to consider a worst situation, we model a scenario where the wind is always directed from an infected individual to a susceptible person. as shown in figure , while the increased ventilation slightly affects the aerosolization rate of respiratory droplets, it has a significant impact on the spreading distance of droplets. the majority of droplets are moving with the airflow after their horizontal velocity settles down to the wind speed, which usually happens in a short time due to a small . therefore, the droplet spreading distance has been dramatically increased as the wind velocity increases, with a maximum value of m in a gentle breeze (vair = m/s). in addition, the spreading of aerosol particles is greatly increased as well, since they are smaller in size and travel with the wind. in summary, ventilation has both favorable and adverse consequences. while fresh outdoor air can effectively dilute the accumulation of infectious aerosol particles, it expands transport distances of pathogen-carrying droplets and aerosol particles. this poses stringent requirements on the meticulous design of ventilation configurations in non-hospital facilities, so as to cut off the transmission of covid- . all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. is entirely probable. in this study, we establish a comprehensive model which integrates emission of speech droplets, droplet evaporation, heat transfer and kinematic theories of droplet propagation to all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. provide a tentative answer to the controversial question of how weather conditions may affect the covid- pandemic. when combined with systematic epidemiological studies, our results may shed light on the course of development of the current pandemic. the main findings of this study can be summarized as: ( ) hot and dry weather can reduce infections caused by droplet contact, but the risk of transmission via aerosol particles is increased. ( ) cool and humid weather can effectively suppress the formation of aerosol particles, but it also facilitates the spreading of large droplets. ( ) the current social distancing standard is insufficient in eliminating all droplet contacts. in some extremely cool and humid weathers, the required physical distance may reach as far as m. ( ) alternatively, a relaxed standard of . m is able to block % of viruses carried by respiratory droplets (excluding that carried by aerosol particles) and shows negligible weather dependence. ( ) the current pandemic may not ebb in the upcoming summer in the northern hemisphere. more data on the infectivity of sars-cov- under different weather conditions, especially in the form of aerosol particles, are necessary to make a definitive conclusion. ( ) measures should be taken to contain covid- transmission caused by aerosol particles in summer, especially when humidity is low. proper face-covering may serve as a solution to prevent infectious pm . and pm from entering our respiratory tracts. ( ) ( ) the effect of weather on the transmission of covid- is not monotonic. adaptable strategies by incorporating the regionality, weather and modes of transmission should be applied to contain the transmission. all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. when a droplet with an initial diameter of d and temperature t is moving in air with temperature t ∞ and relative humidity rh, the evaporative flux of the droplet is determined by the difference of vapor pressure near the droplet surface pvs and of the ambient environment p v∞ . ( , (s ) where is the mass of the droplet, t is the time, d is the diameter of the droplet, is the molecular mass of the droplet, is the binary diffusion coefficient of the air, r is the universal gas constant and p is the total pressure of the air. c is the correction factor due to temperature where t is the temperature of the droplet and λ is a constant specifically for water. sh is the sherwood number. (s ) re and sc are the reynolds number and schmidt number, which can be calculated as: where ⍴a is the density of the air, vair is the wind speed, v is the droplet velocity and μ is the dynamic viscosity of the air. pvs is the vapor pressure at the droplet surface and is lowered by the dissolved substances in its solution, which can be described by the raoult's law , where fw is the mole fraction of water in the solution and pv is the saturation vapor pressure at temperature t. the composition of a respiratory droplet can be extremely complex and may contain pathogens, proteins, salt, and surfactants. in this study, we assume the respiratory droplet as a physiological saline solution with . % weight fraction of sodium chloride. during the evaporation process, sodium chloride begins to precipitate once the saturating concentration has been reached. the as-all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted may , . . https://doi.org/ . / . . . doi: medrxiv preprint formed nacl crystal will serve as a nest where sars-cov- can reside. its diameter dr after dryout can be calculated as: where ms is the mass of nacl initially dissolved in the droplet and ⍴s is the density of nacl crystal. the heat transfer between the droplet and the air is dominated by evaporation, convection, and radiation. an energy balance equation can be derived as: where cp is the specific heat capacity of the droplet, ka is the thermal conductivity of the air, lv is the latent heat of vaporization and Γ is the stefan-boltzmann constant. nu is the nusselt number. (s ) = is the prandtl number, where ca is the specific heat capacity of the air. the displacement of velocity of the droplet can be calculated by considering gravity, buoyancy and air drag as the dominating factors. (s ) where is the gravity and ⍴ is the density of the droplet. cd is the drag coefficient, which can be determined by the following equation. (s ) fb is the random brownian force, which will be discussed in the next section. in this study, moist air is used to calculate the dependence of gas properties on rh. those temperature dependent parameters are taken from . ( ) all simulations of droplets were stopped if ) the droplet has completely dehydrated, i.e., d≤dr, where dr is the diameter of droplet nuclei formed by residues; or ) the droplet has descended to the level of another person's hands, i.e., |lz|≥ h/ , where lz is the vertical displacement. all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted may , . . https://doi.org/ . / . . . doi: medrxiv preprint most respiratory droplets are smaller than µm. once they dry out, the droplet nuclei that are left behind are usually smaller than µm. therefore, the movement of such particles becomes sensitive to impacts from fast moving air molecules, which poses a random component (s ) the fluctuating force fb has a gaussian distribution with the moments specified in equation s . therefore, the effect of brownian force fb can be estimated by comparing it to the gravity. (s ) figure s . effect of brownian force at different length scales all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted may , . . https://doi.org/ . / . . . doi: medrxiv preprint figure s presents the comparison of fb to gravity at different nuclei diameters. it is found that the brownian force fb is comparable to gravity only if the nuclei size becomes smaller than . µm. in this case, the corresponding initial diameter of the droplet calculated from equation s must be smaller than . µm. however, respiratory droplets are larger than µm according to previous measurements. ( ) the effect of brownian force on the movement of droplet nuclei can be accounted for in an alternative way. assuming that the droplet nuclei are at equilibrium in that gravity equals to the air drag, then the motion of those nuclei become purely diffusive and the dependent displacement can be described as: where v* is the fluctuating velocity resulting from the random brownian force. the time-averaged displacement is equal to , but the mean square displacement can be evaluated as: (s ) therefore, the average deviation of droplet nuclei in a duration of t is: (s ) where dr is the diameter of the droplet nucleus. for t = k and dr = µm um, we find that its expected moving distance is only . m in seconds, which is negligible in the transmission of both aerosol particles and droplets. to conclude, we find that the effect of brownian motion on the transmission of respiratory droplets and droplet nuclei is negligible, in that ) the fluctuating brownian force is trivial compared to the gravity for the size of interest (d > µm); ) the deviation of those particles from their original induced by brownian motion is negligible. all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted may , . . https://doi.org/ . / . . . doi: medrxiv preprint to validate our model, we firstly investigated the evaporation of stagnant water droplets (t = ℃) evaporating in dry air (t ∞ = ℃, rh = ) and compared the results to an experimental work by ranz and marshall.( ) as shown in figure s figure s (b). generally, our results agree well with and the overshoot of our model results may be attributed to the small differences in water and air parameters that were adopted. the size and distribution of speech droplets, i.e., respiratory droplets expelled by speaking, are taken from a work published by j. p, duguid.( ) here we present a probability density distribution of different initial diameters of speech droplets in figure s . all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted may , . . https://doi.org/ . / . . . doi: medrxiv preprint figure s . probability density distribution of the initial diameter of speech droplets once the droplet has dried out, as-formed aerosol particles will suspend in air for a long time and eventually fall on the ground due to gravity. if there is no airflow in vertical direction, the vertical movement of aerosol particles is solely controlled by gravity, buoyancy and air drag. because the downward velocity vz of droplet nuclei are usually on the order of - - - m/s, re<< and therefore we can assume a stokes flow around the droplet nuclei. (s ) where mr is the mass and r is the radius of the droplet nucleus. equation s can be solved with initial condition of vz = v at t = , where vt is the terminal velocity of the droplet. is the time constant. (s ) ve = g ( -⍴a/⍴) is the falling velocity of the aerosol particle by assuming gravity is entirely balanced by buoyancy and air drag. all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted may , . . https://doi.org/ . / . . . doi: medrxiv preprint we first examine the evaporation dynamics of a sneezing droplet (t = ℃, v = m/s) in t ∞ = ℃ and rh = . . the time-dependent characteristics of an evaporating sneezing droplet is shown in figure s . figure s . evolution of (a) droplet diameter and (b) droplet temperature of a sneezing droplet. the initial condition of the droplet is taken as t = ℃ and v = m/s. the environment is set to be t ∞ = ℃, rh = . and vair = m/s. figure s demonstrates the strong dependence of droplet evaporation dynamics on the initial diameter of a sneezing droplet. in figure s (a), the diameter of a small droplet (d = μm) experiences a rapid decrease. for a large droplet, the diameter firstly decreases linearly, because the evaporative flux at this point is primarily determined by the vapor pressure difference; eventually its diameter experiences a sharp decrease in that the increasing surface-to-volume ratio further intensifies the evaporation. figure s (b) presents the temperature profile of a droplet during evaporation. note that the x axis in this figure is in logarithmic scale. apparently, the temperature of all droplets rapidly decreases to the wet bulb temperature twb within one second, owing to the large latent heat required to evaporate. therefore, the effect of heat transfer is not significant on the evaporation dynamics, as the droplet stays at twb throughout the evaporation process. all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. figure s shows the evaporation dynamics of a speech droplet that has a smaller initial velocity. the environment is taken as the typical indoor air, i.e., t ∞ = ℃, rh = . and vair = . m/s. generally, the speech droplet shares the similar behaviors with the sneezing droplet, as the respiratory droplets are sensitive to air drag and its velocity can decelerate to the wind velocity rapidly. if the concentration of sars-cov- is constant in all respiratory secretions, then the number of viruses nv in a respiratory droplet is determined by its size. (s ) where n is the average number per unit volume. based on the size distribution presented in figure s and j. p, duguid( ), we calculated the percentage of viral load in each diameter range ( figure s (a)). (s ) all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted may , . lx for droplets with different initial diameter d . in order to obtain the distance-dependent viruses that one may receive, we also computed the traveling distance lx for different d and weather conditions ( figure s (b) ). by combining figure s (a) and (b), we are able to plot the distance-dependent viral load in figure s , which characterizes the effectiveness of social distancing at different distances. figure s . effectiveness of practicing social distancing at different distance all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted may , . . https://doi.org/ . / . . . doi: medrxiv preprint figure s (b) presents the traveling distance of different droplets at four weather extremes, i.e., cold and humid (t ∞ = ℃, rh = . ), cold and dry (t ∞ = ℃, rh = ), hot and dry (t ∞ = ℃, rh = ), hot and humid (t ∞ = ℃, rh = . ). we find that the horizontal traveling of small droplets (d < μm) is strongly dependent on weather conditions; however, large droplets are inert and become insensitive to weather change. since most pathogens exist in large respiratory droplets, the curve of distance-dependent viral load in figure s is not sensitive to weather conditions. therefore, we only demonstrate the viral load curve under normal indoor conditions (t ∞ = ℃, rh = . , vair = . m/s), and a weather-independent criterion can be used for relaxed social distancing. by integrating equation (s ), the suspension time ts that is required for a particle to deposit on the ground can be calculated as: we then calculated the average suspension time tm of pm . under different weather conditions, as shown in figure s (a). generally, pm . can suspend in air for around hours. we also find that the hot and dry temperature gives rise to a longer suspension time for pm . , as shown in figure s (b). the suspension time ts varies dramatically from hours to around hours when the diameter changes from μm to μm. all rights reserved. no reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted may , . . https://doi.org/ . / . . . doi: medrxiv preprint figure s . average suspension time of pm . under different weather conditions assume the percentage of droplets that can turn into pm . in speech droplets is p(d ). dr is the diameter of the aerosol particle after dehydrating. then the number of pm . that can be produced by constant speaking is ∑ ( ) , where n is the number of produced droplets per second. after ts, the number of the corresponding aerosol particles reaches equilibrium, as the number of newly produced particles is now equal to that of aerosol particles falling on ground. therefore, the total mass of pm . can be calculated: (s ) in this study, n is equal to droplets per minute.( ) based on equation s , the total mass of pm . has been computed under different weather conditions in figure (d). an interactive web-based dashboard to track covid- in real time a pneumonia outbreak associated with a new coronavirus of probable bat origin pei, others, a new coronavirus associated with human respiratory disease in china others, clinical characteristics of coronavirus disease in china functional assessment of cell entry and receptor usage for sars-cov- and other lineage b betacoronaviruses first-wave covid- transmissibility and severity in china outside hubei after control measures, and second-wave scenario planning: a modelling impact assessment asymptomatic transmission, the achilles' heel of current strategies to control covid- presymptomatic sars-cov- infections and transmission in a skilled nursing facility guggemos, others, transmission of -ncov infection from an asymptomatic contact in germany monitoring transmissibility and mortality of covid- in europe association of public health interventions with the epidemiology of the covid- outbreak in wuhan 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control of epidemic-and pandemic-prone acute respiratory infections in health care (world health organization natural sources and experimental generation of bioaerosols: challenges and perspectives disease transmission via drops and bubbles study on the initial velocity distribution of exhaled air from coughing and speaking the size and the duration of air-carriage of respiratory droplets and dropletnuclei temperatures of expired air under varying climatic conditions a survey of wind speeds in indoor workplaces physico-chemical characteristics of evaporating respiratory fluid droplets airborne or droplet precautions for health workers treating covid- ? the impact of pm . on the human respiratory system building evidence for health: green buildings, current science, and future challenges role of ventilation in airborne transmission of infectious agents in the built environment-a multidisciplinary systematic review airborne transmission of exhaled droplet nuclei between occupants in a room with horizontal air distribution can n respirators be reused after disinfection? how many times we find that almost % of viruses produced by one expiration are carried in droplets with d > μm. therefore, the droplet contact transmission could be surprisingly dangerous how far droplets can move in indoor environmentsrevisiting the wells evaporation-falling curve the interdependence of evaporation and settling for airborne freely falling droplets condensation in the continuum regime the size and the duration of air-carriage of respiratory droplets and dropletnuclei evaporation from drops aerosol emission and superemission during human speech increase with voice loudness key: cord- -poh y o authors: v, antony aroul raj; r, velraj; haghighat, fariborz title: the contribution of dry indoor built environment on the spread of coronavirus: data from various indian states date: - - journal: sustain cities soc doi: . /j.scs. . sha: doc_id: cord_uid: poh y o coronavirus spread is more serious in urban metropolitan cities compared to rural areas. it is observed from the data on the infection rate available in the various sources that the cold and dry conditions accelerate the spread of coronavirus. in the present work, the existing theory of respiratory droplet drying is used to propose the mechanism of virus spread under various climates and the indoor environment conditions which plays a greater role in the virus spread. this concept is assessed using four major parameters such as population density, climate severity, the volume of indoor spaces, and air-conditioning usage which affect the infection spread and mortality using the data available for various states of india. further, it is analysed using the data from various states in india along with the respective climatic conditions. it is found that under some indoor scenarios, the coronaviruses present in the respiratory droplets become active due to size reduction that occurs both in sessile and airborne droplet nuclei causing an increase in the spread. understanding this mechanism will be very useful to take the necessary steps to reduce the rate of transmission by initiating corrective measures and maintaining the required conditions in the indoor built environment. immediately after the th anniversary of spanish flu [ ] , the deadliest outbreak in the recorded history, wherein approximately million people were killed which is more than the death toll from the first world war, now the new corona pandemic is threatening the entire world. the other major pandemics during the th century were asian flu , and hong kong flu which killed to million people during each era. in the last two decades, the epidemics of infectious diseases are occurring more often and spreading faster and further than ever. the reason is due to change in the lifestyle that leads to climate change leading to a biological imbalance in the system and thus we continuously learn about the unpredictable power of nature. there has been some suggestion by the authorities that the most effective approach to prevent the transmission of covid among the population are: keeping social distance and washing hands. the rationale for such a policy is that virus transmission occurs through direct contact and droplet transmission, and public health professionals believe that using facial masks and gloves is an efficient way in preventing virus spread. it is a general belief that population density is an important parameter in deciding the spread of the covid- virus; however, it is observed that any single case [ ] in india. jonathan kay [ ] has prepared a comprehensive international database of large covid- infection clusters or super spreading events in the spread of coronavirus for february and march . the commonality of the outbreak observed by him is that all the infections were indoor with people closely packed. the main sources of infections are home, workplace, public transport, social gathering, and restaurants. top outbreaks have happened in the prison, religious houses, meat packing facilities, weddings, funerals, business networking events, call centers, and choir. outbreaks happened outdoor is a small percentage of around %. the author has also mentioned that studies have to be done on the effect of indoor conditions such as temperature and rh in the spread of the virus. the various other factors are classified as:  minimum infectious dose of virus: a minimum dose of about sars cov infectious virus particles is required to start a pathogenesis cascade that can cause new infection [ ] . the successful infection is a product of the dosage of virus and time for exposure. a person can get infected by a strong dose of a virus for a shorter period or a weak dose of the virus for a longer period. for example if virus particle is required for infection it can happen by particles in minutes or by particles in minutes.  number of droplets released and speed of release: a cough by a person releases about droplets at mph, a sneeze releases droplets at mph and during the breath, about droplets are released at very low velocity [ ] . the droplets released by sneeze and cough can travel a longer distance and stay in the air for a longer period of time [ ] .  age of the infected person: the amount of the virus released depends on the age of the infected person. it is lesser if the age is less than . it increases up to and then decreases with age. when the viral load builds up the person becomes symptomatic [ ] .  enclosed environments: any crowded indoor environment with poor air circulation and high density of people with high breathing and panting due to physical activity of the infected person such as loud talking, laughing, singing, dancing and playing has resulted in an increase in breathing rate and the number of droplets released causing high spread rate [ ] and [ ] .  social and large public gathering: physical contact between the individuals as part of social and public gathering procedures such as hugging, handshaking, kissing also has resulted in fomite transmission. further, it is understood from various data and literature that cold and dry conditions accelerate the rate of spread of coronavirus [ ] - [ ] . this infers that climate severity is an important parameter in the spread of the virus. hence the major objective of the present work is to propose the mechanism of virus spread under various climates and the indoor environment conditions maintained through the existing theory of respiratory droplet drying. further, it is aimed to perform a statistical study on the dependence of mortality and infection in the indian states with respect to four major parameters such as population density, climate severity, volume of indoor spaces, and air-conditioning usage based on monthly data for march and april. this study is done to confirm whether the trend and correlation from the analysis support for the drying of respiratory droplets under dry conditions proposed in the present work. understanding the mechanism of production of dry pockets in various indoor air environments by the heating, ventilating and air conditioning (hvac) systems is very essential to take appropriate measures and to reduce the rate of transmission. the mechanism of drying of respiratory droplets and transmission potential is explained initially using the various sources available in the literature. the present work shows how the conventional cooling and heating mechanism in the indoor environment creates the possible drying potential for the respiratory droplet using the psychrometric chart for different climatic zones such as (i) hot and humid zone, (ii) cold and humid zone (iii) cold and dry zone (iv) hot and dry zone. the effect of this drying potential on the size reduction of the droplets and its effect on the spreading of viruses is also analysed. in order to assess the concept proposed, the number of infected persons and the mortality from several states of india where different climatic conditions prevail during march and april, , are compared using the selected parameters. the population density is one of the parameter chosen as there is a general agreement that the population density is the reason for its spread. the effect of climate severity in a particular state is brought through the parameters such as monthly average relative humidity, monthly average peak temperature, and monthly average minimum temperature. in any country, % of the total power generated is utilized in the building sector in which % of the energy is utilized for building air-conditioning. hence percent of the total energy generated in the country is used by the hvac system. hence the parameter energy j o u r n a l p r e -p r o o f utilisation is considered as another parameter which is proportional to the dry pocket creation during the period of analysis through the hvac system. power infrastructure [ ] , is also used as a parameter to indicate the volume of the contained indoor built environment in the state. population density, power generation capacity [ ] , and corona infection and mortality data [ ] were taken from wikipedia and the weather details taken from the ishrae weather data [ ] . the the size of the droplet will not undergo size reduction if the surrounding is in high temperature and high humidity due to less potential difference for heat and mass transfer. the virus in the droplet nucleus is less active if the size remains larger with more water content. the droplet coming from the infected person will be initially at the body temperature of o c. when it tries to attain equilibrium with the surrounding lower temperature the heat available from the droplet itself will be utilized for evaporation. when the surrounding air is dry (low relative humidity) and cold, the size of the particle is reduced by combined heat and mass transfer [ ] - [ ] . in hot and dry conditions the heat transfer potential is less, however, the mass transfer potential is high. the mass transfer effect will be more pronounced when the relative humidity is very low. if the j o u r n a l p r e -p r o o f surrounding air is humid, water cannot evaporate and the droplet size is not reduced. water content in the particle plays an important role in diluting the virus so that it is less active and less harmful. also, the salt (sodium chloride and potassium chloride) in the respiratory droplet is hygroscopic and acts as a desiccant to absorb the moisture from the humid air to increase the size of the droplets. the virus gets diluted with water content and become less active. thus, a humid environment naturally makes the virus less active [ ] . further, in hot and humid conditions, the mucus membrane in the respiratory tract will be wet which will humidify and dilute the droplet nuclei. however in dry locations, the mucus membrane becomes dry and the fluid over lining the cells becomes more viscous and the little hair cilia which normally protects our lungs from deep settling of particle, cannot filter out the virus. after entering the lungs, the virus can cross the one cell layer separating the air path in the lungs and the blood path, and it can infect the blood very easily. the in the hot and humid as well as warm and humid zone regions, the surrounding air has high temperature and humidity, and hence the temperature and humidity potential available for reduction in the size of the droplet is lesser. however, when the air for the indoor environment is conditioned, the air is cooled and dehumidified in the air handling unit and so the potential in cold and humid zones (a condition referred as ch with o c, % rh), although there is no potential for drying, a small amount of sensible heating from ch to ch ( o c, % rh) represented with a drying potential (s -ch ) and on further heating to comfort temperature ch , ( o c, % rh) the droplet drying potential (s -ch ) increases greatly due to relative humidity of %. under such circumstances, the sensible heaters used for the heating system of the room will reduce the relative humidity of the room and will lead to the size and weight reduction of the droplet nuclei and increases the virus activity. the droplet nuclei containing the virus may become airborne( figure ). thus in cold and humid places, the indoor environment with low relative humidity will serve as pockets for virus survival. thus, the virus can be active in cold and humid regions in these moderately dry pockets mentioned above. the cold and dry zone (a condition referred to as cd with o c, % rh) is a highly unsafe condition since the drying potential already exists at low temperature. a small sensible heating without humidification, in this case, increases the drying potential cd ( o c, % rh) and further heating will lead to cd ( o c, % rh), which increases the drying potential to a higher level and there is an additional possibility of the virus becoming airborne. in an environment with low humidity and low temperature, due to combined high heat and mass transfer potential leads to fast drying and size reduction of the respiratory droplets and the virus is almost active in all the locations. in hot and dry climates, the drying potential for the droplet is higher at hd and hd . if a cooling and dehumidification system is used in a hot and dry climate this will increase the drying potential and thus the virus activity to a dangerous level. cooling with humidification like spray washer will improve the humidity level and will reduce the risk of viral contamination. drying of the respiratory droplet due to heat and mass transfer potential existing in various zones mentioned above moves the droplet nuclei to the region of low specific density as explained in the psychrometric chart so that they become lighter, buoyed up and become airborne. it is understood from the theory of respiratory droplets drying under various climatic zones that the virus is very active in cold and dry environment irrespective of conditioned or non-conditioned space [ ] . hence this climatic zone has the most vulnerable transmission potential for the coronavirus even in the outdoor environment. in the other zones, based on the condition maintained by the hvac systems the transmission potential will differ. the various states and the union territories in india are shown in figure and the climatic zones prevailing in india in various regions are shown in figure . table shows the population density, - [ ] . this confirms that the decrease in rh which increases the drying potential causes the increase in viral spread. hence it is understood that humidity will play a major role than the temperature, as the mass transfer potential for the respiratory droplets will be high at low humid conditions. it is also a well-known fact than for any drying phenomenon, mass transfer is the major influencing factor than the heat transfer. the effect of population density is the least from the correlation due to lock down and social distancing procedure. this will play a major role if the lockdown is released in the state. table correlation and regression for infection -april april, the sun position is straight to these states that leads to large usage of the hvac system. hence the spread rate is very high. however, questions may arise that in the neighboring states of kerala and karnataka, the high spread rate is not reported which is due to the following reason: in all these states the major spread is reported in the capital city where the air conditioning system usage is the highest. in karnataka, bangalore, the capital city is located at a higher altitude (partial hill station) and hence the air-conditioner usage is less and avoided the high spread. the state kerala normally referred to as "god's own place" because of its lush greenery (full of forests,  it is concluded from the present study that the region with low humidity has a higher spread potential even in the outdoor environment. hence the high spread states like maharashtra, gujarat, madhya pradesh rajasthan, and delhi with hot and dry weather conditions, the spread may continue till south-west monsoon begins in the middle of june. hence the existing lockdown cannot be released till mid-june in those states particularly in the cities like bombay and delhi.  in the southern indian states, the spread rate due to the outdoor environment is very low. as the summer intensity increases, the effect due to the outdoor environment will further decrease. however, the increase in the use of air-conditioners in the built indoor environment may increase the spread rate. in these states, as summer continues till august, proper measures should be taken while using hvac systems with the correct set conditions mentioned particularly in the cities like chennai.  it is also concluded from the present study that the spread rate may reduce in the cold countries in the northern part of the world as summer begins. however, before the next winter starts, it is advisable to modify the kind of heating system adopted to avoid dry conditions in the indoor environment. presently, the humidity control is not available in most of the commercial window, and split type air-conditioners and experimental research outcomes are also not available to prescribe the safe demarcation of the relative humidity in the hvac systems. hence, it is suggested now to set higher temperatures and relative humidity without compromising the comfort. also, it is advisable to avoid spending long hours in the closed dry environment until the corona spread is controlled. the authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. managing epidemics, key facts about the major deadly disease covid- superspreader events in countries: critical patterns and lessons, quillette coronavirus: here's how germs are spread and where you're most likely to catch them short-range airborne route dominates exposure of respiratory infection during close contact stability of sars-cov- in different environmental conditions effects of air temperature and relative humidity on coronavirus survival on surfaces optimize occupant health, building energy performance and revenue through indoor-air hydration using the indoor environment to contain the coronavirus, an engineering lesson gone viral. es magazine accepting airborne transmission of sars-cov- : our greatest fear and greatest opportunity, es magazine power system operation corporation limited monthly reports indian society of refrigeration and airconditioning simplified analysis of heat and mass transfer model in the droplet evaporation process evaporation, and dispersion of respiratory droplets from coughing indoor air comparing the markov chain model with the eulerian and lagrangian models for indoor transient particle transport simulations effects of temperature variation and humidity on the mortality of covid- in wuhan high temperature and high humidity reduce the transmission of covid- the effects of temperature and relative humidity on the viability of the sars coronavirus k key: cord- -ra njvcz authors: kumar, sanjay; lee, heow pueh title: the perspective of fluid flow behavior of respiratory droplets and aerosols through the facemasks in context of sars-cov- date: - - journal: nan doi: nan sha: doc_id: cord_uid: ra njvcz in the unfortunate event of current ongoing pandemic covid- , where vaccination development is still at the initial stage, several preventive control measures such as social distancing, hand-hygiene, and personal protective equipment have been recommended by health professionals and organizations. among them, the safe wearing of facemasks has played a vital role in reducing the likelihood and severity of infectious respiratory disease transmission. the reported research in facemasks has covered many of their material types, fabrication techniques, mechanism characterization, and application aspects. however, in more recent times, the focus has shifted towards the theoretical investigations of fluid flow mechanisms involved in the virus-laden particles prevention by facemasks. this exciting research domain aims to address the complex fluid transport that led to designing a facemask with a better performance. this review paper discusses the recent updates on fluid flow dynamics through the facemasks. key design aspects such as thermal comfort and flow resistance are discussed. furthermore, the recent progress in the investigations on the efficacy of facemasks for prevention of covid spread and the impact of wearing facemasks are presented. finally, the potential research directions for analyzing the fluid flow behavior are highlighted. the person-to-person transmission of infectious respiratory diseases occurs primarily due to the transportation of virus-laden fluid particles from the infected person. the contagious fluid particles originate from the respiratory tract of the person and are expelled from the nose and the mouth during breathing, talking, singing, sneezing, and coughing. [ ] [ ] [ ] these particles have been broadly classified into two types: aerosols (aerodynamic particle size < µm) and droplets (aerodynamic particle size ≥ µm- µm). [ ] [ ] [ ] the finding indicated that the transmission phenomena of these expelled virus particles by patients would be dependent on droplet sizes. larger respiratory droplets, once expelled from the mouth or nose, undergo gravitational settling before evaporation; in contrast, the smaller droplets particles evaporate faster than they settle, subsequently forming of the aerosolized droplet nuclei that can be suspended in the air for prolonged periods and travel in air over long distances. the research studies have revealed that the severe acute respiratory syndrome (sars) epidemic in and the current global pandemic of coronavirus disease (covid- ) predominantly transmitted by contact or through the airborne route. [ ] [ ] [ ] [ ] several preventive strategies such as safe distancing, contact tracing, isolation of the infected person, hand hygiene, and facemasks have been widely employed against the rapid spread of these diseases. [ ] [ ] [ ] [ ] among them, the use of the facemasks have proven to be one of the most effective protective measures against the airborne virus transmission. [ ] [ ] [ ] [ ] [ ] [ ] the research suggested that face coverings could essentially reduce the forward distance traveled by a virus-laden droplet, and thus has a great potential to provide personal protection against airborne infection. , recently, the world health organization who has recommended using facemasks for initial control of covid- spread. in general, facemasks fall in the category of respiratory protection equipment (rpe) whose primary function is to protect the wearer from airborne viruses and contaminated fluids. there are various rpe types, ranging from simple homemade reusable cloth-based masks to surgical facemasks and n respirators to self-contained breathing apparatus. , [ ] [ ] [ ] [ ] different types of masks provide different levels of protection to the wearer. surgical facemasks are loose-fitting, fluid-resistant, single-time use, and disposable, designed to cover the mouth and nose. these masks are fluid resistant and intended for reducing the emission of large respiratory droplets released during coughing and sneezing. , however, there is a possibility of leakage around these facemask's edge during the inhaling and exhaling process. such a dynamic leakage allows the direct contact of fluid droplets from the outside air to the wearer and vice-versa. such respiratory masks may also not provide adequate protection against extremely fine aerosolized particles, droplets, and nuclei. for efficient trapping of droplets, the facemask filters should contain microscopic pores; however, the minute-sized pores prevent air ventilation, which creates an uncomfortable situation for the wearer. hence, a better tradeoff between the pore sizes and the breathability is desirable for the suitable facemasks. some mask types come with inbuilt respirators such as filtering facepiece respirator, p respirator/gas mask, self-contained breathing apparatus, full face respirator, and kn respirators provide better breathability of the users. the name designation 'n ' in the n respirators refers to the filtration of . μm sized particles with % efficiency. the filtration mechanism of n facemasks operates on three possible principles: diffusion, inertial impaction, and electrostatic attraction. the smaller particles (< micron) usually get diffused and stuck on the filter's fibrous layers. whereas particles of typically micron or larger realize the inertia effect, preventing them from flowing across the fibers in the filtration layers slam into the mask layers and filtered. n masks are designed for single-use because of potential contamination of filter layers, resulting in rapid degradation of their filtration efficiency. however, several innovative techniques have been demonstrated for decontaminating and reusing n masks. , some recent n respirator masks are fabricated using the electrocharged polymers or electrospun nanofibers. , these materials have intrinsic electrostatic properties to attract the small-tolarge oppositely charged particles, which help in better filtration of small-size particle transmission. , because of the ongoing covid- pandemic, a significant demand for facemasks has been reported worldwide, while stimulating research about their efficacy for filtering expelled droplets from the mouth and nose of the infected person. in this regard, considerable efforts have been made in the past for the evaluation of facemasks performance. the quantitative performance of the facemasks has been typically characterized by evaluating the filtration efficiency (fe) and the total inward leakage (til). [ ] [ ] [ ] [ ] the filtration efficiency refers to the percentage of blocked particles by the tightly-fitted facemasks. the filtration efficiency can be calculated as = ( − ( ⁄ )) × %, where , are the particle count in the upstream feed prior to filtration and in the downstream filtrate, respectively. til is defined as the percentage of particles entering the mask through both the filter and the leakage between mask and face. the total inward leakage is calculated by dividing the particle concentrations on the outside and inside the facemasks. the protection factor of the facemasks can be determined from the expression; pf = /til. higher pf value of the masks perform better in virus transmission control. furthermore, the fluid penetration resistance performance of the facemasks have been evaluated as per the astm f /f m - standards. , however, this test method does not evaluate facemasks' performance for airborne exposure pathways or in the prevention of the penetration of aerosolized fluids deposited on the facemask. in recent times, some qualitative analysis has been demonstrated for the rapid design characterization of facemasks. while these experimental studies are essential for the broad characterization and design evaluation of respiratory facemasks, further theoretical and numerical methods and algorithm-based investigations provide a better insight into the facemask's fluid flow dynamics and the droplet leakage through the facemask openings. if the facemask is donned for a prolonged period, the captured fluid vapor on the filter surface may reduce the filtration efficiency. this saturation effect of the facemasks has been usually neglected in the experimental studies. to involve these factors, an alternative approach, the computational fluid dynamics (cfd) method, can be invaluable for understanding the fluid-particle flow behavior through the facemasks. the fluid dynamics based numerical techniques have gained momentum in the field of the facemask research domain. the computational fluid flow models have shown their potentials in an improved prediction of the spreading of respiratory virus-laden droplets and aerosols, sensitive to the ambient environment, and crucial to the public health responses. this review paper focuses on the fluid flow aspects of the facemasks and their efficacy in virus transmission control. following a brief introduction to the respiratory infectious diseases and their control strategies (section i), the respiratory droplet transportation mechanisms in conjunction with the possible governing equations required for estimating the transport phenomena have been presented in section ii. then, the droplet transport behavior through the facemasks has been described in section iii. key design aspects for the facemasks have been explained in section iv. section v covered the recent progress in investigating the efficacy of facemasks for preventing virus spread. the impact of using the facemasks have been discussed in section vi. the concluding remarks and a brief outlook for future research directions are summarized in section vii. during the sneezing or coughing process, the dispersion of saliva droplets or aerosols from the mouth to the ambient, and eventually on the floor accomplish in several stages. the complete transmission cycle involves complex flow phenomena, ranging from air-mucous interaction, breaking of droplets, turbulent conical jets, droplet evaporation and deposition, flow-induced particle dispersion, and sedimentation. after exhalation from the mouth or nose, the saliva droplet movement is initially led by the inertia force, followed by the formation of a conical jet (vortical flow) near the mouth. once the droplets are expelled from the mouth, the inertia force gradually decreases, and other forces like gravity control the dispersion of larger size droplets, while drag and brownian forces control the smaller size droplets. after traveling up to a particular distance, these virus-laden droplets settle down on the floor. thus, there are two major possible pathways for the respiratory virus transmission: airborne inhalation of smaller droplets, which are suspended in ambient air for a more extended period and carrying to the longer distance, and contact (direct or indirect between people and with contaminated surfaces) of large size droplets. the fluid flow behavior of these droplets has been modeled using two different phases: continuous phase for the small size droplet nuclei and discrete phase for large size droplets. the fluid flow is governed by the navier-stokes and mass transfer equations which are as follows. continuity: momentum: where , , ⃗ , , , denotes the density ( − ), time ( ), flow velocity ( − ), pressure ( ), diffusion coefficient and kinetic viscosity, respectively. the conservation laws can be written in tensor form as: here, ⃗ represents the flow velocity (m/s) and is the source term that represents other forces such as gravity, lorentz force, etc. which also leads to momentum accumulation. for the newtonian fluids, there is a linear relationship between shear stress and velocity gradient. so, the viscous stress tensor can be defined by: in the overall vector form of the constitutive equation, where t denotes the transpose of the second velocity gradient outer product. for a newtonian fluid with constant µ and ρ, the momentum equation can be rewritten as: also, the fluctuation velocity component for the laminar-to-turbulent airflow field can be predicted by the reynolds-averaged navier-stokes equations (rans) model. where are the damping factors to reflect the anisotropic magnitude of the fluctuation velocity in the near-wall region. these are the random numbers from the standard normal distribution. the cough spreading phenomena can be predicted by solving the diffusion equation ( ) in conjunction with some source and sink terms. vuorinen et al. developed diffusion-based monte-carlo models to realize a transmission phenomenon via inhalation of aerosols in the ambient flow field. the source and sink terms have been included in conjunction with eqn. ( ) . the source term represented the transient location of the infected persons while the sink term has been used for the ventilation surface. the developed models were capable of predicting the aerosol dispersions at more realistic locations like generic public place and supermarkets where cough may release from the walking person. for the droplets with the high droplet-to-air density ratio, the droplet trajectories have been predicted by solving a series of translation equations (lagrangian approach) of the discrete phase with the assumptions of stationary droplets and limited thermophoresis. continuous dispersion of saliva droplets throughout the computational domain has been considered in the computations. also, some basic parameters like velocity, mass, and position of each droplet have been computed at every time step. the translational equation for the saliva micro-droplet trajectory is given by, where , , , are the stokes drag force, gravity, lift or buoyancy force, and brownian motioninduced force, respectively. also, , , , , ⃗ are the mass, radius, volume, density, and velocity vector of the saliva droplets, respectively. , ⃗ are the fluid density and the fluid velocity vector, respectively. the drag coefficient values depend on the droplet's reynolds number and can be calculated from, here, = |⃗ ⃗ −⃗ ⃗ | . in above expressions, the droplet distribution is an important factor as their size decides the travel path distance, and eventually the infection risk. so, for coughing simulation the droplet breakup approach is used. pendar and páscoa used rosin-rammler breakup approach in their coughing simulation work which is expressed as: where and are the exponential factors and average radius of the droplet, respectively. these parameters are based on the saliva flow rate. recently, several studies have attempted to understand the dynamics of droplet formation and transport. cummins et al. investigated the dispersion of spherical droplets in the presence of a sourcesink pair flow field. the maxey-riley equation was used to describe the finite-sized spherical particle motion in an ambient fluid flow. the presented non-dimensional mathematical models were based on the newton's second law of motion in which the forces acting on the particle involved the gravity force, the drag force, an added mass force, the force due to the undisturbed flow, and a basset-boussinesq history term. the analytical results suggested that droplets with a smaller size (< μm) moved a greater distance because of gravity's smaller impact. in comparison, the larger size droplets (> μm) traveled a relatively long distance before getting pulled into the sink by their more considerable inertia. however, the dispersion of intermediate size droplets ( μm - μm) was found to be complicated under the influence of both drag and gravity forces. busco et al. used the computational fluid dynamics approach to predict droplets and aerosols spread. the biomechanics of a human sneeze, including complex muscle contractions and relaxations, were included in the simulation by imposing a momentum source term to the coupled eulerian-lagrangian momentum equations ( ) . the instantaneous magnitude of the sneezing momentum source term has been defined as | ( )| = ( )⁄ , where p(t) is the experimental pressure signal, and l is the characteristic equivalent length of the human upper-respiratory system ducts. the experimental results validated the developed model for the estimation of droplets and aerosols spreads. das et al. investigated the airborne virus transmission through sneezed and coughed droplets and aerosols. the ejected droplet motions were estimated both for still and flowing air conditions by solving the langevin differential equation using monte-carlo numerical method. the langevin equations for the transport of the droplets of mass (m) in the still air is given as, and are the coordinate and velocity shift in each discrete time step , respectively, and stands for the cartesian components of the position and velocity vectors. the first term in the righthand side of eq.( ) represents the dissipative force. the second term stands for the diffusive (stochastic) force where ξ(t) that is regulated by the diffusion coefficient d. is the gravitation force term acting on a droplet of mass m. in the expression, the value of the drag coefficients is obtained using the stokes formula, = , here is the droplet radius and is viscosity. the diffusion coefficient d is obtained from the einstein relation, = , where = . × − ⁄ is the boltzmann constant and t is the temperature in kelvin. as shown, the langevin differential equations contain a stochastic source term (diffusive force), which is usually ignored in the eulerian-lagrangian approach. also, environmental factors such as temperature, humidity, and airflow rate, which could influence the air droplet dynamics, were included. the results revealed that the small droplets travel a larger distance and remain suspended in the air for a longer time under the influence of airflow, supporting the mandatory use of facemasks to prevent the virus. vadivukkarasan et al. experimentally investigated the breakup morphology of expelled respiratory liquid. it was revealed that the droplet formation from the ejected fluid during coughing or sneezing occurred due to three possible mechanisms: kelvin-helmholtz (k-h) instability, rayleigh-taylor (r-t) instability, and plateau-rayleigh (p-r) instability in sequence. the flapping of the expelled liquid sheet was the result of the k-h mechanism, and the ligaments formed on the edge of the rim appeared due to the r-t mechanism, and finally, the hanging droplet fragmentation was the result of the p-r instability. droplet evaporation is one of the crucial factors that affect transmission phenomena. the evaporation rate of the droplets depends on the difference between the saturated vapor pressure of the fluid droplet surface and the vapor pressure of the surrounding air (ambient temperature and humidity). the other factors, such as the mass-diffusion coefficient and the relative velocity between the droplet and surrounding gas, influence the evaporation rate. the non-dimensional parameters such as reynolds, nusselt, and sherwood numbers govern the droplet evaporation phenomena. moreover, the condensation and evaporation effects between the ambient water vapors and the water liquid in cough droplets can be considered by solving the mass and energy balance for each droplet. mass balance: energy balance: where is the average mass flux of evaporable component on the surface that can be expressed as: where is the density of the ambient air, , and ,∞ are the mass fractions of evaporable component on the droplet surface and in the gas phase far from the droplets, respectively. ℎ is the sherwood number. several other researchers have studied the flow behavior of evaporating droplets. recently, weiss et al. investigated the clustering and evaporation of droplets using the gas phase and droplet coupling equations. the evaporation of droplets and spreading of vapors into the ambient condition were mostly governed by few parameters: the reynolds number, which is related to the shear rate, the stokes number, and the mass loading, which is the ratio between the mass of the liquid to the gas phase. the results suggested that the clustering and evaporation of droplets are primarily affected by the mass loading and stokes number while the taylor-scale reynolds number was small. when the mass loadings decreased, and the stokes number increased, the droplets dispersed more evenly with a faster evaporation rate. chaudhuri et al. presented a chemical reaction mechanism based collision rate model for prediction of the growth rate of the infected population for the early phases of a covid- like pandemic. besides, they developed a theoretical model for the aerodynamics of respiratory droplets by considering the evaporation characteristics of levitated droplets. the evolution of the droplets was characterized by a complex interaction of aerodynamics, evaporation thermodynamics, and crystallization kinetics. the fidelity of proposed model was further confirmed by the experimentation. respiratory droplet transmission is considered critical for the rapid spread and continued circulation of viruses in humans. in recent years, the respiratory droplets flow behavior through the facemasks has typically well-predicted using the computational fluid dynamics (cfd) techniques. the navier-stokes equations have been used as basic governing equations to solve the velocity field in a multi-dimensional computational domain. these equations have been used for the analytical assessment of the respiratory performance of the facemasks and other respirators. dbouk and drikakis performed the fluid dynamics analysis of the respiratory droplets transmission through and around a facemask filter. the compressible reynolds-averaged navier-stokes equations and the k-ω turbulence model were employed. zhang etl. analytically investigated the carbon dioxide co transportation performance inside the ventilator mask. the d model of the ventilator mask is shown in fig. a. classical navier-stokes theorem and masstransport equations were used to estimate the co residual concentrations below the nostrils. the governing equations were solved using the finite element solver ansys fluent . software. the following governing equations were used in the simulation; (i) at the entrance of the ventilator mask, the inlet pressure = . × , the average concentration of co = . %. (ii) at the exhaust holes: outlet pressure = , (iii) inlet boundary condition at the nostrils: the averaged velocity = × sin ( ), expiratory phase time t = ~ . s, inspiratory phase time t = . ~ . s, and the averaged concentration of co excreted from the nostrils was set as %. the airflow inside the ventilator mask was considered to be turbulent flow. fig. b shows the distribution of the average residual co concentration inside the ventilator mask varying with time during a complete respiratory cycle. as shown from the curve, initially, the co concentration increased with the increasing exhaled air and reaches the peak value of . %, and then it declined gradually with the decrease of the exhaled air and reaches down to the value of . % at the end time of expiratory cycle. based on these results, the ventilator mask was redesigned by changing the exhaust hole to the bottom side and the local residual co concentration was decrease to . %. bates et al. performed computational fluid dynamics simulations to access the respiratory airflow in the human upper oral airway with airway wall movement. the breathing flow rate data was acquired by imaging the breathing cycle of the participant while wearing of a size- anesthesia facemask (fig. c) . the air pressure drop and flow velocity were estimated by solving the navier-stokes equations for the moving mesh vertices in the finite volume domain. the governing equations for moving mesh of the finite volume form is given by: momentum equation: where is time, is the volume of each cell in the mesh, is the air density, ⃗ is the air flow rate, ⃗⃗⃗⃗ is the mesh velocity as calculated from the mesh displacement for each control points, is a vector representing the surface of each mesh cell, is the identity matrix, and is the viscous stress tensor. these equations were solved using the large eddy simulation (les) techniques. the instantaneous air flow resistance was calculated as the pressure loss between two locations divided by the air flow rate through them. fig. d shows the estimated airflow resistance through several different regions of the extra thoracic airway during the complete breathing cycle. the aerosol droplets transmission phenomena through the facemasks have also been investigated analytically. the facemask leakage factor has been considered in the analytical models. lei et al. predicted the fluid leakage between an n filtering facepiece respirator (ffr) and a headform using the computational fluid dynamics (cfd) simulation approach. the mass flow rate at the faceseal and through the filter medium was calculated under three different boundary conditions: varying breathing velocity, varying viscous resistance coefficients of the filter, and the freestream air flows. the filter-to-faceseal leakage (ftfl) ratio for the respirator was obtained by dividing the mass flow rate through the filter medium and the faceseal leakage. a higher ftfl ratio refers to the higher percentage of airflow passing through the filter medium than the faceseal leakage. the results revealed the nonlinear increase in the ftfl ratio with increasing breathing velocity values and decreasing the filter viscous resistance coefficient values. furthermore, the freestream flow had limited influence on the airflow inside the respirator resulting in nonsignificant variations on the ftfl ratio. perić et al. thermal comfort is an essential aspect of a facemask as it may affect the compliance of the use of facemask during summer or in tropical countries. there were reported incidence of skin rashes, increased heat stress, sweating, and discomfort due to prolonged wearing of a facemask in hot and humid conditions. to improve the thermal comfort level of facemasks, researchers have developed some unique facemasks by using the nanocomposites. polymer-based nanofibers with large surface area-to volume ratio have shown great potential for use in facemasks to achieve both high filtration efficiency and sufficient air permeability. . (a-c) show the schematic, photographs, and scanning electron micrographs of the proposed hybrid nanofiber-based facemask. the comparative pm capture efficiency and air permeability results have demonstrated the superiority of presented facemask over the commercial masks (fig. d, e) . moreover, the thermal image revealed that the fiber/nanope facemasks had high transparency to the human body radiation (cooling effect). in contrast, the commercial facemasks blocked a large portion of it. they further modified the nanope substrate with ag coating and demonstrated that fiber/ag/nanope had a warming effect. zhang et al. reported the use of an active ventilation fan to reduce the dead space temperature and co level. an infrared camera (irc) method was used to elucidate the temperature distribution on the prototype ffr's outside surface and the wearer's face, surface temperature was found to be lowered notably. both inside and outside temperature resulted from the simulation were found to be in good agreement with experimental results. however, the inward blowing fans may compromise the filtering effectiveness of the facemask. there are commercially available facemasks fitted with one-way valve for facilitating the removal of humidity and expired air within the space between the facemask and the face. however, during the covid- pandemic, one of the main reasons for wearing the mask is not only to protect the inhalation of virus, but also to prevent the spread of virus into the air if the wearer happens to be a carrier of the virus. if the wearer is a healthy subject, the use of a one-way valve and ventilation fan would indeed mitigate the buildup of humidity and carbon dioxide within the dead space. zhu et al. reported a three-dimensional model of normal human nasal cavity to simulate the volume of fraction of both fresh air and respired air within the nasal cavity. the model consisted of large rectangular domain outside the nasal cavity representing ambient air, human nasal cavity and partial of the pharynx. this was the first reported piece of work that modelled the details of nasal cavity instead of just the nostrils as openings for the flow simulations. the advantage for this simulation was that the flow field within the space between the nostrils and facemask could be more accurately simulated as the boundary condition could be specified away from the nostril at the pharyngeal area. two cases were simulated. case i refers to a human face with a n respirator onto human face, and case ii refers to a human face without a respirator. the results showed that above % of inspired air was respired air in case i compared to less than . % in case ii. during expiration, the volume of fraction (vof) of respired air in both cases was above %. the streamlines at peak inspiration were relatively smooth while entering the cavity in both cases; while at peak expiration large vortex was observed within the air space between human face and respirator in case i. for future studies, one could explore the in vivo experimental studies with the use of miniaturized and wireless sensors for monitoring not just the temperature, but also the humidity and carbon dioxide content within the space between the nostrils and the facemask. the sensors need to be small so as not to disrupt the flow fields. if a single sensor cannot be small enough for the measurement of all the three parameters, one may need to have separate sensors and repeat the experiment for the same human subject. another important parameter affecting the comfort of the wears is the flow resistance of the facemask. in principle, if the flow resistance is lower while maintaining the same filtering efficiency, the comfort level will be enhanced. however, the facemask's flow resistance is just an indicator and does not specify the wearer's breathing resistance. while the flow resistance could be measured using a typical setup for correlating the fluid flow rate to the pressure drop across the facemasks, the breathing resistance could only be measured using a human subject or a replica of the nasal pharyngeal system. lee and wang presented the pioneering work of measuring the nasal airflow resistance during inspiration and expiration using a standard rhinomanometry and nasal spirometry. a modified full-facemask was produced in-house to measure nasal resistance using n ( m ) respirators. the results showed a mean increment of % and % in inspiratory and expiratory flow resistances, respectively, with n respirators. there was also an average reduction of % in air exchange volume with the use of n respirators. the same group did a follow-up study investigating the change of human nasal functions after wearing an n respirator and surgical facemask. the human subject study involved healthy healthcare workers. each of the volunteers attended two sessions and wore an n respirator in session (s ) and surgical facemask in session (s ) for hours. the mean minimum cross-sectional area (mmca) of the two nasal airways via acoustic rhinometry and nasal resistance via rhinomanometry was measured before and immediately after the mask. the equipment could not perform in vivo measurement with the facemask on. rhinomanometry was repeated every minutes for . hours after the removal of masks. a questionnaire was distributed to each of the volunteers during the hours mask-wearing period to report subjective feelings on the discomfort level of breathing activity. among volunteers who completed both the two sessions, the mean nasal resistance immediately increased upon removing the surgical facemask and n respirator. the mean nasal resistance was significantly higher in s than s at . hours and . hours after removing the masks (p< . ). there was an increase of nasal resistance upon removal of the n respirator and surgical facemask, potentially due to nasal physiological changes. n respirator caused higher post-wearing nasal resistance than surgical facemask with different recovering routines. this was the first time that the effect of long duration wearing a facemask was objectively monitored. however, the during of three hours for the wearing of a facemask was deemed to be too short under the current covid- simulations, and human subject study for a longer duration of wearing facemask should be attempted. the research could also be enhanced using miniaturized pressure, temperature, humidity, and gas sensors for in vivo monitoring of the air condition within the space between the nostrils and the facemask. such experimental data would be useful for validating numerical models for assessing the comfort level for wearing different types of facemask. another potential approach is to develop a replica for replacing human subject for such long duration study, similar to the use of an acoustic head for replacing human subjects in the more extended duration noise exposure study. zhu et al. reported another investigations on effect of long duration wearing of n and surgical facemasks on upper airway functions. a total of volunteers of national university hospital singapore were participated for the study. each of the volunteers wore both n respirator and surgical facemask for hours on two different days. during the period of mask wearing, relative airflow rates were recorded. the study revealed that the increased level of discomfort to the user with time while wearing the masks. moreover, n respirator caused higher post-wearing nasal resistance than the surgical facemask with different recovering routines. the current studies recognized that the airborne transmission of aerosols produced by asymptomatic individuals during speaking and breathing as a key factor leading to the spread of infectious respiratory diseases such as covid . , [ ] [ ] [ ] however, the spread of these airborne diseases has been successfully controlled up to a certain extent by using the facemasks. , , , [ ] [ ] [ ] in the ongoing global pandemic of the covid , where vaccine developments still at a phase trial stage, the respiratory protective equipment such as facemasks has proven to be a complementary countermeasure against the spread of the novel coronavirus. in this regard, several researchers have performed theoretical and experimental investigations of virus transmissibility through the facemasks and alternatives. stutt et al. developed the holistic mathematical frameworks for assessing the potential impact of facemasks in covid pandemic management. the results revealed that professional and home-made facemasks were highly efficacious to reduce exposure to respiratory infections among the public. also, when people wear the facemasks alltime at the public places, the certain epidemiological threshold, known as the effective reproduction number, could be decreased below , leading to the prevention of epidemic spread. ngonghala et al. developed a parametric model for providing deeper insights into the transmission dynamics and control of covid- in a community. they used the covid data from new york state and the entire us to assess the population-level impact of the various intervention strategies. the results suggested that the consistent use of facemasks could significantly reduce the effective reproduction number. the highly efficacious facemask, like surgical masks with estimated efficacy of around %, could lead to the eradication of the pandemic if at least % of the residents use such masks in public consistently. the use of low efficacy masks, such as cloth masks with an estimated efficacy of %, could also lead to a significant reduction of covid- burden. yan et al. evaluated the effectiveness of different respiratory protective equipment in controlling infection rates in an influenza outbreak. they used a previously developed risk assessment model to show n respirators' efficacy, low-filtration surgical mask (adult), high-filtration surgical mask (adult), high filtration pediatric mask, and low filtration pediatric mask. the study revealed that donning these masks with a % compliance rate resulted in a significant reduction in transmission risk, and with % compliance rate nearly eradicated the influenza outbreak. prasanna simha and rao quantitatively investigated the distance of travel of typical human coughs with and without different masks: disposable three-ply surgical masks and n masks. in their study, the schlieren method, a highly sensitive, non-intrusive flow imagining technique, was used to visualize the human cough flow features. the experimental statistics showed that the propagation of a viscous vortex ring mainly governed cough flow behavior. while wearing regular face masks, the cough droplets traveled approximately half the distance traveled by expelled droplets without a mask. however, n was found to be most effective in limiting the spread of cough droplets. leung et al. performed experimental studies to investigate the efficacy of surgical facemasks to prevent respiratory virus shedding. the surgical facemasks' efficiency was measured against the coronavirus, influenza virus and rhinovirus of two broad particle sizes, respiratory droplets (≥ µm) and aerosols (droplet nuclei with aerodynamic diameter ≤ µm). the results indicated that surgical facemasks could efficaciously prevent transmission of human coronaviruses and influenza viruses into the environment in respiratory droplets, but no significant reduction in aerosols. moreover, the steep rise in demand for medical facemasks during the current pandemic covid has resulted in a subsequent breakdown of the global supply chain that led to an acute shortage in the market. to mitigate this discontinuous supply chain system, scientists have put much effort into exploring alternative fabrics with sufficient filtering capacity that are readily available and affordable. kähler and hain performed a detailed analysis of the efficacy of facemasks to prevent virus spread. in the first step, the transmission of droplets released by the mouth when breathing, speaking, and coughing was characterized. then, the filtering capacity of the various facemasks was analyzed. the experimental results have shown that most household materials tested do not provide much protection against the virus transmission via droplets and, therefore, unsuitable as materials for protective masks. however, filtering facepiece respirators (ffr) performance-based masks such as ffp (europe en - ), n (united states niosh- cfr ), ds (japan jmhlw-notification , ), and kn (china gb - ) offer adequate protection, as they are only permeable to a tiny fraction of few micron-sized droplets. konda et al. evaluated the filtration efficiency of various commonly available fabrics, including cotton, silk, chiffon, flannel, various synthetics, and their combinations, which were used in the fabrication of cloth masks. the filtration performance of these fabrics was conducted by generating the aerosol particles at the cloth sample's upstream side. the aerosol particulates ranging from ~ nm to ~ ten μm scale sizes, particularly relevant for respiratory virus transmission, were produced by commercial sodium chloride (nacl) aerosol generator. also, the air with a controlled airflow rate was drawn through the sample using a blower fan. the filtration efficiency of each sample was computed by measuring the particles' concentration upstream and downstream as = − × , where and are the mean particle concentrations per bin upstream and downstream, respectively. moreover, the pressure drop across the facemasks and the air velocities were measured using a digital manometer and a hot wire anemometer. the experimental investigations revealed that the materials such as natural silk, a chiffon weave ( % polyester− % spandex fabric), and flannel ( % cotton− % polyester blend) provided good electrostatic filtering of particles. also, fabric with tighter weaves and low porosity, such as cotton sheets with high thread count, have resulted in better filtration efficiencies. for instance, a tpi (thread per inch) cotton sheet can provide average filtration efficiencies of ± % (in the nm to nm range) and . ± . % (in the nm to μm range). a cotton quilt with batting provides ± % ( nm to nm) and . ± . % ( nm to μm). surprisingly, four-layer silk (e.g., scarf) was found to be effective with an average filtration efficiency of > % across the ten nm− μm particle size range. moreover, the hybrid masks made by combinations of two or more fabric types, leveraging mechanical and electrostatic filtering, could be an effective approach for better filtration (fig. a) . verma et al. performed the qualitative investigations for assessing the effectiveness of easily available facemasks such as bandana (elastic t-shirt material, threads/inch), folded handkerchief (cotton, threads/inch ), stitched mask (quilting cotton, threads/inch) and other commercial masks. they observed that a stitched mask made of quilting cotton was most effective, followed by the commercial mask, the folded handkerchief, and, finally, the bandana. their observations also suggested that a higher thread count by itself is not sufficient to provide a better droplet filtration capability. the material types and fabrication techniques have a significant impact on the performance of facemasks. davies et al. examined the efficacy of homemade masks as an alternative to commercial surgical masks. various household materials such as % cotton t-shirt, scarf, tea towel, pillowcase, antimicrobial pillowcase, vacuum cleaner bag, cotton mix, linen and silk were evaluated for the capacity to prevent bacterial and viral aerosols transmission. the performance of these household facemasks was compared with the standard surgical mask. the experimental outcomes showed that these homemade masks could reduce the likelihood of infection, but not efficient for the complete elimination of risks. a similar conclusion has been made in a previously published review article by rossettie et al. and loupa et al. recently, ho et al. investigated the droplet filtration efficiency of the self-designed triple-layer cotton masks, their performance was compared with the standard medical mask. all tests were performed in two different locations; in a regular bedroom and a car with air conditioning. the particles with a size range of - nm were taken into consideration, and the filtration efficiency was measured. other factors like environmental conditions (temperature and relative humidity) and cough/sneeze counts per hour were measured for each measurement. the results revealed that cotton and surgical masks could significantly reduce the number of microorganisms expelled by participants with the filtration efficiency of . % and . %, respectively (fig. b) . however, the surgical mask was three times more effective in blocking transmission than the cotton mask. in a recent study, fischer et al. performed testing of different facemasks or mask alternatives ranging from the kind worn by healthcare professionals to neck fleeces and knitted masks. fig. c shows the photographs of the facemasks and alternatives considered in the investigation. a comparison was made on the dispersal of droplets from a mask wearer's breath while wearing one of the face coverings to the results of a controlled trial where their mouth was fully exposed. the study revealed that some mask types matched standard surgical masks' performance, while some mask alternatives, such as neck fleece or bandanas, offered little protection against infection. the neck fleece was found to increase the risk of disease by having a "droplet transmission fraction" of % (fig. d) . besides, they demonstrated a simple optical measurement method to evaluate the efficacy of facemasks to reduce respiratory droplets transmission during regular speech. fig. e shows the schematic of developed setup. the proposed optical system is inexpensive and easy-to-operate, even by non-experts. furthermore, the use of face shields has widely been used along with standard face masks. face shields are generally made of transparent plastic sheets. they offer several advantages: comfortable to wear, easy-to-clean, clear conversations between the speakers with visible facial expressions, and reduce autoinoculation by preventing the wearer from touching their face. also, face shields prevent the user's face from the direct contact of liquid droplets. more recently, verma et al. investigated the effectiveness of the face shields and exhalation valves in the respiratory droplets transport context. they performed experimentation in an emulated coughing and sneezing environment for qualitative visualizations analysis. the results indicated that although face shields block the initial forward motion of the fluid jet, the expelled droplets can move around the visor with relative ease and spread out over a large area depending on environmental conditions. also, for the facemasks equipped with an exhalation port, the droplets pass through the exhalation valves. based on the observations, they opined that high-quality cloth or surgical masks perform better than the face shields and exhalation valves. in the past few decades, especially post-outbreak of the severe acute respiratory syndrome (sars) in , wearing the facemasks has grown extensively. the people from asian countries like china, singapore, thailand, japan, etc. can be easily seen donning facemasks in public places. there are well proven-studies about the prevention of airborne pathogens transmission by covering the mouth and nose using the facemasks. the recently published article by gandhi and rutherford, claimed that the universal facial masking might help reduce the severity of disease and enhance the wearer's immunity. however, prolonged use of facemasks has some side effects on human respiratory health, such as carbon dioxide builds up, drowsiness, and breathing problems because of restricted fresh airflow, and unusual heart rate. , if a facemask is donned for a longer period, the filter gets wet because of facial sweat, and vapor is formed inside the facemasks due to the breathing, resulting in clogging of particulates. also, wearers get a false sense of security, encouraging them to spend more time in public places. other potential side-effects of facemasks wearing include skin irritation, uncomfortable feeling due to the arrival of exhaled air into the eye, comprised quality and the volume of the speech during the conversations. , , moreover, there are some environmental concerns associated with the use of single-use facemasks. some of these facemasks are made from layers of plastics, which may not bio-degrade easily, thus creating a massive burden on the environment. a recent analysis has reported that if every person in the uk used one single-use facemask each day for a year, it would create , tonnes of contaminated plastic waste, roughly ten times higher than that of using reusable masks. the new coronavirus is continuously evolving and spread all over the world. researchers from all disciplines, especially the medical professionals and engineers, are continuously working on the facemasks design improvement for a better performance against the virus transmission. zhou et. al. presented an electrospun polyetherimide (pei) electret nonwoven material based bi-functional smart facemask to remove the sub-micron particulate matter and generate electricity. the facemask could harvest sufficient energy from the airflow to supply power to the inbuilt lcd panel. the lcd screen was used to display the measured breathing rate. hossain et al. developed a rechargeable n facemask that composed of a charged polypropylene electret fiber made an intermediate layer for capturing the foreign particles. these particles are trapped through the electrostatic or electrophoretic effects of the polypropylene terephthalate (pet) layer. the mask has a provision for the in-situ recharging of the polypropylene electret for maintaining its filtration performance. williams et al. proposed a facemask used for the sample collection of respiratory sars-cov- virus. they have successfully presented a facemask prototype the detects exhaled mycobacterium tuberculosis, a deadly lung infection, and now working for sampling for the sars-cov- virus. the facemask consisted of four d printed polyvinyl alcohol (pva) sampling strips attached inside it. the sampling matrices trapped the particulates during exhalation and was further post-processed for the virus diagnosis. face-mask sampling offered a highly efficient and non-invasive method for respiratory disease diagnosis. the presented approach showed great potential for diagnosis and screening, particularly in resource-limited settings. moreover, several innovative facemask prototypes with better filtration performance are available in the market. recently, korean electronics and appliance company lg® ltd. has developed an air purifier wearable mask (puricare™) equipped with battery-operated miniature fans that draw in the fresh air and help reduce stuffiness. the massachusetts institute of technology and brigham and women hospital, boston's researchers have developed the, a silicone-based transparent reusable facemask with a comparable performance level with n respirators. the facemasks have shown their potentials for preventing the spread of respiratory disease. a variety of facemasks ranging from a simple homemade cloth mask to the ventilated respirators, have played their role in the current covid- pandemic. in general, the facemasks have been experimentally characterized by determining the filtration efficiency and total inward leakage ratio. also, the fluid flow dynamics-based numerical methods have gained much attention to investigating the facemask performances. the present article has also highlighted the insufficiencies of assessing the breathing resistance of the wearers with the facemask by just examining the flow resistance of the facemask. in the longer term, there may be a need for a more elaborate system approach including the study and modeling of how the human lung would respond to the increase in breathing resistance due to the use of facemask, drawing the analogy of modeling the behavior of the heart for the blood circulation system. this article summarizes the perspective of the fluid dynamics of the facemask filtration performance, including droplet and aerosol transports, droplet evaporation, and facemask aerodynamics. furthermore, recent investigations for the efficacy of the facemasks in the context of respiratory virus transmission have been discussed. proc. natl. acad. sci infection prevention and control of epidemic-and pandemic-prone acute respiratory infections in health care national center for immunization and respiratory diseases (ncird), division of viral diseases face masks and coverings for the general public: behavioural knowledge, effectiveness of cloth coverings and public messaging advice on the use of masks in the context of covid- : interim guidance standard test method for evaluating the bacterial filtration efficiency (bfe) of medical face mask materials using a biological aerosol of staphylococcus aureus, astm f /f m - , standard test method for resistance of medical face masks to penetration by synthetic blood (horizontal projection of fixed flow analyses to validate sars-cov- protective masks the southwest respiratory and critical care chronicles lg revolutionizes personal clean air with puricare™ wearable air purifier engineers design a reusable, silicone rubber face mask the first author would like to acknowledge the financial support from the ministry of education rsb research fellowship singapore. the data that support the findings of this study are available from the corresponding author upon reasonable request. key: cord- -wz jan d authors: li, hongying; leong, fong yew; xu, george; kang, chang wei; lim, keng hui; tan, ban hock; loo, chian min title: airborne dispersion of droplets during coughing: a physical model of viral transmission date: - - journal: nan doi: nan sha: doc_id: cord_uid: wz jan d the covid- pandemic has focused attention on airborne transmission of viruses. using realistic air flow simulation, we model droplet dispersion from coughing and study the transmission risk related to sars-cov- . although most airborne droplets are - $mu$m in diameter, the droplets with the highest transmission potential are, in fact, - $mu$m. use of face masks is therefore recommended for both personal and social protection. we found social distancing effective at reducing transmission potential across all droplet sizes. however, the presence of a human body m away modifies the aerodynamics so that downstream droplet dispersion is enhanced, which has implications on safe distancing in queues. based on median viral load, we found that an average of . viral copies is inhaled at m distance per cough. droplet evaporation results in significant reduction in droplet counts, but airborne transmission remains possible even under low humidity conditions. the current coronavirus disease outbreak is an unprecedented global crisis with confirmed cases in the millions. the exceptional infectiousness of the severe acute respiratory syndrome coronavirus (sars-cov- ) has focused attention on the nature of its transmission pathways, with suspicion for an airborne route. [ ] [ ] [ ] airborne transmission depends on three main factors, namely, stability of virus, air circulation and droplet deposition. sars-cov- is found to be stable in aerosol for up to the three hours of an experiment similar to its predecessor sars-cov- which in certain circumstances, achieved airborne transmission. airborne transmission of sars-cov- cannot be dismissed even though epidemiological studies giving an r between and do not support airborne transmission as the major route of transmission. recent air sampling conducted in airborne infection isolation rooms has found pcr-positive particles of sizes in excess of μm despite extensive air changes. during a cough or sneeze, mucosalivary fluid is expelled into the surrounding air in the form of droplets. , droplets greater than μm in diameter are termed as respiratory droplets whereas those less than μm in diameter are droplet nuclei. the size of the droplets affects the range of dispersal significantly. respiratory droplets tend to settle quickly and contaminate surrounding surfaces within a short distance, , whereas droplet nuclei can remain airborne for hours and present a long-range transmission risk. as a first line of defence against the pandemic, many countries have adopted what is commonly known as 'social distancing' where individuals are advised, sometimes legally mandated to maintain a certain distance from other individuals in public. mathematical models suggest that enforced physical separation could be an effective measure when deployed swiftly during a viral outbreak, based also on simulations of past viral outbreaks. the actual recommended distance varies from m (singapore), . m (australia), feet (cdc, usa) to m (uk). generally public guidelines range from to m, and the 'science behind these numbers', as policy makers put it, is loosely based on an early seminal work. in a recent study based on turbulent cloud physics, cough droplets are reported to spread up to - m. further, researchers at wuhan hospitals found corona-virus residues in floor samples up to m from identified sources. hence, even though the rationale behind social distancing is robust, there is clearly no consensus as to what constitutes a safe separation distance, even for health workers treating infected patients. fluid dynamics plays an important role in almost every aspect of this pandemic. a brief survey of cough dispersion studies yields theoretical puff model and plume model , supported by visualization techniques such as schlieren , shadowgraph , and particle image velocimetry , . notably, numerical methods, such as computational fluid dynamics (cfd) based on reynolds averaged navier-stokes (rans) turbulence models produce high resolution flow fields and concentration data, which not only compensate for slow instrumental speeds of analytical techniques, but are also adaptable to different environments and scenarios, such as passengers in an aircraft cabin, and more recently, a cough dispersion study in an outdoor environment under significant wind speeds, whose results are useful in integrated transmission modeling. it is important to note that droplet dispersion model may infer transmissibility but not the actual infection risk. that will take an infectious dose, which refers to the number of viral particles to establish an infection in half of individuals, which depending on the type of virus. risk assessment of airborne infection should also account for actual viral transport. in this study, we performed numerical simulations of droplet dispersion from a single cough based on single person and two person settings under realistic indoor conditions and assess viral transmission through airborne droplets. we consider a standing person who initiates a sudden, involuntary cough in an indoor environment. for reference we shall label the person the 'cougher'. our objective here is to assess the droplet dispersion potential under representative conditions: slight breeze from behind towards the cougher at a speed · m/s, an ambient air temperature of °c and a relative humidity of % (typical humidity in an air-conditioned environment). as detailed in the supplementary information, the model cough is inclined downwards at an average of · °, follows a characteristic air flow pattern , at breath temperature of °c, and emits a cluster of droplets with a standard size distribution , and viral loading we collect all droplets past designated distances, specifically · , · , · and · m from the source and characterize their respective size distributions time-averaged up to s since the onset of the cough, and adjusted for wind speed ( · m/s). the droplet count probability is a probability function obtained by taking the ratio of the number of droplets of a certain size and the width of the corresponding size interval based on the original size histogram. to assess viral transmission potential, we calculate the number of viral copies found in each droplet in terms of the viral load (copies per volume). the median viral count probability is a probability distribution obtained by taking the product of median sars-cov- viral load ( · × copies/ml) and the droplet count probability distribution. the viral loading found in saliva is assumed to be homogeneously distributed among droplets emitted during a cough. to assess the extent of exposure, we collect droplets deposited on the listener model surfaces, over the entire body (surface area · m ) and the mouth region ( · cm ), assuming mouth breathing, and including normal breathing cycles. separately, we include a scenario where the listener is wearing a mask (aspect ratio · ) and account for droplets landing on the mask ( cm ). the droplet deposition count probability is a probability function obtained by taking the ratio of the number of deposited droplets of a certain size and the interval of that size based on the original size histogram. the median viral deposition count probability is a probability distribution obtained by taking the product of median sars-cov- viral load ( · × copies/ml) and the droplet deposition count probability distribution. total deposited viral counts are obtained by integrating the respective median viral count probability distributions within size distribution limits ( - µm). pulmonary deposition efficiency is not considered, since all droplets are in micron size range and do not escape readily via exhalation. in addition, we do not distinguish between exposure to ingested or inhaled droplets, and trapped droplets do not re-entrain. for the base case with a single cougher, figure shows snapshots of - µm droplet dispersion up to s following a cough, side and top-down view, without (top) and with evaporation physics (bottom). generally, larger droplets (in red) separate from the cloud and settle in seconds with a dispersion range of barely m; smaller droplets (in blue) are buoyant and spread over large distances but may also evaporate rapidly into residues known as droplet nuclei. for non-evaporative case ( figure ; top), the droplet cloud starts off as a fast moving puff from the oral region but quickly disperses into a plume inclined at an angle from ° to ° ( s) from the chest. top-down view shows that the lateral droplet dispersion in depth is relatively constant, and by inspection, the plume can be effectively confined within a ° forward wedge. droplets near the sides of the virtual wedge travel faster than those near the center due to entrainment of air flow into the wake. for the evaporative case, significant reduction in droplet counts is observed seconds from the cough (figure ; bottom). at relative humidity of %, the lifetime of a droplet - µm is in the order of seconds (supplementary figure s ). small droplets rapidly evaporate into droplet nuclei, which continue to remain airborne for a long time due to their small size. as evaporating droplets decrease in size, the settling times are increased, resulting in a horizontal plume at hip level. droplets are also observed to become more mono-disperse (a decrease in diversity of droplet sizes) compared to non-evaporative case. top-down view shows minimal lateral dispersion for the remaining droplets. taking the ° forward wedge plume from the non-evaporative case, it is likely that evaporated droplets, or droplet nuclei, would follow similar dispersion trends. the droplet count probability depends on the droplet size distribution and distance from the cougher ( figure ). the mode of the distribution lies between and µm; closer to µm at short distances (< m) but closer to µm at longer distances. increase in distance results in reduction of droplet counts across all droplet sizes. interestingly, we find that droplets between and µm represent the highest transmission potential in terms of droplet sizes. fewer in numbers compared to - µm droplets, these - µm droplets contain much higher viral counts due to their larger volumes. larger droplets greater than µm contain even higher viral count per droplet, but they tend to settle rapidly and therefore present little airborne transmission potential except under strong wind conditions. exposure to virus via droplets depends on distancing, as well as wind speed and direction ( figure ). for · m distancing without evaporation, the median viral count accumulates rapidly to in less than s due to high velocity droplet transport from the cough jet, which is substantially faster than the background wind drift. between to s, viral counts are elevated from copies up to due to the passage of a cloud of large droplets drifting close to the ground before settling (figure ; - . s); these droplets contain high viral counts. as distancing increases, the droplets become more wind dispersed, in this case, at a wind speed of · m/s. in particular, it takes approximately s for viruses to be projected over a distance of m. this delay may provide sufficient time for simple reactive measures, such as stepping away or wearing a surgical mask. for the evaporative case with · m distancing, the median viral count accumulates rapidly to , then decreases as smaller droplets with lifetimes under s evaporate into nuclei. between · to s, viral count increases from copies up to also due to the passage of a cloud of large droplets drifting close to the ground. compared to the non-evaporative case, this increase is more significant, because large droplets tend to evaporate slowly compared to small ones (supplementary information), and as droplet lifetimes are increased as they shrink in size and they remain airborne for longer periods of time. in addition, the non-volatile components are conserved, so the viral loads (in copies per unit volume) in evaporating droplets are higher than the original viral loads released from the source. upon complete droplet evaporation, viruses persist in the dry residue as airborne nuclei, which continue to pose infection risks over extended distance and time. here, the viral counts shown in figure represents droplet transmission and excludes viruses contained in airborne nuclei. the number of viral copies required to establish an infection in half of individuals, or infectious dose (id), is wide-ranging and depends significantly on the type of virus. the id for sars-cov- is currently unknown but expected to be small, based on how fast the virus has spread globally. since the viral load sampled from patients on admission day is more than times the median load, reading off at a rescaled viral dose of ~ ( / ) would suggest significant infection probabilities. for m distancing, figure shows snapshots of - µm droplet dispersion up to s following a cough, side and top-down view, without (top) and with evaporation (bottom). with a listener model as an obstacle to air flow, the aerodynamics is modified so that the droplet plume is elevated and its angle is now horizontal from the cougher's chest level up to s following the cough. the presence of the listener at m has effectively increased the dispersion range of the droplet plume, with practical consequences. observe that the head of the listener is engulfed by the droplet plume when it should not be at that distance ( figure ) . also, now since air has to move around the listener, the lateral dispersion length is now defined by the characteristic width of the listener (shoulder to shoulder), which by inspection, results in a ° wedge, instead of the ° wedge previously obtained for single cougher case ( figure ). further downstream, the lateral plume angle is horizontal and as before, the droplets further from the center travel faster than those near the center due to entrainment of air in the listener's wake. for the evaporative case, significant reduction in droplet counts is observed seconds from the cough (figure ). unlike the non-evaporative case, the dispersion of evaporating droplets is found to be relatively unaffected by the presence of the listener. dispersion of droplet nuclei is expected to follow air streamlines due to their small sizes. figure shows the air flow field with listener m away at · and · s from the cough. at the mouth level, the velocity field is initially dominated by the high velocity air jet from the cough. both the width of the cough jet and the decay of jet speed fall within expected ranges reported in experimentally measured cough profiles. at the waist level, the flow field is unaffected by the cough jet. the median viral deposition count probability based on sars-cov- viral load ( · × copies/ml) shows significant viral deposition on the body surface ( figure ) . interestingly, the highest viral counts found on the body are deposited by droplets of sizes - µm at m and - µm at m, which is the opposite trend for droplet counts ( - µm at m; - µm at m). this is because large droplets - µm settle preferentially at distance - m, leading to significant reductions in viral counts. total deposited viral counts are · viral copies on the listener's body, · on mask, and · on mouth (inhaled). when extrapolated to day- viral load, the inhalation exposure increases to · copies, which remains lower than the infectious dose (id) of most common viruses. increasing distancing to m results in significant reductions in viral deposition counts on the body and transmission risks from droplet inhalation. young children may be at greater risk from droplet transmission compared to adults ( figure ). inspection of the droplet plume shows maximum droplet count densities at characteristic heights at · m for m distancing, and · m for m. a useful guideline for height-related risk would be within a height difference of cm at a distance of m, and cm a distance of m, depending on the height of the cougher. most airborne droplets are - µm in diameter, but droplets with the highest transmission potential are, in fact, - µm, due to their higher viral content (figure ). surgical masks are known to be effective at trapping these larger droplets, so they are recommended for use as necessary. our results suggest that social distancing is generally effective at reducing droplet counts across all droplet sizes. specifically, an increase in distancing from . m to m significantly reduces potential exposure to large droplets greater than µm, and further increase in distancing to m further halves the transmission potential across all droplet sizes. understanding the infectious dose of sars-cov- is essential to quantitative risk assessment. under low humidity conditions, small droplets evaporate rapidly in a fraction of a second, whereas moderately large droplets can persist over a few seconds and remain airborne ( figure ). evaporated droplet residues, or nuclei, contain high viral densities and present long ranged airborne transmission risks. smaller and lighter, these droplet nuclei contain viral residues in a compact form and could remain airborne for long period of time, projecting transmission risks over long distances. the effect of desiccation on the viability of sars-cov- found in droplet nuclei is currently not well understood. interesting aerodynamics come into play when a person obstructs the airflow downstream from the cough (figure ) . counter-intuitively, the person being m away from the cough may not only fail to obstruct the plume itself, but instead enhance its dispersion range further downstream. this suggests that a m distancing rule between individuals in a queue may have adverse consequences. the airflow result for m distancing also has practical consequences for face shield users. based on our modelling results, the droplet plume for a person at m follows the air flow over the chest (figure ) , so the droplets reach the face region from a bottom-up direction which circumvents the face shield. therefore, the face shield may be ineffective as a protection against droplets based on aerodynamic considerations. an improvement to the face shield design could be a chin plate that prevents air flow from the chest upwards; air could instead be drawn in from the back of the head around the sides. based on median viral load, an average of · viral copies is inhaled m away from a single cough. this seemingly low figure could still be amplified through successive coughs at higher viral loads and accumulated over time. droplets deposited on skin and clothes could still lead to secondary transmission modes such as face touching. the present study has several limitations. first, the cough model is idealized. the droplet size distribution is based on cough tests and measurements of some , droplets captured on slides and the cough airflow based on test subjects. these sources, while representative, do not account for significant variations in coughing intensity and duration. second, droplets emitted through vocalization and sneezes are not considered in this study. third, the height of the cougher can affect the dispersive range of droplets, especially larger droplets which tend to settle rapidly on emission. this effectively increases the droplet transmission potential from taller infected persons. fourth, a light prevailing wind with constant speed is assumed for indoor conditions, but wind speed significantly affects the dispersion range of droplet. under outdoor conditions, wind speeds can reach up to several meters per second, leading to dispersion ranges that exceed currently accepted social distances even under strongly evaporative conditions. fifth, this study does not distinguish between viable and non-viable viruses, only viral count and load. sixth, the evaporation physics used here is based on weak coupling between droplets, so droplets evaporate rapidly into smaller droplet nuclei which persists airborne. a separate study on the evaporation of droplets with non-volatile content is currently in progress. from our data, we conjecture that the concept of "airborne" or "droplet" transmission as applied to a respiratory pathogen may be relative. physical factors, such as wind speed and direction, interact with biological ones, such as infectious dose, to determine the likelihood with which the coughing sick infect others in their immediate vicinity. the size distribution of droplets emitted in a cough is reproduced from a seminal study by duguid , as shown in supplementary table s based on saliva samples of hospitalized patients, the median sars-cov- viral load is found to be . × copies/ml, with a range from . × to . × copies/ml. day- viral loading from admission day samples was reported to be . × copies/ml and this sets the transmission risk limit for our modelled source. assuming that salivary viral loading rates are conserved in droplets emitted during a cough, the viral content in a droplet can be determined depending on its size. droplets with diameters greater than µm neglected in this study due to their extremely fast settling rates and low dispersion potential. for modelling purposes, droplets are generated based on discrete size distributions and injected randomly within mouth region at the start of the simulation. the problem mentioned above is governed by fluid flow, droplet movement as well droplet evaporation for the evaporation scenario. the governing equations then include navier-stokes equation, proper turbulent flow model as well as discrete phase movement and droplet evaporation equations, respectively. the governing equations for fluid mass and momentum with turbulence are where κ is the turbulent kinetic energy and ε is the dissipation of turbulent energy, expressed where c ε and c ε are constants . and . respectively, σκ and σε are . and . respectively and gk is the production of turbulence kinetic energy. eddy viscosity µτ is expressed as where cµ is equal to . . the source terms in continuity and momentum (equations s and s ) accounts for fluid loss via evaporation, in addition to solving the flow field, species transport equations are also solved. air is assumed to consist three main species components, i.e. o , n and h o vapor. the mass fraction of o and h o is solved by where i j  is the diffusive flux of species i and can be expressed as, where sct is the turbulent schmidt number (taken as . ) and dt is the turbulence diffusivity. the source term of species i is simply the energy conservation equation is, where e is energy, h is the sensible heat, where ddv is the diffusion coefficient of vapor in the air. the mass of the droplet evolves as where md is the droplet mass, md the molecular weight and ad is the surface area. the droplet temperature is governed by thermal balance including latent and sensible heats, where pr is the prandtl number and λ is the thermal conductivity of air. bt is the spalding heat transfer number, where d m  is the droplet evaporation rate and qd is the heat energy transferred to the droplet. the evaporation model is verified in independent tests on , and µm droplets under relative humidity levels , . and . (supplementary figure s ) . at relative humidity . , a µm droplet evaporates completely in . s, and a µm in s, which is comparable to simulation time scales, so evaporation is clearly an important factor in droplet dispersion. we compare our evaporation model against other studies and find agreement on droplet evaporation times across droplet sizes, based on reynolds numbers, humidity and temperature gradients. , supplementary figure s clinical characteristics of hospitalized patients with novel coronavirus-infected pneumonia in wuhan, china the coronavirus pandemic and aerosols: does covid- transmit via expiratory particles? transmission routes of -ncov and controls in dental practice airborne transmission of sars-cov- : the world should face the reality detection of air and surface contamination by sars-cov- in hospital rooms of infected patients environmental factors affecting the transmission of respiratory viruses aerosol and surface stability of sars-cov- as compared with 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of cough-jet on airflow and contaminant transport in an airliner cabin section the size and the duration of air-carriage of respiratory droplets and droplet-nuclei exhaled droplets due to talking and coughing droplet expulsion from the respiratory tract violent expiratory events: on coughing and sneezing consistent detection of novel coronavirus in saliva a discrete numerical model for granular assemblies an investigation of particle trajectories in two-phase flow systems evaporation from drops advanced models of fuel droplet heating and evaporation kinetics and evaporation of water drops in air how far droplets can move in indoor environments: revisiting the wells evaporation-falling curve key: cord- -mjg un l authors: khamar, pooja; shetty, rohit; balakrishnan, nikhil; kabi, prasenjit; roy, durbar; basu, saptarshi; sinha roy, abhijit title: aerosol and droplet creation during oscillatory motion of the microkeratome amidst covid- and other infectious diseases date: - - journal: j cataract refract surg doi: . /j.jcrs. sha: doc_id: cord_uid: mjg un l purpose: to quantify the atomization of liquid over the cornea during flap creation using microkeratome using high-speed shadowgraphy. setting: laboratory investigational study. design: laboratory study. method: in an experimental setup, flap creation was performed on enucleated goat's eyes (n = ) mounted on a stand using one use-plus sbk moria microkeratome (moria sa) to assess the spread of aerosols and droplets using high-speed shadowgraphy. two conditions were computed. a constant airflow assumed uniform air velocity throughout the room. a decaying jet assumed that local air velocity at the site of measurements was smaller than the exit velocity from the air duct. results: with the advancement of the microkeratome across the wet corneal surface, the atomization of a balanced salt solution was recorded on shadowgraphy. the minimum droplet size was ∼ μm. the maximum distance traversed was ∼ . m and ∼ . m assuming a constant airflow (setting of refractive surgery theater) and decaying jet condition (setting of an operating theater with air-handling unit), respectively. conclusions: the microkeratome-assisted lasik flap creation does seem to cause spread of droplets. the droplet diameters and velocities did not permit the formation of aerosols. therefore, the risk of transmission of the virus to the surgeon and surgical personnel due to the microkeratome procedure seems to be low. results: with the advancement of the microkeratome across the wet corneal surface, the atomization of a balanced salt solution was recorded on shadowgraphy. the minimum droplet size was ∼ mm. the maximum distance traversed was ∼ . m and ∼ . m assuming a constant airflow (setting of refractive surgery theater) and decaying jet condition (setting of an operating theater with air-handling unit), respectively. the microkeratome-assisted lasik flap creation does seem to cause spread of droplets. the droplet diameters and velocities did not permit the formation of aerosols. therefore, the risk of transmission of the virus to the surgeon and surgical personnel due to the microkeratome procedure seems to be low. j cataract refract surg ; n: - copyright © published by wolters kluwer on behalf of ascrs and escrs a s of late may , the covid- pandemic had affected countries worldwide with more than million positive patients and more than , deaths. infectious disease outbreaks are challenging because they can overburden the healthcare facilities. the severe acute respiratory syndrome coronavirus (sars-cov- ) is a viral infection caused by the new coronavirus. it has rapidly become the world's th public health emergency of international concern. the primary route of transmission of sars-cov- is through direct contact with the respiratory secretions and droplets of an infected person. the virus might survive on different surfaces for days and heighten the risk of transmission. airborne transmission of a disease is defined as the transmission of infection by large droplets over short distances or through aerosols (smaller droplets) over large distances. , various surgical procedures performed by ophthalmologists might generate aerosols from viral shedding areas, such as the conjunctiva and tears. it has been reported that the sars-cov- can be detected in the conjunctival swabs of patients with covid- . although there are no conclusive reports on transmission of the virus from the conjunctiva and tears, all precautions while examining and operating on patients with ophthalmic indications should be taken because many patients might be asymptomatic carriers of the virus. lasik is one of the most commonly performed ophthalmic surgeries worldwide. the lasik flap can be created using a microkeratome that typically oscillates the blade at to cycles per minute and produces aerosol when it comes in contact with a wet ocular surface. high-frequency oscillations are known to generate aerosols. the droplets and aerosols can be studied using the schlieren and shadowgraph imaging technique although the former is more complicated to implement in clinical procedures such as the microkeratome. in shadowgraphy, a bright strobe led source is used to cast the shadow of the fast-moving droplets and aerosols onto the sensor of an ultra-high-speed camera. , therefore, we quantified the aerosol and droplet generation during flap creation using the moria one use-plus sbk microkeratome (moria sa) and assessed their trajectory using high-speed shadowgraphy and fluid mechanics principles. the experiment was conducted on enucleated goat eyes (n = ) to avoid experimenting on cadaveric human eyeballs as per the guidelines laid down by the global eye bank association and eye bank association of india, which prohibited retrieval of cadaveric eyes during the ongoing pandemic for the safety of healthcare personnel. the goat eyes have been widely used for training and research purposes in ophthalmology. the clarity of the cornea in the enucleated goat eye was inspected visually. the goat eye was inflated by injecting with a balanced salt solution (beaver-visitec international) through the optic nerve. after the initial preparation, the goat eye was mounted on a base such that the whole cornea, limbus, and some part of sclera were completely visible to the operating surgeon for ease of surgical maneuvering (figure , a). the one use-plus sbk moria microkeratome was used to create a corneal flap on the goat's eye. a standard flap of . mm in diameter and mm in depth with a nasal hinge using a- ring was aimed. the flap creation was attempted once a vacuum of mm hg was achieved. a bss ( . ml) was used to wet the corneal surface prior to flap creation (figure , b) . a new blade was used for each goat eye. the temperature of the experiment room was set at °c using a room air conditioner, and the humidity was set in the range of % to % using a dehumidifier. these settings were the same as the ones used in the operating rooms meant for refractive surgery in our hospital. our refractive operating rooms also included room air conditioners and dehumidifier. shadowgraphy technique was used to visualize the droplets generated during flap creation with the microkeratome. for objects in motion, an appropriate choice of camera shutter speed was chosen to avoid blurred images. figure , a shows a high-speed ccd camera (mini ux , photron usa, inc.) on the right, positioned opposite to a high-power led source (constellation , veritas) on the left. two sets of macrolenses were used for imaging with the camera. a mm lens (nikkor af f . , nikon imaging japan, inc.) was used to visualize the trajectory of the droplets emanating from the site of incision. a mm lens (atx pro f . d, kenko tokina co. ltd.) was used to image and estimate the droplet size distribution (figure , b). in this case, the aperture was maintained at f/ for maximum depth field. the surgical procedure was performed in a way such that the direction of primary trajectory of the aerosols and droplets was perpendicular to the lens camera. this allowed the trajectory to remain within the given depth of focus of the imaging system. the acquisition rate of the camera was set at fps and the shutter speed at / seconds. to estimate the spread of the aerosols and droplets, the size distribution was extracted from the images using the "analyze particles" plugin of imagej (open source image; java-based image processing platform) and used for further calculations. a simple d analysis was used. during the course of flap cut, a droplet of diameter d mm ejected with a velocity u d (horizontal component) was measured. operating theaters other than the ones used for refractive surgery have high efficiency air filtration systems that create a flow of air around this droplet. thus, the profile of the airflow might be a constant airflow (such as the refractive surgery operating theater) or a decaying jet (our other operating theaters) based on the relative positioning of the air duct and the operating table. in a decaying jet, it was assumed that the operating table was located at a horizontal distance (l o ) from the air duct. then, the airflow velocity (u air ) was modeled as: where u in was the exit velocity from the duct, k (∼ . ) was the turbulent entrainment constant, and d duct was the diameter of the duct. , thus, equation provided a measure of the local airflow velocity at the operating table. in a constant airflow scenario, u air was equal to u in throughout the operating room. the appropriate governing drag equation for the droplet is given below: , v d is the settling rate of the droplet, m f is the viscosity of air ( . × À pa.sec), r f is the density of air ( . kg/m ), r d is the density of droplet ( kg/m ), and g is the acceleration due to gravity ( . m/sec ). the droplet evaporates and settles due to gravity simultaneously. the evaporation timescale can be estimated from the d law, whereas the appropriate settling rate (v d ) from the stokes equation is as follows : the calculation assumes that the point of surgical incision is at approximately m height from the operating theater floor. thus, the timescale of droplet settling was obtained from equation as follows: for the constant airflow condition, the value of u air was estimated to be approximately . m/s, which was as per the certified inspection report of the operating theatres at the narayana nethralaya eye hospital. for the decaying jet condition, u in was assumed as approximately . m/sec. the rated capacity of the airhandling units in our operating theaters ( in number) ranged from to ft /min, and the number of air changes per hour was not less than . the properties of air at a temperature of °c were used in all the equations. with the advancement of the microkeratome through the stroma, the atomization of water was visible on the shadowgraphy image (figure , a and b) (supplemental digital content , video in supplementary model, available at http://links.lww.com/jrs/a ). most of the droplets were generated in a direction that was at an angle of °to the direction of advancement of the microkeratome over the cornea. shadowgraphy in the direction of advancement of the microkeratome had technical challenges because the surgeon hands and microkeratome itself blocked the camera field of view. figure , a shows the setup imaged using the . mm lens before the start of the flap cut. the droplet trajectories were visualized in figure , b by superimposition of sequential images. it was apparent that the smaller droplets travelled farther from the point of ejection. for example, a droplet of diameter mm traveled . mm in the horizontal direction, whereas a droplet of diameter mm traveled only . mm in the same direction (both measured at the same vertical depth of . m from the point of ejection). these distances were calculated assuming that there was no air circulation (ie, u air = u in = . ) in the theater. given the limitation of the . mm lens in imaging the smaller droplets, a . mm lens was used for shadowgraphy as shown in figure , c. the droplet size distribution was extracted from the java-based image processing platform and is presented in figure , d. the most prevalent droplet diameters were in the range of to mm, whereas droplets larger than mm were very few in numbers. we have computed the maximum traversal of a droplet based a constant airflow and decaying jet. as shown in figure , e, the value of x (axial distance) showed a monotonic decrease with increasing diameter (d) of the droplet for both the conditions. naturally, the constant airflow resulted in greater axial distance for the same droplet diameter. a power law fit showed the distance traveled by the droplets in case of a decaying jet as x ≈ × d À . , whereas the same for constant airflow was x ≈ × d À . . the maximum distance traversed was approximately . m and approximately . m, assuming a constant airflow (setting of refractive surgery theater) and decaying jet condition (setting of an operating theater with air-handling unit), respectively. the value of u d used for these calculations was approximately . m/s and was estimated from the high-speed shadowgraphs. an effective risk assessment of different surgical procedures can help mitigate the risk of transmission to healthcare shadowgraphy when combined with imaging at a high speed ( fps and / seconds of shutter speed) and with a high-resolution camera ( mm per pixel) can capture particle sizes as small as mm. it is known that droplets in the size range of . to mm mostly contribute to the spread of airborne diseases. thus, it is critical to estimate the distance traveled by the ejected droplets to ascertain their potential as infection vectors. the horizontal distance (x) traveled by the droplet is dependent on both the evaporation timescales and the settling timescales and is finally determined from the smaller of the quantities. because the smallest detected droplet diameter was approximately mm, the process was controlled primarily by the settling timescale. because the smallest droplet diameter detected was greater than mm, it was highly unlikely that any droplet smaller than mm up to mm in diameter existed because a diameter of mm is usually considered as the upper limit for aerosol. however, the calculations presented in this study did not account for the clustering effect observed in sprays. in our experimental model, we used a balanced salt solution for lubricating the cornea prior to the flap creation by the microkeratome. the wetting of the corneal surface might be a contributory factor in aerosol generation. thus, aerosol and droplet generation were observed during the advancement of the microkeratome over the corneal surface. we believe that it was due to the atomization of the balanced salt solution secondary to the oscillatory movements within the microkeratome. lubricating the corneal surface before use of microkeratome for flap creation is essential to prevent the epithelial erosions. thus, this might be a potential source of viral transmission from an asymptomatic patient to the operating surgeon during the procedure. most of the droplet diameters ranged from to mm during microkeratome-assisted lasik (figure , d) . droplets smaller than mm were nonexistent. although the initial size of the droplets was too large to be classified as an aerosol, subsequent viscous shear against air might reduce them to about . to . times the original size. given the droplet size distribution and their velocities, it is highly probable that they will settle on a surface before they evaporate in smaller sizes. thus, the surgeons and other personnel in the surgical area need to take adequate measures to avoid contact with the settled droplets. it should be noted that figure , e does not provide the distribution of volume of the balanced salt solution distributed over the range of droplets. nonetheless, the larger droplets tend to settle faster, travel less distance, and have lower risk of aerosolization. an understanding of the stochastic nature of droplet creation from the motion of the microkeratome is required. atomization of the balanced salt solution film on the corneal surface depends on several factors, for example, frequency of oscillations, speed of advancement of the blade in the direction of flap cut, thermophysical properties of the fluid, and make of the device. nonetheless, our experiments showed that the droplet diameters were bounded between and mm in the all the captured frames of the shadowgraphy videos (figure , e) . for each eye, as many as frames were captured over a -second period. however, the distribution of the droplet sizes between the frames differed sharply because of the stochastic (random) nature of droplet creation in such experiments. this is a well-known phenomenon in the field of droplet fluid mechanics. thus, assessing repeatability between frames or between the eyes is physically unrealistic. we evaluated nearly frames ( eyes) and focused on the frames that yielded the smallest droplet diameter. in this study, this diameter was mm and was well within the detection limits of the system ( mm per pixel). an example of such a droplet distribution was provided in figure , e. the iphone video showed that direct visualization of droplets through surgical microscope or with the naked eye was possible during the advancement of the microkeratome. however, the quantification of the spread distances, droplet diameters, and presence of aerosols cannot be performed from the iphone video itself. however, the minimum viral load required in aerosols to cause a successful transmission of covid- has not been established. theoretically, even a single virus might be sufficient to transmit a respiratory infection. the excimer laser ablation plume did not seem to transmit the human immunodeficiency virus, herpes virus, and varicella zoster virus because they did not seem to survive the ablation. , furthermore, there is no report confirming the presence of sars-cov- in the excimer laser plume and consequently its transmission. therefore, the sars-cov- seems unlikely to pose a health hazard through laser ablation in lasik and smile. furthermore, femtosecond laser flap creation is a safer alternative to microkeratome because there are no oscillating blades involved. in addition, the results of this study applied to all infectious diseases that have the potential to be transmitted through aerosols and droplets. after ablation in photorefractive keratectomy and application of mitomycin, slow washing of the surface with a balanced salt solution is recommended because this might lead to droplets/aerosol formation. this needs to be evaluated in future studies. topical povidone-iodine drops prior to lasik for a contact period of minutes can reduce the effectivity of the sars-cov- virus below detectable levels. in conclusions, microkeratome-assisted lasik flap creation resulted in generation of droplets. however, it would be too premature to confirm its role in the transmission of the sars-cov- virus. although most of the refractive surgery patients belong to the younger age group who might have less mortality, they are more likely to be asymptomatic carriers of the virus. thus, precautions such as face mask on the surgeon and patient, use of betadine as a potent antiviral and bacterial disinfectant prior to the surgery, and use of a protective shield between the surgical area and personnel to reduce the risk of transmission, if at all present, should be strictly followed. a limitation of the study was the d nature of analyses. a more refined d analysis of the droplet trajectories might shed more light on the physics of droplet creation by the microkeratome. another limitation was that only model of microkeratome was tested because this was the only model available in our hospital, and different makes might have different oscillatory settings. the severe acute respiratory syndrome coronavirus virus can spread through aerosols and droplets. in ophthalmology, procedures that might have the propensity to create aerosols and droplets exist. as the microkeratome oscillated during the flap cut, large droplets measuring greater than mm were created. these droplets could travel up to distances of . m. however, the droplets were too large and will settle down on surface before aerosolization could occur, and the risk of aerosolization and transmission through these droplets was very low. adequate precautions should be followed during flap cut with microkeratome. severe acute respiratory syndrome coronavirus (sars-cov- ): an overview of viral structure and host response detail/ - - -statement-on-the-second-meeting-of-the-international-health-regulations aerosol and surface stability of sars-cov- as compared with sars-cov- recognition of aerosol transmission of infectious agents: a 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experimental fluid mechanics the role of particle size in aerosolised pathogen transmission: a review analysis of droplet clustering in air-assist sprays using voronoi tessellations modeling the role of respiratory droplets in covid- type pandemics toward understanding the risk of secondary airborne infection: emission of respirable pathogens do intact viral particles survive excimer laser ablation? lack of virus transmission by the excimer laser plume inactivation of sars coronavirus by means of povidone-iodine, physical conditions and chemical reagents hospitalization rates and characteristics of patients hospitalized with laboratory-confirmed coronavirus disease -covid-net, states disclosures: none of the aerosol and droplet creation during oscillatory motion of the microkeratome amidst covid- and other infectious diseases phd high-speed shadowgraphy showed droplets generated during flap cut with microkeratome. however, aerosolization of these droplets was unlikely because these droplets would settle on surface before aerosolization key: cord- -l gyl authors: netz, roland r.; eaton, william a. title: physics of virus transmission by speaking droplets date: - - journal: proc natl acad sci u s a doi: . /pnas. sha: doc_id: cord_uid: l gyl to make the physics of person-to-person virus transmission from emitted droplets of oral fluid while speaking easily understood, we present simple and transparent algebraic equations that capture the essential physics of the problem. calculations with these equations provide a straightforward way of determining whether emitted droplets remain airborne or rapidly fall to the ground, after accounting for the decrease in droplet size from water evaporation. at a relative humidity of %, for example, droplets with initial radii larger than about μm rapidly fall to the ground, while smaller, potentially virus-containing droplets shrink in size from water evaporation and remain airborne for many minutes. estimates of airborne virion emission rates while speaking strongly support the proposal that mouth coverings can help contain the covid- pandemic. to make the physics of person-to-person virus transmission from emitted droplets of oral fluid while speaking easily understood, we present simple and transparent algebraic equations that capture the essential physics of the problem. calculations with these equations provide a straightforward way of determining whether emitted droplets remain airborne or rapidly fall to the ground, after accounting for the decrease in droplet size from water evaporation. at a relative humidity of %, for example, droplets with initial radii larger than about μm rapidly fall to the ground, while smaller, potentially virus-containing droplets shrink in size from water evaporation and remain airborne for many minutes. estimates of airborne virion emission rates while speaking strongly support the proposal that mouth coverings can help contain the covid- pandemic. covid- | virus transmission | speaking droplets | sars-cov- t he physics of water droplets is a well-studied subject, and its relevance to virus transmission is long known ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) . it is a subject that has aroused renewed interest because of the covid- pandemic and has motivated scientists to perform new kinds of experiments. recently published laser light-scattering experiments of anfinrud and coworkers ( , ) show that the number of oral fluid droplets emitted into the air while speaking is orders of magnitude larger than previously detected using less sensitive methods ( ) and that blocking such droplets is easily accomplished with a cloth mouth cover ( , ) . previous physics calculations of droplet evaporation to determine whether droplets containing viruses remain floating in air or rapidly fall to the ground typically involve numerical simulations, which hide the fundamental mechanisms ( ). in addition, the mathematics employed is too complex to be understood by other than physical scientists. we have investigated various aspects of this problem and present simple and transparent algebraic equations that capture the essential physics. derivations of all equations are given in ref. . our equations answer two important questions. first, how long does it take for a virus-containing droplet of a given size to fall to the ground by gravity to potentially contaminate a surface? second, for a given relative humidity, how much time does it take for water evaporation to reduce a virus-containing droplet to a size that leaves it floating in air for a sufficiently long time to allow direct transmission of the virus to another person? the answer to the first question is easily obtained by simply equating the gravitational and stokesian viscous forces on a falling object (mg = πηrv) to obtain the terminal velocity (v). this simplistic treatment must be justified and is given in ref. . the mean time for a particle to reach the ground is where τ sed is the mean time for a droplet of radius r to reach the ground from a height, z , with both r and z in units of micrometers. the prefactor, ϕ = η/( ρg) = . × − μm·s, is calculated from the viscosity of air at °c, η = . × − g·μm − ·s − , water density ρ = − g/μm , and the gravitational constant g = . × μm/s . a few examples are instructive. in the absence of water evaporation, droplets placed initially at z = . m (the average height above ground for the mouth of a standing human adult) with radii of , , or μm will require . × s (∼ . h), s, and . s, respectively, to fall to the ground. whether or not a virus-containing droplet will remain airborne to cause an infection requires determination of the rate of evaporation of water, which is defined by the diffusion equation in terms of the water vapor concentration profile outside of the spherical droplet. the most important effect to consider in the size regime of interest is the cooling of the droplet from the heat loss due to water evaporation, which can be determined by solving the coupled heat flux and water diffusion equations and slows down evaporation ( ) . the osmotic effect of nonvolatile droplet contents further decreases the evaporation rate by reducing the water vapor pressure at the droplet surface ( ) . there are three different size regimes that require different theoretical treatments ( ): droplet radii r < nm, nm < r < μm, and r > μm. we can ignore consideration of droplets with r < nm because they are in the size regime of single virions (τ sed = several days), which are not emitted without a surrounding layer of oral fluid. droplets larger than μm fall rapidly to the ground, so are of less concern here. they are dealt with theoretically elsewhere ( ) . we shall, therefore, only be concerned with the regime nm < r < μm. in the following, we assume that the droplet has escaped from any surrounding water vapor cloud ( ) to be in ambient air. the time (τ ev ) it takes for complete evaporation of a pure water droplet of initial radius r , including cooling, is where rh is the relative humidity, θ = αd w c g v w = . × μm /s at °c is a constant with units of diffusion, and the numerical prefactor, α = . , accounts for evaporation cooling effects ( ) . the diffusion constant for a water molecule in air, d w , is . × μm /s, the water number concentration, c g , in saturated air is . × μm − , and the water molecular volume, v w , in liquid water is . × − μm , all at °c. the theory is more complex for inclusion of the osmotic effect of the nonvolatile contents of a droplet, the so-called droplet nucleus. in this case, the mean time for a droplet of initial radius r to shrink to a radius r from water evaporation is given by where r dn is the equilibrium droplet nucleus radius, which, based on a solute volume fraction for saliva of . , is estimated to be ∼r / . the last term in eq. accounts for the vapor pressure reduction due to solutes. at r ≤ . r dn , the evaporation time enters the solute-dominated regime and diverges, albeit only logarithmically, in the limit r → r dn . therefore, for times prior to achieving perfect equilibrium, the logarithmic term is small enough to be neglected, and eq. simplifies to at a relative humidity of rh = . , a common value for room air, the mean evaporation times for droplets with initial radii, r , of , , and μm are . ms, . s, and s, while the corresponding sedimentation mean times, τsed, from eq. are . × s, s, and . s. consequently, the -and -μm droplets will dry out and stay floating for even longer, which will be determined by the radius of the droplet nuclei, r dn . thus, droplets with an initial radius of r o = μm will shrink to a droplet nucleus radius of ∼ μm in t r dn ( ) ≈ . s (eq. ), with the droplet nuclei remaining airborne for about min (eq. ). it is useful to define a "critical radius," r crit , where the evaporation and settling times are equal, that is, t(r dn ) = τ sed . r crit is obtained by combining eqs. and (with r dn = r / ) to give for rh = . and z = . m, the critical radius is μm. this means that droplets with radii greater than μm will fall to the ground before drying out, while droplets with radii less than μm will remain floating in the air in a dry state. a more accurate value for the critical radius of ∼ μm is obtained by solving equations that take into account evaporation of droplets while sedimenting ( ) . can we say anything useful about the number of emitted virions while speaking? table shows the calculated values for initial droplet radii (r ) from μm to μm, using previously determined droplet production rates while speaking and saliva virion concentrations, which predicts that the number of emitted virions per minute while continuously speaking ranges from to ∼ × . comparing the evaporation times at a relative humidity of % with the sedimentation times in table shows that, for all radii in this range, droplet nuclei remain airborne for times sufficiently long that their airborne lifetime will be determined by the turnover time of the air handling system (see ref. ). it is not known what fraction of the virions in these concentration measurements are infectious, but it has been argued that, in some systems, as few as a single active virion can cause an infection ( ) . the very large range of virion emission rates in table calls for both an accurate determination of the fraction of airborne virions that are infectious and accurate droplet size distributions at the high rate of emission determined by laser light scattering ( , ) . overall, the above analysis strongly supports the concept that simply speaking can be a major mechanism of person-to-person covid- transmission and that covering the mouth in public, as suggested by the work of anfinrud and coworkers ( ) ( ) ( ) and others ( , ) , could help to more rapidly contain and potentially end the pandemic. data availability. all study data are included in the article. table . theoretical virion emission rates (k), evaporation times (t(r dn )), and sedimentation times (τ sed ) for initial radii (r ) and for droplet nuclei radii (r dn = r / ), all for z = . m, °c, and % relative humidity (rh = . ) r (μm) k* (virions per min) t(r dn ) † (min) τ sed (droplet, r ) ‡ (min) τ sed (droplet nuclei,r / ) ‡ (min) × . . *calculated from k = ( / ) π r ab, a ' droplets per min ( , ) , average b = x − virions per μm (maximum b = . × − virions per μm ) ( ). † calculated from t(r dn ) ' x − r min. ‡ calculated from τ sed = min/r . on air-borne infection-study ii droplets and droplet nuclei the size and the duration of air-carriage of respiratory droplets and droplet-nuclei droplet fate in indoor environments, or can we prevent the spread of infection? how far droplets can move in indoor environments-revisiting the wells evaporation-falling curve influenza virus aerosols in human exhaled breath: particle size, culturability, and effect of surgical masks violent expiratory events: on coughing and sneezing airborne spread of expiratory droplet nuclei between the occupants of indoor environments: a review emit consortium, infectious virus in exhaled breath of symptomatic seasonal influenza cases from a college community disease transmission via drops and bubbles respiratory virus shedding in exhaled breath and efficacy of face masks visualizing speech-generated oral fluid droplets with laser light scattering the airborne lifetime of small speech droplets and their potential importance in sars-cov- transmission talking can spread covid- " (video recording mechanisms of airborne infection via evaporating and sedimenting droplets produced by speaking one is enough: in vivo effective population size is dose-dependent for a plant rna virus virological assessment of hospitalized patients with covid- airborne transmission of sars-cov- : the world should face the reality acknowledgments. we are indebted to philip anfinrud and adriaan bax, whose experiments and insights motivated this work, and thank adriaan bax for many helpful discussions. this work was supported by the european research council via advanced investigator grant agreement , and the intramural research program of the national institutes of diabetes and digestive and kidney diseases of the nih. key: cord- - eaqn eu authors: lai, alvin c.k.; cheng, y.c. title: study of expiratory droplet dispersion and transport using a new eulerian modeling approach date: - - journal: atmos environ ( ) doi: . /j.atmosenv. . . sha: doc_id: cord_uid: eaqn eu understanding of droplet nuclei dispersion and transport characteristics can provide more engineering strategies to control transmission of airborne diseases. droplet dispersion in a room under the conventional well-mixed and displacement ventilation is simulated. two droplet nuclei sizes, . and μm, are selected as they represent very fine and coarse droplets. the flow field is modeled using k–ε rng model. a new eulerian drift-flux methodology is employed to model droplet phase. under the conventional ventilation scheme, both fine and coarse droplets are homogeneously dispersed within approximately s. droplet nuclei exhibit distinctive dispersion behavior, particularly for low airflow microenvironment. after s of droplet emission, gravitational settling influences the dispersion for μm droplets, and concentration gradient can still be observed for displacement ventilation. after the outbreak of severe acute respiratory syndrome (sars) and avian influenza in east and southeast asia, there has been increasing research interest in studying the transport and control of airborne bacteria and viruses indoors (beggs et al., ; chao and wan, ; li et al., ; nicas et al., ) and in confined environments such as aircraft cabin (mangili and gendreau, ) . nosocomial transmission is also receiving significant attention in the medical literature (tellier, ) . in a review, eickhoff ( ) estimated that as high as % of all hospital-acquired infections occurred through airborne transmission. transmission of airborne disease is a function of the concentration of respirable infectious particles in air and the contact time. when a contagious individual coughs or sneezes, droplets containing infectious particles (bacteria, viruses) are released. the larger ones fall to the floor within a few meters. smaller droplets remain airborne long enough that the moist coating of saliva and mucus evaporate, leaving a residual dry nucleus of the droplet, that may include one or more bacteria or viruses (referred to droplet nuclei). by applying a simple water vapor balance calculation and using major components of mucus, nicas et al. ( ) the equilibrium diameter and the evaporating time required to reach the equilibrium state. due to the presence of the nonvolatile compounds in mucus, the droplet nuclei equilibrium size is roughly half of the original droplet size and the evaporating time is in the order of . s. similar finding is also reported by another review article (morawska, ) . depending on the original (and final) size, droplet nuclei can remain suspended in air for several hours, hence they can travel over long distances, distribute widely throughout indoors, and lead to airborne transmitted infections. aerosol droplet dispersion and transport in a ventilated enclosure depend on the ventilation scheme, particle size, density, concentration, source location, etc. among all the parameters, the ventilation scheme is the most important parameter influencing the droplet transport and dispersion indoors. the global airflow pattern affects significantly on the overall distribution of pollutants. high-level supply and high-level return (hereafter referred to well-mixed) scheme is the most popular ventilation arrangement for commercial buildings. high velocity, cooled air discharges through supply grills and warm air exhausts through return grills. for displacement ventilation systems low momentum, cooled air is supplied to lower part of the room and is exhausted through high ceiling return grills. previous studies using passive gaseous as contaminant sources concluded that with heat sources, displacement ventilation is more favorable to remove the pollutants without mixing to the whole indoor environments (brohus and nielsen, ; he et al., ) . droplet nuclei are aerosols, and some of their physical characteristics are very distinct from those of the gaseous counterparts. gravitational deposition and inertia are among the most important characteristics that distinguish aerosols from gaseous, and the importance of both features increases with size. nevertheless, some previous studies used passive gaseous as surrogates to investigate the transport and dispersion of aerosols (beggs and sleigh, ; qian et al., ; zhao et al., ) or applied well-mixed assumption to estimate the risk of droplet exposure (nazaroff et al., ; rudnick and milton, ) . plausible reason of using gas surrogate is that generation of gaseous is relatively straightforward, and the detection is fairly simple with very high accuracy. on the other hand, generation and real-time detection of aerosol droplets concentration are more complicated. due to the complexity of the indoor airflow, the temporal and spatial distributions of droplet transport must be solved by computational fluid dynamics (cfd). either eulerian or lagrangian frameworks can be employed to resolve the particulate phase. the author has developed a new eulerian methodology (drift-flux model), and the model has been validated experimentally for a scaled chamber. detailed descriptions of the model can be found elsewhere lai and chen, ; wang and lai, ) . the key objectives of the present work are (i) to apply the new eulerian approach to study droplet dispersion and transport in a ventilated room, and (ii) to highlight the influence of droplet sizes and ventilation scheme on mixing characteristics. to investigate droplet nuclei dispersion and transport using the new drift-flux approach, an enclosure with two identical model occupants with heat energy dissipated is selected (fig. ). there is one occupant emitting droplets (source) and faces directly to another occupant (receptor). the only differences between the well-mixed and displacement ventilation configurations are the inlet boundary conditions, location and geometry. for the wellmixed ventilation, a high-level supply grill is used while for displacement ventilation, a floor supply is employed. table shows the details of the room geometry and the boundary conditions. the geometry of a human occupant was originally suggested by brohus and nielsen ( ) . an opening, .  . m, measured at . m above floor, locating at the centerline of the head is added to simulate the mouth of the occupant. two planes are defined in the geometry; a breathing plane and a mid-plane. the breathing plane is . m above and parallel to the x-y plane. the mid-plane is symmetrical about the middle line in the x-z plane. table shows the details of the geometry of the model occupant used for this study. the wall temperature is set to k while the surface of the model is specified by body temperature . k. it has been reported that the initial emission velocity can be up to m s À (wells, ) . recent study recording the coughed airflow of healthy males shows the velocity ranges from to m s À (zhu et al., ) . in the present study, the source emits unit density spherical droplet nuclei lasting for . s with initial velocity m s À . two recent review articles demonstrate the time scale of evaporation. nicas et al. ( ) estimated that the shrinkage time from the original droplets to droplet nuclei is rapid and is in the order of . s. morawska ( ) also draws similar conclusion showing a very rapid evaporation rate. she modeled three pure water droplet sizes, , and mm. for the two smaller droplet sizes, the time required to evaporate to the equilibrium size ranges from . to . s. this time scale is at least an order of magnitude shorter than the residence time of the droplet nuclei suspended in the room, hence the approach adopted here is to ignore the ''evaporation period'' and model the droplet nuclei directly. nicas et al. ( ) also summarized the droplet size data available from the literature, and the size ranges from submicron to over mm. it is understood that the expiratory droplets follows a certain size distribution, however, in this work, two representative droplet nuclei sizes, . and mm, are chosen. the smaller size represents those fine droplets of which inertia and gravitational settling can be ignored, and their motions follow the air streamline. on the other hand, the coarse size represents the upper size limit that can be inhaled, deposited into lungs, and cause health problems. to simplify the model, the droplets are assumed trapped once they touch any surfaces and do not resuspend or break-up. these assumptions are valid for the present low air velocity environment. coagulation effect has been examined by applying a simple estimation (hinds, ) . the particle table room configuration wall b breathing plane source z x y nicas et al. ( ) . the result reveals that the coagulation effect can be neglected. renormalization group (rng) k-e turbulent model is adopted here to simulate the airflow. the rng k-e model is more appropriate for indoor airflow simulation, and better agreement between simulated results and measured data has been achieved compared to the standard k-e and other turbulence or laminar models (chen, ; posner et al., ) . a generic commercial cfd code fluent (fluent, ) was used to simulate the airflow. the piso algorithm was employed to couple the pressure and velocity fields. grid independent tests were performed and the optimal grid densities for the well-mixed and displacement ventilation geometries are , and , cells, respectively. since two dummy heat sources (occupants) are involved, there are buoyancy flows around the occupants. here, air density is defined as a function of temperature by a piecewise-linear function. the simulation was performed on an sgi onyx shared server. a simplified eulerian drift-flux model has been developed to take full advantage of the extremely low volume fraction of indoor particles lai and chen, ) . the term ''drift-flux'' (or drift velocity) stands for particle flux (or velocity) caused by effects other than convection, i.e. gravitational settling and diffusion for the current work. the advantage of this approach is the feasibility of incorporating other external forces i.e. electrostatic (wang and lai, ) into the model. as the convective velocity of the particle phase is the same as the air phase, the complexity of the two-phase flow system is greatly reduced. the governing equation for particle transport in turbulent flow field is given as where u is the air phase velocity vector, c i is the particle mass concentration, kg m À (or number concentration, m À ) of particle size group i (here-after the subscription i denotes particle size group), v s;i is the particle settling velocity, p is the particle eddy diffusivity, and d i is the brownian diffusion coefficient and s c i is the mass concentration source term. the drift-flux methodology is incorporated into fluent by a user-written sub-program. the performance of the new eulerian model is compared with a lagrangian approach, as discrete phase tracking has been employed to solve many types of two-phase engineering problems for more than a few decades. zhao et al. ( ) conducted an order analysis and concluded that for indoor aerosol particles, only drag force, brownian force and gravity, were important. the lagrangian particle tracking is carried out by fluent builtin features. the equation of motion of a small aerosol particle can be written as where u p;i and u i are the velocity of the particle and fluid, respectively, t is the particle relaxation time (lai and nazaroff, ) , n i ðtÞ is the brownian force per unit mass, r p and r are the particle and air density, respectively, and g i is the gravitational acceleration. in the following section, some eulerian and lagrangian predictions will be presented sideby-side. for the lagrangian approach, a sampling plane must be defined prior to counting the particles. here, the droplets within . - . m (for breathing plane) and . - . m (for midplane) are selected. the purpose of including the lagrangian approach is to compare the results qualitatively only. it must be emphasized here that direct quantitative comparison of these two approaches is impossible as the variables and governing equations solved are different. fig . shows the velocity field at the mid-plane for the two ventilation schemes at time '' '' (momentarily before injection). for the well-mixed ventilation, the inlet jet flow causes air recirculation in the room, and the jet velocity is significantly higher than the neighboring region. in this figure, elapsed times which represent the arrival of the droplet puff to some specific locations are labeled. for instances, under the well-mixed ventilation, the expiratory droplets takes approximately . s to reach the receptor's face, s to reach the wall a, s to the receptor's legs, s to the wall b. all the above times mentioned refer to the elapsed times from the commencing of the droplet emitting process. as expected, the displacement ventilation exhibits a very different airflow pattern. cooled, low velocity air flows at near floor level absorbing heat from the two occupants, and a vertical thermal plume dominates the airflow field in the boundary layer around each occupant. droplet cloud takes approximately s to reach the exhaust. except for the mid-plane, the airflow velocity is fairly weak in all other regions. although it is not the prime objective to study the statistical properties of the lagrangian approach, a brief justification for the selection of the injection number seems necessary prior to discussing the results. three injection numbers were tested; , , and , . particles escaped through the outlet and deposited to the receptor's head region were recorded and counted. inferring from fig. , there is no statistical difference between the results of , and , injections. hence, , injections were selected for all lagrangian simulations. fig. shows the combined results modeled by the drift-flux and lagrangian approaches at the breathing plane and the mid-plane for . and s elapsing from the commencing of the droplet emitting process. the high-speed droplet nuclei emitted from the mouth opening carry high momentum. they impact to the face of receptor directly resulting in significant particle loss. inferring from the results, it can be observed that the two approaches predict fairly similar profiles, and the essential feature of the droplet dispersion is captured by the current eulerian model. fig. depicts the mid-plane results for . mm and mm droplets under both ventilation schemes at and s. it is found out that for the same ventilation scheme, the difference between the two droplet sizes is not significant. the two modeling approaches give close matches, but this time the number of particles tracked are much less than those in fig. . as mentioned, the droplet dispersion depends on the bulk air movement and the physical properties of the droplet itself. the insignificant difference between two droplet sizes is attributed to the relatively short elapsed time presented here. even for mm droplets with unit density, the settling velocity is just  À m s À , hence it needs very long time to distinguish the dispersion characteristics (cf. fig. ) . at those elapsed times reported, the droplet trajectories follow closely to the airflow pattern (cf. fig. ) . for instances at s for well-mixed ventilation, the puff just arrives at the receptor's legs, and it matches very closely to the bulk airflow pattern. once the droplets are emitted, due to the much lower surrounding airflow speed they encountered, the droplets start to decelerate to attain the same velocity as the surrounding air, and then thereafter considered to be airborne. particle relaxation time (t) is used to characterize the time required for the particle to ''relax'' to become airborne where c c is cunningham slip correction factor, d p is the droplet diameter, and m is the kinematics viscosity of air. for the present system, the relaxation time ranges from À to À s. with these negligible relaxation times, the droplets decelerate almost instantaneously, and hence the droplets follow closely the airflow. as expected the concentration profile is significantly different between the two ventilation schemes. for the well-mixed scheme, due to the much higher airflow velocity (in the x-direction) compared to the displacement scheme ( m À s vs. . m s À ), the droplets reach the vertical wall a in approximately s. after the impact, many droplets are deposited to the wall, and the rest follows the large recirculation eddy. the predictions are very different for the displacement ventilation. in contrast to the well-mixed scheme where the airflow in x-direction dominates, the velocity in x-direction is very slow for the displacement ventilation. due to this characteristic, the transport of droplets in that direction is fairly weak, and the droplets move slowly to the exhaust outlet. fig. shows the dispersion at s for the two ventilation schemes at the mid-plane; under the well-mixed scheme, . mm droplets are well-mixed, whereas large concentration gradient can still be observed under the displacement ventilation. in fact, the droplets do not disperse to most regions of the room until s (refers to fig. ). under such a single emission event studied here, droplets under displacement ventilation take approximately times longer than that for the well-mixed ventilation to achieve moderate room dispersion. some salient features regarding the two approaches are worth discussion. first, under the lagrangian methodology each particle has a unique id, and hence the position for each particle can be tracked throughout the entire simulation domain and time. in risk exposure applications, this feature seems attractive only for some cases such as to investigate the individual ''contribution'' of multiple sources. for a single source, particle tracking feature is not important most of the time. instead, for many exposure assessments, the spatial and temporal concentration levels are the vital pieces of information needed. due to its discrete phase nature, the post-processing of the lagrangian simulation for the results shown in figs. , and is not trivial. in these figures, a -cm thick ''slice'' is chosen and particles enclosed in the slice are counted. if a thicker slice is chosen, it cannot represent the correct spatial concentration; on the other hand, if the slice is too thin, there may be no particle contained. the selection is, however, quite arbitrary. there is one transformation methodology, called particle-source-in-cell (psic), which can convert the discrete particle trajectories into concentration (crowe et al., ) . by using the residence time the particle stays in a pre-determined cell volume, the particle mass flow rate can be transformed to concentration. however, particle trajectories are still required prior to applying the transformation. this means that the accuracy of the transformation depends critically on the number of the injections. in contrast, since the droplet phase is treated as a continuum, the drift-flux approach can directly present the concentration magnitude over the entire spatial domain. this feature is very attractive for exposure assessment. secondly, due to the nature of the governing equations resolved, direct comparison between lagrangian and eulerian results is impossible. here a qualitative comparison is performed by counting the ''discrete particles'' in fig. and comparing to the scalar magnitude. thirty three, , and are counted in the -cm slices of figs. (a)-(d), respectively, and the trend is consistent with the scalar legend. in the future, more comprehensive comparison can be made by performing volume integration to get the spatial-average concentration. fig. depicts the mid-plane results by the lagrangian and drift-flux approaches at and s. since the droplets are already homogeneously mixed at s for the well-mixed system which is presented in fig. , only the results for displacement ventilation are shown. due to the relatively few suspended droplets, for those lagrangian simulation results, the slice thickness is increased to cm. apparent difference between the . and mm is observed at these two longer elapsed times. sedimentation is observed for mm particles as more droplets are found at the lower region, while for . mm particles no apparent settling is seen. in fact, a particle-free region is found for the . mm droplets. the same observation is found for the lagrangian simulation for mm: more discrete droplets can be found near ground level. literature results have shown similar conclusions. a recent study also shows that mm particle concentration in a chamber exhibits inhomogeneity, and can be attributed by the turbulent diffusion and gravity (richmond-bryant et al., ) . chang et al. ( ) performed a detailed large eddy simulation on indoor particles under natural ventilation. he found out that, due to the larger inertia and gravitational settling, coarse particles (pm ) can move easily from one circulation region to other ones while fine particles (pm . ) are easily influenced by the surrounding complex indoor air pattern. based on the literature and the current results, it reveals that droplet nuclei may exhibit distinctive dispersion behavior, particularly for low airflow microenvironment. approximately about % of droplets are less than mm in terms of number (nicas et al., ) . these droplets can still be inhaled and deposited deep to lungs. hence, the present result has important implication; using passive gaseous as surrogates of droplet nuclei or applying the well-mixed assumption may cause incorrect exposure risk assessment results. in spite of the low relaxation time, deposition and gravitation effects may influence the accuracy if they are not properly taken into accounted. an alternative eulerian drift-flux model is adopted to simulate dispersion of droplet nuclei in a ventilated room. two particle sizes ( . and mm) are chosen to mimic very fine and coarse droplet nuclei. results show that both lagrangian and drift-flux approaches give similar concentration profiles. however, there are a few inherent drawbacks for the lagrangian approach including the difficulty in generating particle density plots at a certain plane, and more importantly the uncertainty in the number of droplets injected may lead to inaccurate conclusion, particularly if the number of droplet suspension is low. on the other hand, using the drift-flux approach with proper account on sedimentation gives straightforward concentration profile. in addition, the computational time and resources required for the drift-flux are much less than those required for the traditional lagrangian particle tracking methodology (typically less than %). this advantage becomes more significant for complex geometries with substantial grid elements. inferring from the results presented, it can be observed that for the well-mixed ventilation scheme, the dispersion pattern is dominated by the high velocity airflow, and the different between droplet sizes is not obvious. the droplets are homogeneously mixed within min. when the global airflow speed is lower, the distinctive characteristics of coarse size start to appear. ten micrometer droplets begin to settle at the lower region of the room under displacement ventilation. a quantitative method for evaluating the germicidal effect of upper room uv fields methodology for determining the susceptibility of airborne microorganisms to irradiation by an upper-room uvgi system personal exposure in displacement ventilated rooms numerical investigation of airflow pattern and particulate matter transport in naturally ventilated multi-room buildings a study of the dispersion of expiratory aerosols in unidirectional downward and 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tuberculosis transmission toward understanding the risk of secondary airborne infection: emission of respirable pathogens measurement and prediction of indoor air flow in a model room dispersion of exhaled droplet nuclei in a two-bed hospital ward with three different ventilation systems transport of airborne particles within a room risk of indoor infection transmission estimated from carbon dioxide concentration review of aerosol transmission of influenza a virus a new drift-flux model for particle transport and deposition in human airways airborne contagion and air hygiene numerical study of the transport of droplets or particles generated by respiratory system indoors study on transport characteristics of saliva droplets produced by coughing in a calm indoor environment key: cord- -av ev ta authors: kähler, christian j.; hain, rainer title: fundamental protective mechanisms of face masks against droplet infections date: - - journal: j aerosol sci doi: . /j.jaerosci. . sha: doc_id: cord_uid: av ev ta many governments have instructed the population to wear simple mouth-and-nose covers or surgical face masks to protect themselves from droplet infection with the severe acute respiratory syndrome coronavirus (sars-cov- ) in public. however, the basic protection mechanisms and benefits of these masks remain controversial. therefore, the aim of this work is to show from a fluid physics point of view under which circumstances these masks can protect against droplet infection. first of all, we show that the masks protect people in the surrounding area quite well, since the flow resistance of the face masks effectively prevents the spread of exhaled air, e.g. when breathing, speaking, singing, coughing and sneezing. secondly, we provide visual evidence that typical household materials used by the population to make masks do not provide highly efficient protection against respirable particles and droplets with a diameter of . – μm as they pass through the materials largely unfiltered. according to our tests, only vacuum cleaner bags with fine dust filters show a comparable or even better filtering effect than commercial particle filtering ffp /n /kn half masks. thirdly, we show that even simple mouth-and-nose covers made of good filter material cannot reliably protect against droplet infection in contaminated ambient air, since most of the air flows through gaps at the edge of the masks. only a close-fitting, particle-filtering respirator without an outlet valve offers good self-protection and protection against droplet infection. nevertheless, wearing simple homemade or surgical face masks in public is highly recommended if no particle filtrating respiratory mask is available. firstly, because they protect against habitual contact of the face with the hands and thus serve as self-protection against contact infection. secondly, because the flow resistance of the masks ensures that the air stays close to the head when breathing, speaking, singing, coughing and sneezing, thus protecting other people if they have sufficient distance from each other. however, if the distance rules cannot be observed and the risk of inhalation-based infection becomes high because many people in the vicinity are infectious and the air exchange rate is small, improved filtration efficiency masks are needed, to take full advantage of the three fundamental protective mechanisms these masks provide. at present, humanity is threatened by the severe acute respiratory syndrome coronavirus (sars-cov- ) pandemic. the risk of severe infection with the virus depends heavily on physical factors of the infected persons and the quality of the medical system. according to a recent study the estimated infection fatality ratio (ifr), averaged over all age-groups including those who don't have symptoms, is between . % - . % with an average of . % (verity et al., ) . these numbers look small, and the fatality risk may seem acceptable, and therefore the danger is often marginalized. this is surprising considering that the apollo crew, the space shuttle astronauts and the allied soldiers during the iraq war took a deadly risk of this magnitude. only very few people take such risks voluntarily and with full consciousness. for comparison, the lethal risk of a fatal accident with a commercial aircraft was : in and even such a small risk is not taken by some people. considering that the ifr of the seasonal flu is about . - . % (centers for disease, ) or even much lower (wong et al. ) the mortality rate of sars-cov- appears to be significantly higher than for influenza flu. although the numbers for sars-cov- are quite preliminary and the estimates may drop over time (verity et al., , faust, et al., it is quite clear that the strategy of herd immunization of the population is not an option, as the number of victims would be far too high. great hopes for coping with the pandemic currently rest on the development of a vaccine. unfortunately, it is completely uncertain when an effective and well-tolerated vaccine will be generally available to contain the pandemic. drugs such as chloroquine, remdesivir, lopinavir and ritonavir are also considered to be great sources of hope in the fight against the coronavirus disease (grein at al., ) . however, even if one of the drugs should prove to be effective, there is no guarantee that the drug can be made available to the world population in sufficient quantities. in addition, it is possible that, despite the use of drugs, going through a severe course of disease can lead to lifelong neuropsychiatric sequelae (troyer et al., and zandifar & badrfam, ) or cause other diseases (ackermann et al., and varga et al., ) . containing the pandemic is therefore the only viable way to quench the spread of the virus. but containing the pandemic is a difficult task as about % of sars-cov- infections are caused by people with a presymptomatic and asymptomatic course of infection (he et al., ) . therefore, due to the absence of symptoms, many people do not know that they are infected and are spreading the virus and these people make it very difficult to trace the transmission chains. furthermore, about % of infected people are responsible for % of infections (kupferschmidt, and lloyd-smith et al., ) . people who have many social contacts at work or in their private lives and who do not protect themselves and others sufficiently by observing the rules of distance and hygiene, or who consider the risk of the virus to be low, appear to be a serious problem in the actual pandemic. for these reasons, the government must act at various levels to avert great harm to the population. the effectiveness of the containment strategy depends on . how societies are able to protect themselves personally against infection through hygiene, social distance and technical aids such as protective masks, glasses, gloves, . how well the infrastructure is in place to identify the infection chains and effectively contain the spread, e.g. through mobile data collection, isolation or a lockdown, . how well the seriously ill can be treated in hospitals. in view of these prospects, it seems necessary for the time being to prevent the spread of the virus and to treat those infected as well as possible. in order to ensure the latter, the capacities of the health system must not be overloaded. but it is clear that this condition means that the pandemic will last for years without a vaccine. to not overload the medical system, governments are pursuing the concept of containment by means of a lockdown because it proved successful in st. louis during the spanish flu of . this approach is quite effective when the population obeys the rules, but the impact on the state, economy and society is devastating when the lockdown lasts longer than a few weeks. therefore, this concept is not a viable way to contain the pandemic in the long term. consequently, it is necessary to fight the infection where it occurs. understanding the transmission pathways is the key to finding effective measures to block the infection and to reliably protect healthcare workers and the population. contact infection were initially assumed to be the main transmission route of sars-cov- . today, hygiene measures and the avoidance of shaking hands effectively prevent this path of infection. droplet infection is currently assumed to be the main transmission route over short distances . since this path of infection is via the air, the rules of distance are effective (soper, and wells et al., ) . but it is also known that sars-cov- can remain infectious in aerosols for more than hours, at least under laboratory conditions at high humidity (van doremalen et al., and pyankov et al., ) . it is therefore conceivable that infections can also occur under special conditions over long distances, provided that the local virus concentration reaches the minimum infection dose due to poor air exchange in rooms. a significant proportion of the aerosol exhaled by humans has a diameter of less than μm (johnson et al., ) when breathing, speaking, singing and coughing. it is also known that the size and number of droplets increases with the volume of the voice (asadi et al. and loudon & roberts, ) and it is known that upper respiratory tract diseases increase the production of aerosol particles (lee et al., ) . water droplets of this size evaporate within a few seconds at normal humidity (liu et al. and rensink ) . droplets with a diameter of μm for instance are evaporated after about s at % relative humidity and larger droplets sink quickly to the ground and evaporate (marin et al., . if the viruses are released as "naked" viruses together with the salt after the droplets have evaporated, the spatial concentration decreases rapidly over time, as the viruses no longer move in a correlated manner but quickly separate due to the chaotic turbulent flow motion. the viral load thus decreases rapidly in time and space, making infections over long distances or long periods of time increasingly unlikely. for this reason it is most important to understand the transmission of the virus over short distances. hygiene regulations and social distancing are very effective in blocking short distance infections. during the lockdown, the distance rules can usually be adhered to, but what happens when the actual lockdown is over and the people meet again in a confined space? then additional effective and efficient protection is essential to stabilise infection rates. since the viruses are spread by contact and droplet infection, technical devices are required that effectively intervene in the chain of infection and effectively block infection. an effective protection is the respiratory mask as known since years (soper, ) . the sars outbreak in hong kong suggested that the use of simple face masks may have contributed to an overall reduction in the incidence of viral respiratory infections lo et al., ) . another study has shown that even a simple surgical mask can effectively reduce sars infection (seto et al., ) . these results are supported by recent articles (leung et al., b , howard et al., . it was surprizing that for months, who, the cdc and many public health professionals in europe advised against wearing face masks unless someone has covid- or cares for someone who has covid- (feng et al., and leung et al., a) . this recommendation was based on three allegations. first, it was said that there is no scientific evidence that face masks can protect against droplet / aerosol infections. second, it was argued that the population will not be able to wear the masks properly. third, the statement that people will feel safe when wearing masks and then become careless and take risks was frequently made. at the same time, these experts have stressed that health professionals urgently need face masks to protect themselves effectively. this contradiction has created uncertainty among the population and called into question the credibility of the experts. it is a fact that particle filtration masks are recognized as legal occupational safety equipment and that the wearing of these masks in contaminated areas is required by labor law. there is therefore no doubt that these masks, when used correctly, provide effective protection within the specification range. the effectiveness of simple mouth-and-nose covers and surgical masks is less well accepted. the international council of nurses (icn) estimates that, on average, % of all confirmed cases of covid- are among healthcare workers (icn, ) . this illustrates that surgical masks may not provide the reliable protection against droplet infection, as anticipated. it is therefore very important to distinguish clearly between the different mask types when talking about their protective function. unfortunately, this was not done sufficiently by the virologists and politically responsible persons in the initial phase of the pandemic. also the second argument is questionable. why should the people of western societies not be able to protect themselves as many people in east asian countries have long been doing? many people in east asian countries have already recognized through numerous pandemics that proper masks work effectively. it does not seem right to regard the western population as unteachable or even incapable. the third argument is also false, because the opposite is true according to scientific studies (kimberly et al., , scott et al., and ruedl et al., . if people protect themselves personally, they have dealt with the danger and therefore they benefit from the protection of the safety device and from the less risky behaviour due to insight. the reason why these facts were not appreciated by the experts is due to the attempt to prevent competition for protective masks between medical personnel and the public. in the meantime, the general perception of the protective effect of face masks has become generally accepted. in the usa, the cdc has changed its guidelines and recommended that the public wear fabric face masks. in other countries, too, it is now recommended to protect themselves with suitable masks. however, it is recommended by governments and professionals to wear only simple mouse-and-nose covers that can be manufactured by the people themselves or surgical masks to avoid distribution battles with medical staff for certified and comfortable particle filtration masks. but the big question is, how effectively these homemade mouth-and-nose covers and surgical masks can protect against droplet infection. the answer is highly relevant to guide public behaviour (leung et al., a) . one study suggests that a surgical face mask and masks made of dense cotton fabrics apparently cannot effectively prevent the spread of sars-cov- into the environment through the coughing of patients with covid- (bae et al., ) . another study suggests that any mask, no matter how efficiently it filters or how well it is sealed, has minimal effect unless used in conjunction with other preventive measures such as isolation of infected cases, immunisation, good respiratory etiquette and regular hand hygiene (kwok et al., ) . these findings contradict the results in , lo et al., and seto et al., . due to the contradiction, it is understandable that experts in the media have expressed the opinion that there is no scientific evidence for the effectiveness of masks and therefore the wearing of masks in public was not recommended for a long time. the fallacy of politicians and virologists, however, was to generalize the results obtained with simple mouth-and-nose covers to all masks without differentiation. in order to clarify whether or to what extent these masks offer effective protection against droplet infection and to understand why research results differ on this simple scientific question, we have carried out these tests. first, we analyse the flow blockage caused by surgical masks when coughing, as this is essential for the protection of others and because coughing is a typical symptom of covid- . second, we qualify the effectiveness of different filter materials and masks to determine the protection ability against droplets. finally, we prove the effect of gap flows at the edge of surgical and particle filtrating respiratory masks. in contrast to the medical studies cited, we apply engineering research methods of fluid mechanics. the use of this research approach has several reasons: firstly, the detachment of droplets in the lungs and throat and their convective transport through the mouth into the atmosphere until inhalation as well as the deposit and evaporation of droplets is a purely fluid mechanical process. secondly, the effective blocking of the flow with suitable masks is a research subject of fluid mechanics. thirdly, the filtering of particles from an air stream with the aid of suitable materials is also a purely fluid mechanical problem as well as the gap flow. finally, this approach also has the advantage that the results are reproducible in a statistical sense, since the boundary conditions are well defined. we are not studying whether an infection really occurs in a special case, but whether an infection is physically possible in general. in the first sets of the experiments, outlined in section . , the flow field generated by coughing without and with a surgical mask is examined as coughing sets the air strongly in motion and because coughing is a typical symptom of covid- . to measure the flow field quantitatively in space and time we use particle image velocimetry (piv) (raffel et al., ) . for the measurements a m long testing room with a cross section of m × m was seeded with dehs (di-ethyl-hexyl-sebacat) tracer particles with a mean diameter of μm (kähler et al., ) . dehs was used as these droplets do not evaporate as quickly as water droplets. the tracer particles provided by a seeding generator (pivtec gmbh, germany) were illuminated in a light-sheet generated with a frequency doubled nd:yag laser (spitlight piv - , innolas laser gmbh, germany). the light-sheet was oriented normal to the mouth opening and parallel to the symmetry axis of the body and the longitudinal axis of the room. the light scattered by the tracer particles were recorded with back illuminated scientific cmos cameras (pco.edge . , pco ag, germany) equipped with zeiss distagon t* lens with a focal length of mm and mm. the triggering of the system components was achieved with a programmable timing unit (lavision gmbh, germany). the recorded series of images were evaluated with a commercial computer program (davis, lavision gmbh, germany). these quantitative piv measurements allow to determine the area that can be contaminated due to the exhaled air, the velocity of the exhaled droplets and the turbulence properties of the flow. in the second set of experiments, discussed in section . , common household materials currently used by the population and some medical staff to make simple masks at home were tested but also a surgical mask and a ffp mask to visualize their filtering properties. the tested materials are given in table . for the investigation, a test set-up was installed which largely fulfilled the officially prescribed test conditions in europe (din en ). the materials were installed one after the other in a fixed position in front of the inlet of a rectangular flow channel with a cross-section of . m × . m, as shown in fig. . the material was held in place with a special clamping device that seals tightly to the duct to avoid leakage flows. to explore the filtering performance of the different materials the movement of small aerosol droplets passing through the media was observed visually in front of and behind the filter material with a digital camera. we only use droplets whose diameter is less than μm, since the removal of the smallest droplets in an air stream is the greatest challenge in mask development. if these droplets can be effectively filtered out effectively, then all droplets larger than μm can also be filtered. the droplets were generated from dehs with an aerosol generator (agf . , palas gmbh). dehs was used again as these droplets are long lasting. consequently, bias errors due to evaporation effects can be neglected. a nd:yag double-pulse laser (evergreen , quantel, france) was used to illuminate the droplets. the output beam was fanned out with a few lenses to form a mm thin light-sheet. the light-sheet was located in the middle of the flow channel parallel to the flow direction as indicated in fig. . the scattered light emitted by the illuminated aerosol in the light-sheet plane was recorded with a highly sensitive pco edge . scmos camera equipped with a zeiss distagon t* lens with a focal length of mm. the triggering of the system components and the data recording was realized again with the software davis from lavision. the flow velocity was driven by the pressure difference between the atmosphere and the flow box. the flow rate through the filter material was adjusted approximately according to the din en test standard ( liter/minute). the volume flow rate and the movement of the droplets through the filter material was measured optically with high spatial and temporal resolution using piv. to calculate the volume flow rate the average flow velocity within the light-sheet plane in the flow channel was measured and it was assumed that this velocity is homogeneous over the cross section of the channel. this assumption is justified as the filtering materials are homogeneous and the inflow condition is constant across the filtering material. with the know size of the cross section the volume flow rate can be calculated. the pressure drops provided in table are calculated from the measured pressure drops and the volume flow rate. it is assumed that the pressure loss is proportional to the square of the volume flow rate. the pressure drop across the filter material was measured with a testo (testo se & co. kg, germany) pressure transducer with an uncertainty of about pa for the third set of experiments, analysed in section . , simple flow visualizations using smoke were performed in order to demonstrate the effect of the gap around the mask edge. a person exhaled air seeded with tracer particles while wearing surgical and ffp masks. in the first series of experiments, one person performed a single severe cough while the piv system was measuring the flow field data. the video in the supplementary material shows the temporal evolution of the process. the results displayed in this subsection show instantaneous velocity fields of various independent timeresolved flow field measurements. color-coded is the magnitude of the local flow velocity and the vectors indicate the direction of the flow movement at a given time step. in areas where the flow movement remains close to zero over the whole recording time (blue colour), no droplets can penetrate as only the flow can move the particles to other areas. large droplets with a diameter of one millimetre or more, such as those produced when sneezing (lok, ) , can fly ballistic over long distances, and occasionally ballistic flying droplets are produced when certain sounds are spoken. but sneezing is not a typical covid- symptom so that this will not we considered here. the small droplets that are normally produced when breathing, speaking, singing and coughing are immediately slowed down and then move with the flow velocity of the ambient air. it is therefore important to study the air set in motion by exhalation. furthermore, the small droplets are particularly dangerous because they can be inhaled deep into the lungs. figure a shows that the spread of the exhaled air forms a cone like shape similar to a free turbulent jet (see video). the flow velocity is reaching values up to m/s near the mouth, but due to the widening of the cone caused by the turbulent mixing and entrainment (reuther et al., ) the flow velocity decreases in streamwise direction. the widening of the area in motion reduces the viral load significantly with distance. a single strong cough sets the air in motion over a distance of less than . m in the experiments. distances of more than . m can be considered safe according to these results, since no droplets can reach such large distances when accelerated by a single cough. however, if the cough lasts longer, greater distances can be achieved, as shown in fig. b . for this reason, it is important to dynamically increase the distance to a person if the coughing stimulus is about to last longer. the results in fig. c illustrate how the spread of the airflow from the mouth during coughing is very effectively inhibited by a surgical mask. physically the mask ensures that the directional jet like air movement with high exit velocity from the mouth is converted into an undirected air movement with low velocity behind the mask. this is because the exhaled air increases the pressure inside the mask compared to the atmosphere outside, and the pressure difference creates a flow movement in all directions. this effect is of utmost importance for limiting the virus load in the environment. the results show that even a simple mouth-and-nose cover or a surgical mask can effectively protect other people in the vicinity because the mask prevents the droplets from spreading over a wide area. a simple mask with sufficient flow resistance therefore provides very effective protection for people m m . m . m in the surrounding area when infected and wearing the mask. wearing a mask is therefore absolutely useful to protect others according to our quantitative measurements. figure d shows the spread of exhaled air when speaking. it can be clearly seen that a greater spread of the exhaled air appears than when coughing with a mask. consequently, wearing a mask during normal face-to-face conversations and of course also when talking on the smartphone in a human environment is extremely useful to stop the transmission of the sars-cov- infection via droplets. it must also be taken into account that persons with a presymptomatic or asymptomatic course of infection will infect other persons most likely during face-toface conversations. a mask will therefore make an effective contribution to suppressing this significant path of infection. in this section we want to find out if the material of simple mouth-and-nose covers, surgical masks and ffp masks can protect the user from droplet infection, if the surrounding air is contaminated with sars-cov- . in this case, the mask material must have good filtering properties to stop small droplets that typically occur when speaking, singing and coughing. since large droplets are easily filtered out by simple materials, we focus on small droplets in the range between . and μm because they are produced in large fractions when speaking, singing and coughing and they can penetrate deep into the lungs. the droplets were distributed approx. mm in front of the filter materials. in order to make the motion of the droplets and the filtering ability of the materials clearly visible an inhomogeneous droplet distribution was generated. the flow direction is from left to right and the flow state of the incoming air is laminar. if the intensity of the scattered light emanating from the droplets is large in front of the filter material (left image) and close to zero behind the filter material (right image), the droplets are almost completely filtered out through the material. if, on the other hand, no significant reduction in intensity can be detected behind the filter material, the filter effect is negligible. the area of the filter mount and the channel edges are not shown in the following images, since no relevant flow and droplet information is visible in these areas. the results presented are qualitative, but intended to be this way to provide readers with visual evidence of the particle penetration through different candidate filter media. a better impression of the filter efficiency is obtained by viewing the second video in the supplementary material. the comparison of the two pictures in fig. (left) shows that almost all droplets pass the tested surgical face mask unhindered. consequently, this mask does not provide serious self protection against droplet infection. only a mixing of the droplet distribution takes place due to the porosity of the filter material. it is fatal that medical personnel are often so poorly protected by these masks. but it is also fatal for patients if clinical staff with a presymptomatic or asymptomatic course of infection uses these masks. even worse than the surgical face masks is the hygiene mask, see fig. (right). this mask is designed for catching larger objects such as hair and spook, but tiny droplets, such as those produced when talking, singing and coughing, cannot be filtered out of the air stream by the hygiene mask. it should also be noted that the flow resistance of the hygiene mask is so low that even the protective mechanism described in subsection . does not function effectively. figure reveals the effectiveness of particle filtering with toilet paper with layers, paper towel, coffee filters, and microfibre cloth which also offer no serious protection against droplets in this size range. only very large droplets are retained by these materials and therefore these materials are suitable for their intended use, but not as filter material for small droplets. it is therefore strongly discouraged to make masks from these materials with the aim of protecting oneself from infection. furthermore, a very strong fleece was tested, which serves as a protective coating on ironing boards. the material is mm thick, completely opaque and has a pressure drop of about pa. however, a filter effect is not visible, as indicated in fig. (left) . the droplet clouds flow almost unfiltered through the fleece. even several layers of a dense fabric do not have a proper filtering effect on the considered droplet sizes, which escape mainly when breathing, speaking, singing and coughing. good results could only be achieved with the material of a vacuum cleaner bag with fine dust filter properties, see fig. (right) . despite the small droplets used in these tests, almost all droplets are reliably filtered out. consequently, also no larger droplets will be able to pass through the material. according to the manufacturer swirl, the material filters . % of fine dust down to . μm diameter. this vacuum cleaner bag with fine dust filter therefore has better filtering properties than all tested materials and masks and even an ffp protective mask has poorer filtering properties, as it only has to filter out % of the fine dust down to . μm to meet the specifications (uvex, ). the material of vacuum cleaner bags with fine dust protection is therefore very well suited as a self-protecting mask if only the filter effect is considered. however, because vacuum cleaner bags are not certified clinical products, they may contain unhealthy ingredients that kill bacteria and harmful fibers that may leak from the bag material. it is therefore uncertain whether this material is suitable in practice as a material for a respirator mask. figure (left) illustrates the filtering capabilities of an ffp mask under the test conditions. nearly all droplets are filtered out as expected. therefore, this mask type is very well suited to protect people from an infection by means of aerosols even when the environment is strongly contaminated with infectious droplets. recently, some hospitals in the usa make use of halyard h material to protect their employers from aerosol infection. the test result of the material is displayed in fig. (right). it is clearly visible that the filtering capacity of the material is not sufficient to protect people from infection by aerosols if the environment is contaminated with the sars-cov- . figure shows with different resolution microscopic images of the halyard h material. it is composed to fibers but the density might not be sufficient to filter the particles used in our investigation. there are also tiny holes in the pockets visible, which could be the reason why the aerosol passes through the material, as the flow resistance at the holes is low compared to the other parts of the material. the flow tests clearly show that apart from the vacuum cleaner bag and the ffp mask, the filter effect of the tested materials is not sufficient to protect against droplet infection reliably if the environment is contaminated with sars-cov- . even masks routinely used by medical staff in hospitals and doctor's offices have almost no significant filtering effect on the droplet sizes typically produced when breathing, speaking, singing and coughing. the results are therefore in good agreement with the results from (leung et al., b and davies et al., and kwok et al., . but why has wearing these masks been shown to provide effective protection against infection with the virus in the sars epidemic, as shown in , lo et al., and seto et al., ? because a mask is important not only because of its filtering ability, but to limit the droplet propagation as discussed in section . . so in combination with distances these mask can protect if only a few people are infected in the surrounding. the results in (leung et al., b and bae et al., ) are correct, but they do not consider the full performance of masks, but only a partial aspect. therefore, the conclusions in the articles are not universal. the findings in and lo et al., and seto et al., are understandable when the full performance of masks in blocking infections is considered. unfortunately, wearing a simple mouth-and-nose cover may be less comfortable than wearing a particle filtering face mask. in effect, this can promote a smear infection. since all these transmissions of infection are possible in daily life, wearing a comfortable mask is essential to block human-to-human transmission by smear and droplet infection. to ensure the best possible protection, a particle filtering mask should be used if the number of infected persons in the environment and the viral load in the room is unknown. at present, social distancing practices and universal masking wearing seem to be the best methods of containing viral pandemic without stricter lockdown policies and without vaccines. some recent studies show that even the simple materials we have tested have some filtering ability (davies et al., , drewnick, , konda et al., and van der sande et al., , we do not question these results, although the pressure drops in one study is anomalously low (see supporting information in konda et al., ) , but we state explicitly that a material that does not have an adequate filtering ability equivalent to an ffp /n /kn mask cannot be recommended as a filter material for self-protection against droplet infection. statistically speaking, every loss of performance leads to an increase in the number of infected people and thus to an increase in the number of death. it is therefore very dangerous to recommend materials with some filtering properties as possible materials for self-protection masks. but there is another important aspect that will be discussed next. according to the previous section one might argue that a mouth-and-nose cover or surgical mask made of a good filter material would provide good protection against infection when infected people are in the vicinity or the room is contaminated with viruses. but that will not usually be the case. air takes the path of least resistance. as these masks do not seal tightly enough with the face, droplets can flow unhindered past the edge of the mask when inhaled and exhaled and reach the lungs or the environment. if the mask does not fit properly, this will even be the rule. this is illustrated in fig. were a person is exhaling air during an easy exhalation without physical exertion (left), strong breathing during physical exertion (middle) and when coughing (right). the first video in the supplementary material shows the animated sequences. the analysis shows that it is very important do differentiate between mouth-and-nose cover, surgical mask and particle filtering respirator mask because they differ substantial in their fundamental protection properties. face masks can offer three fundamental different kind of protection: . they effectively prevents a smear infection, as the wearers of the masks no longer perform their habitual grip on the face and thus no longer bring the virus from the hand into the mouth or nose (howard et al., ) . . the flow resistance of the mask greatly limits the spread of viruses in the room. this significantly reduces the risk of infection in the vicinity of an infected person (protection of third parties). . the inhalation of droplets containing viruses can be prevented by using a tight-fitting mask with particle filtering properties (self-protection). the first fundamental protection mechanism can be reached by all face masks if they fit well and sit comfortably. if not, the user will touch the face even more than usual to correct the fit of the mask. as this can increase the risk of smear infection, a good fit of the mask is very important. the first and second fundamental protection mechanisms are fulfilled by all masks that have sufficient flow resistance. if the mask is worn and a candle can easily be blown out despite the mask, the mask does not fulfil this function and should not be used. all three fundamental protection mechanisms can be only achieved with ffp /n /kn or better particle filtering respirator mask. typical materials currently used by the public to build masks reduce the risk of smear infection and effectively prevent the widespread spread of viruses in the environment. therefore, the use of these mouse-and-nose covers and surgical masks are very important to prevent smear infection and droplet infection to others if the distance is not too close. as these masks do not have a significant particle-filtering protective effect against droplets that are typically produced when breathing, speaking, singing, coughing and sneezing they should not be used if the environment is contaminated, like in hospitals, even when the distance rules are followed. to achieve effective self-protection in a virus-contaminated environment, masks with particle filtering properties (ffp /n /kn ) are absolutely necessary from our point of view. if a large number of infected persons are present and distance rules cannot be achieved, a very good particle filtration mask (ffp or better) is strongly recommended. if these general rules are followed and all people use suitable particle-filtering respirators correctly, the transmission of viruses via droplets / aerosols can be effectively prevented. otherwise, these types of masks would never have received certification, nor would they be a core component of the personal protective equipment in hospitals and other environments. therefore, proper face masks can save lives while maintaining social life and securing the economy and the state. but universal masking alone is not enough for two reasons: first, many people are not very good at following rules consistently. therefore, it is advisable to observe the rules of hygiene and distance and to be careful even when wearing a mask. in the event of a car accident, the occupants are also protected by various devices (bumpers, crumple zone, safety belts, airbags, head and legroom, autonomous assistance systems, ...). second, some people are extremely bad at following rules, either because they do not want to or because they simply cannot. these people can become superspreaders. therefore, the early detection of sources of infection and their isolation remains important beside universal masking and the rules of hygiene and distance. pulmonary vascular endothelialitis, thrombosis, and angiogenesis in covid- aerosol emission and superemission during human speech increase with voice loudness effectiveness of surgical and cotton masks in blocking sars-cov- : a controlled comparison in patients estimates of deaths associated with seasonal influenza ---united states physical distancing, face masks, and eye protection to prevent person-to-person transmission of sars-cov- and covid- : a systematic review and meta-analysis. the lancet testing the efficacy of homemade masks: would they protect in an influenza pandemic? aerosol and surface stability of sars-cov- as compared with sars-cov- abscheideeffizienz von mund-nasen-schutz masken, selbstgenähten gesichtsmasken und potentiellen maskenmaterialien assessment of deaths from covid- and from seasonal influenza rational use of face masks in the covid- pandemic. the lancet respiratory medicine compassionate use of remdesivir for patients with severe covid- temporal dynamics in viral shedding and transmissibility of covid- modality of human exposed aerosol size distributions generation and control of tracer particles for optical flow investigations in air universal masking in hospitals in the covid- era aerosol filtration efficiency of common fabrics used in respiratory cloth masks why do some covid- patients infect many others, whereas most don't spread the virus at all? science face touching: a frequent habit that has implications for hand hygiene quantity, size distribution, and characteristics of cough generated aerosol produced by patients with an upper respiratory tract infection the impact of community psychological responses on outbreak control for severe acute respiratory syndrome in hong kong mass masking in the covid- epidemic: people need guidance. the lancet respiratory virus shedding in exhaled breath and efficacy of face masks evaporation and dispersion of exhaled droplets in stratified environment superspreading and the effect of individual variation on disease emergence respiratory infections during sars outbreak where sneezes go singing and the dissemination of tuberculosis solutal marangoni flow as the cause of ring stains from drying salty colloidal drops surfactant-driven flow transitions in evaporating droplets survival of aerosolized coronavirus in the ambient air reducing transmission of sars-cov- . science, eabc particle image velocimetry verdunstung akustisch levitierter schwingender tropfen aus homogenen und heterogenen medien effect of the intermittency dynamics on single and multipoint statistics of turbulent boundary layers interfacial flows in sessile evaporating droplets of mineral water does risk compensation undo the protection of ski helmet use? professional and home-made face masks reduce exposure to respiratory infections among the general population testing the risk compensation hypothesis for safety helmets in alpine skiing and snowboarding effectiveness of precautions against droplets and contact in prevention of nosocomial transmission of severe acute respiratory syndrome (sars). the lancet the lessons of the pandemic are we facing a crashing wave of neuropsychiatric sequelae of covid- ? neuropsychiatric symptoms and potential immunologic mechanisms. brain, behavior, and immunity endothelial cell infection and endotheliitis in covid- estimates of the severity of coronavirus disease : a model-based analysis clinical characteristics of hospitalized patients with novel coronavirus-infected pneumonia in wuhan air-bone infection case fatality risk of influenza a (h n pdm ): a systematic review covid- : considering the prevalence of schizophrenia in the coming decades identifying airborne transmission as the dominant route for the spread of covid- the authors would like to thank stefan ostmann for conducting the mask experiments presented in section . and amirabas bakhtiari for taking the microscopic images in figure . (www.preprints christian j. kähler (prof. dr.) and rainer hain (dr.) • a simple mouth-and-nose cover or a surgical mask is able to effectively limit the spread of air and aerosol when breathing, speaking, singing, coughing and sneezing. • wearing a mask is therefore a very useful contribution to contain a pandemic by protecting people in the vicinity from droplet infection.• however, a mouth-and-nose cover or a surgical mask does not fit tightly enough on the face to protect against droplet infection.• only a particle-filtering half-mask that fits tightly offers protection against droplet infection.• common household materials, however, do not have a sufficient filter effect to protect against droplet infection. key: cord- -c c vi authors: basu, saikat; holbrook, landon t.; kudlaty, kathryn; fasanmade, olulade; wu, jihong; burke, alyssa; langworthy, benjamin w.; farzal, zainab; mamdani, mohammed; bennett, william d.; fine, jason p.; senior, brent a.; zanation, adam m.; ebert, charles s.; kimple, adam j.; thorp, brian d.; frank-ito, dennis o.; garcia, guilherme j. m.; kimbell, julia s. title: numerical evaluation of spray position for improved nasal drug delivery date: - - journal: sci rep doi: . /s - - - sha: doc_id: cord_uid: c c vi topical intra-nasal sprays are amongst the most commonly prescribed therapeutic options for sinonasal diseases in humans. however, inconsistency and ambiguity in instructions show a lack of definitive knowledge on best spray use techniques. in this study, we have identified a new usage strategy for nasal sprays available over-the-counter, that registers an average -fold improvement in topical delivery of drugs at diseased sites, when compared to prevalent spray techniques. the protocol involves re-orienting the spray axis to harness inertial motion of particulates and has been developed using computational fluid dynamics simulations of respiratory airflow and droplet transport in medical imaging-based digital models. simulated dose in representative models is validated through in vitro spray measurements in d-printed anatomic replicas using the gamma scintigraphy technique. this work breaks new ground in proposing an alternative user-friendly strategy that can significantly enhance topical delivery inside human nose. while these findings can eventually translate into personalized spray usage instructions and hence merit a change in nasal standard-of-care, this study also demonstrates how relatively simple engineering analysis tools can revolutionize everyday healthcare. finally, with respiratory mucosa as the initial coronavirus infection site, our findings are relevant to intra-nasal vaccines that are in-development, to mitigate the covid- pandemic. www.nature.com/scientificreports www.nature.com/scientificreports/ simulated predictions of respiratory flow physics and transport therein; see e.g. [ ] [ ] [ ] . of interest are nasal spray simulation studies on in silico models, re-constructed from medical imaging, to measure drug delivery along the nasal passages , in the sinuses , , and on the effects of surgical alterations of the anatomy on nasal airflow [ ] [ ] [ ] [ ] as well as on topical transport of drugs [ ] [ ] [ ] [ ] . the latter addresses the role of airway channel's shape in the context of airflow-droplet interactions. notably, while using medical devices like sprayers, which are inserted at the nostril, the anterior airway geometry gets altered. to simplify the situation though, computational results suggest that such initial perturbations do not greatly change or adversely affect the eventual drug deposits at the diseased sites. despite the abundance of computational research on nasal drug delivery, there is a distinct lack of articulate instructions for guidance on what could be the "best" way to use the commercially available sprayers. first, numerical studies often do not use a realistic distribution of droplet sizes while simulating topical sprays. focusing on specific droplet diameters is resourceful while studying the detailed nuances of transport characteristics in that size range; however this somewhat limits the applicability of the subsequent findings while predicting the performance of real sprays, which have a wide variability of droplet sizes in each spray shot. secondly, the inter-subject anatomic variations also render it difficult to identify a generic spray orientation that can work for all and ensures maximal delivery of drugs at the diseased locations inside the nose. in this study, we have numerically tracked the transport of therapeutic particulates from over-the-counter nasal sprays via inhaled airflow. the computational fluid dynamics (cfd) models of droplet transport and the in silico prediction of their deposition sites along the nasal airway walls have been compared with in vitro spray experiments in d-printed solid replicas of the same anatomic reconstructions. we have proposed a new strategy of nasal spray usage and the recommendation is supported by a significant improvement in target site particulate deposition (tspd), when compared to the prevalent spray use techniques. the study also expounds [ ] [ ] [ ] on the potential of cfd as a tool in nasal ailment treatment and subject-specific prognosis, and can contribute to the emergence of non-invasive personalized therapeutics and treatment strategies. preliminary results pertaining to this work have featured at the american physical society (aps) -division of fluid dynamics annual meetings , and at the international society for aerosols in medicine (isam) congress [ ] [ ] [ ] . anatomic reconstructions. all methods were performed in accordance with the relevant guidelines and regulations, including use of de-identified computed tomography (ct) data from three pre-surgery chronic rhinosinusitis (crs) patients -collected under approval from the institutional review board (irb) at the university of north carolina at chapel hill. we also obtained informed consent for participation in this study (which includes obtaining and use of ct data) from the test subjects. subject www.nature.com/scientificreports www.nature.com/scientificreports/ medical-grade ct scans of the subjects' nasal airways were used to re-construct digital models through thresholding of the image radiodensity, with a delineation range of − to − hounsfield units for airspace , , complemented by careful manual editing of the selected pixels for anatomic accuracy. as part of that process, the scanned dicom (digital imaging and communications in medicine) files for each subject were imported to the image processing software mimics v . (materialise, plymouth, michigan). for this study, we subsequently considered each side of the nose in the in silico models as a distinct nasal passage model, while studying the droplet transport properties when the spray nozzle was placed on that side: (a) subject 's right side constituted nasal passage model (npm ) and his left side was nasal passage model (npm ); (b) subject 's left side was nasal passage model (npm ); and (c) subject 's right side was nasal passage model (npm ) and her left side was nasal passage model (npm ). note that subject 's right-side anatomy did not exhibit a direct access to the diseased intra-nasal targets from outside of the nostril and was not selected for this study. this had to do with the scope of our study design; for details see the section on target site identification. also refer to the discussion section for follow-up comments. to prepare the in silico anatomic models for numerical simulation of the inhaled airflow and the sprayed droplet transport therein, the airway domain was meshed and spatially segregated into minute volume elements. the meshing was implemented by importing the mimics-output in stereolithography (stl) file format to icem-cfd v (ansys, inc., canonsburg, pennsylvania). following established protocol , , each computational grid comprised approximately million unstructured, graded tetrahedral elements; along with three prism layers of approximately . -mm thickness extruded at the airway-tissue boundary with a height ratio of . inspiratory airflow and sprayed droplet transport simulations. laminar steady-state models work as a reasonable approximation while modeling comfortable resting to moderate breathing , [ ] [ ] [ ] . furthermore, with our simulations focusing on a single cycle of inspiration, steady state flow conditions were adopted as a feasible estimate. based on the principle of mass conservation (continuity), and assuming that the airflow density stays invariant (incompressibility), we have with u representing the velocity field for the inspired air. conservation of momentum under steady state flow conditions leads to the modified navier-stokes equations: here ρ = . kg/m represents the density of air, μ = . × − kg/m.s is air's dynamic viscosity, p is the pressure in the airway, and b stands for accelerations induced by different body forces. to simulate the airflow, eqs. ( ) and ( ) were numerically solved through a finite volume approach, in the inspiratory direction. the computational scheme on ansys fluent v . employed a segregated solver, with simplec pressure-velocity coupling and second-order upwind spatial discretization. solution convergence was obtained by minimizing the flow residuals (viz. mass continuity ~− o( ) , velocity components − Õ ( ) ), and through stabilizing the mass flow rate and the static outlet pressure at the nasopharynx of the digital models. a typical simulation convergence run-time with iterations clocked approximately hours, for -processor based parallel computations executed at . ghz speed. the numerical solutions implemented the following set of boundary conditions: ( ) zero velocity at the airway-tissue interface i.e. the tissue surface lining the sinonasal airspace (commonly called no slip at the walls), along with "trap" boundary conditions for droplets whereby a droplet comes to rest after depositing on the wall; ( ) zero pressure at nostril planes, which were the pressure-inlet zones in the simulations, with "escape" boundary condition for droplets that allowed outgoing trajectories to leave the airspace through the nostril openings; and ( ) a negative pressure at the nasopharyngeal outlet plane, which was a pressure-outlet zone, also with an "escape" boundary condition for droplets. the negative nasopharyngeal pressure was adjusted to generate inhalation www.nature.com/scientificreports www.nature.com/scientificreports/ airflow rates with less than % variation from subject-specific measurements of resting breathing. the physical recordings were collected with lifeshirt vests that tracked chest compression/expansion during breathing, and accordingly quantified the inhalation rates (for additional details, see table ). after simulating the airflow, sprayed droplet dynamics were tracked through discrete phase particle transport simulations in the ambient airflow, and the corresponding lagrangian tracking estimated the localized deposition along the airway walls through numerical integration of the following transport equations : the parameters here are u d , representing the droplet velocity; along with u as the airflow field velocity, ρ and ρ d respectively as the air and droplet densities, g as the gravitational acceleration, f b as any other additional body forces per unit droplet mass (as for example, saffman lift force that is exerted by a typical flow-shear field on small particulates transverse to the airflow direction), and c d u u re( )/ ( ) quantifies the drag force contribution per unit droplet mass. here, c d is the drag coefficient, d is the droplet diameter, and re represents the relative reynolds number. mean time step for droplet tracking was in the order of − sec., with the minimum and maximum limits for the adaptive step-size being − o( ) sec. and − o( ) sec., respectively. also note that the solution scheme posits the particulate droplets to be large enough to ignore brownian motion effects on their dynamics. post-processing of the simulated data laid out the spatial deposition trends, which were then tallied against in vitro observations. d printing and physical experiments. to assess the reliability of numerically predicted topical deposition vis-à-vis physical experiments, d-printed anatomic replicas were generated for subject 's airway and hence included both npm and npm . the posterior parts of the solid models were made from the stereolithography material watershed (dsm somos, elgin, illinois). post-digitization, the printing job of the posterior component was sub-contracted to protolabs (morrisville, north carolina). printing of the anterior soft plastic part on a connex d printer was done by ola harrysson's group at north carolina state university (at the edward p fitts department of industrial and systems engineering), using polymer inkjetting process on tangogray flx material. see fig. (a-c) for representative pictures of a digitized model and the corresponding d replica. recording deposits through gamma scintigraphy. intra-nasal topical delivery was tracked through in vitro examination of mildly radioactive spray deposits in the d-printed anatomic replicas. to ensure that the spray axis orientation and nozzle location aligned with the corresponding simulated spray parameters, we used specially designed nozzle positioning devices (npd) inserted at the nostril. the spray bottle was fitted into the npd, while administering the spray via hand-actuation. for each sample test, a bottle of commercial nasal spray nasacort was labeled with a small amount of radioactive technetium (tc m) in saline. at the time of dispensing the spray shots, a vacuum line controlled by a flow-valve was used to set up inhalation airflow through the model, and the flow rate was commensurate with the subject-specific breathing data (table ). corresponding setup is in fig. (d,e) . four independent replicate runs of each spray experiment were conducted, followed by compilation of the means and standard deviations of the drug deposits along the inner walls of the solid models. the topical deposition was proportional to the radioactive signals emitted from the spray solution traces that deposited inside a solid model and was quantifiable through image-processing of the scintigraphy visuals, collected using a bodyscan (mieamerica, forest hills, il) -mm width by -mm height d gamma camera. the pixel domain was × , with an image acquisition time of minutes; and one pixel equated to a cartesian distance of . mm in the digital and d models. table . this table incorporates the parameters for measured and simulated inhalation airflow, in the study subjects. symbols: σ = standard deviation, μ = mean, *⇒ inhalation rate is considered to be twice the minute ventilation, **⇒ target simulated airflow is . % of the measured rate, to account for influence of the subjects' awareness of recording of the breathing process. note that the tidal volume is a measure of the lung volume representing the volume of air displaced between normal inhalation and exhalation, without application of any extra effort. the minute ventilation (air inhaled per minute) is computed from the inspiratory phase of a breath , . www.nature.com/scientificreports www.nature.com/scientificreports/ model segmentation for comparison with numerical data. to facilitate the comparison between the numerical predictions on droplet deposition and the physical observation of gamma scintigraphy signals in the corresponding solid replica, we segregated npm and npm into virtual segments oriented along three different directions. figure lays out the cartesian coordinate directions for the d space. x was perpendicular to the sagittal plane traversing from left to right sides of the nasal models (with the model head facing forward), y was perpendicular to the axial plane traversing from inferior to superior aspects of the models, and z was perpendicular to the coronal plane traversing from anterior to posterior aspects of the models. the virtual segments were oriented along the xy (coronal), yz (sagittal), and zx (axial) planes. parallel to the xy coronal plane, the models contained segments (named, c -c ⇒ sagittal columns); there were compartments (c -c ⇒ frontal columns) parallel to the yz sagittal plane, and there were compartments (r -r ⇒ sagittal rows) parallel to the zx axial plane (see fig. ). for each compartment, the particulate deposition fraction predicted from the simulation was compared with the deposition fraction measured based on gamma signals of the deposited particulates in the corresponding compartment of the d-printed model. to achieve this, signals emitted from the solution traces, that settled along the airway walls, were subjected to image processing analysis. therein, by superimposing the compartmental grid on the radio-images, the signals were extracted from each compartment. in order to align the grid on the image in a manner consistent with the virtual model, three inset discs were designed as reference points on the outer surface of the virtual and d-printed models. americium sources from commercial in-home smoke detectors were inserted into the insets as reference points on the d-model and a radio-image was recorded. for the analysis, the scintigraphy images were processed using imagej by constructing a region of interest (roi) referenced to the fixed americium sources. care was taken to align the emitted visual signals with similar reference regions within the superimposed grid. this was done via manual visualization to achieve a best fit of signal intensity within reference regions. the grid compartment planes positioned using this visual best-fit technique were designated as "reference planes". given the nature of the radioactive signals and the resolution of the radio-image, some www.nature.com/scientificreports www.nature.com/scientificreports/ signal intensity resided outside of reference regions even while using best-fit practices. a reasonable fit could be obtained by shifting the image by one pixel in either direction (positive shift/negative shift). in order to account for this variation, alternative plane positions (see fig. (d)) were created by shifting the reference planes one pixel along the positive and negative axes for each set of cartesian planes. these three sets of compartment planes were positioned in the in silico modeling software using the measured distances from the reference regions. the corresponding cartesian coordinates of these planes were used to assign droplet deposition locations from the computational simulations to grid compartments, for comparison with the in vitro model. in these comparisons, we left out the deposits in the anterior nose (from the cfd data as well as the physical recordings) in order to negate the bright radiation signal coming from that zone in the experimental deposits; and focused only on measurements from the posterior parts of the respective models. note that the anterior nose in an in silico model is in fact the removable soft pliable anterior part in the corresponding d print (e.g. see fig. ). , and (c) depict the gridline schematic on npm and npm , that is used to extract the deposition fractions from the gamma scintigraphy-based quantification of the sprayed deposits in the solid replicas. the models are respectively segregated into sets of compartments: sagittal columns, frontal columns, and sagittal rows. panel (d) shows the perturbation of the base gridline by pixel. representative technetium signals are in panel (e). note: in regard to the axis system, the circle with solid dot implies out-of-plane direction from this page, the circle with cross signifies into-the-plane of this page. www.nature.com/scientificreports www.nature.com/scientificreports/ identification of target site and spray parameters. effect of airflow on droplet trajectories. inertial motion of a droplet is linearly proportional to its mass, and hence is exponentially proportional to the droplet diameter. consequently, for bigger droplets, the inertial motion persists longer before being taken over by the ambient airflow. figure (a) tracks the trajectory of a representative μ droplet. in there, the tiny red circle marks the location where the inertial motion of the droplet got overwhelmed by the ambient flow, beyond which the droplet trajectory was same as the airflow streamline on which it was embedded at the red circle's location. note the contrasting μ droplet trajectory in fig. (b) , where the inertial motion persisted longer. the phenomenon has a significant impact on drug deposition trends. the bigger droplets (≥ μ) show a greater propensity to hit the anterior walls directly owing to their high initial momentum, while smaller droplet sizes penetrate further into the airspace; see e.g. figure (c,d). to ensure that the bigger droplets also reach the target sites, we argue that it would be conducive to harness their inertial motion and direct those droplets actively toward the target when they exit the spray nozzle. this can be feasibly achieved by orienting the spray axis to pass directly through an intended anatomic target zone. , indicate a lack of definitive knowledge on the best ways to use a nasal spray device. different commercial sprayers often offer somewhat contrasting recommendations. however, there is a common agreement (see fig. (a)) that the patient should incline her/his head slightly forward, while keeping the spray bottle upright , . furthermore, there is a clinical recommendation to avoid pointing the spray directly at the septum (the separating cartilaginous wall between the two sides of the in panel (a), the smaller droplet has weaker inertial momentum and the ambient airflow streamline takes over its motion much earlier than that in case of a heavier droplet like the one in panel (b), where the inertial momentum of the μ droplet persists longer. the small red circle in (a) depicts the point where the inertial momentum gets overwhelmed by the fluid streamline. evidently, owing to smaller inertia, the droplets with smaller diameters get predominated by the airflow streamlines earlier than the bigger droplets. this results in a better penetration and spread of sprayed droplets in the nasal airspace, as shown in panel (c), for a different nasal model. on the contrary, spray shots with exclusive share of bigger droplets (e.g. ≥ μ here) tend to follow their initial inertial trajectories, without much effect of the airflow streamlines on their paths, and deposit along the anterior walls of the nasal airspace, as depicted in panel (d). the red boundaries in panels (c) and (d) highlight the difference in particulate penetration into the model, in the two cases. note: these images were created using fieldview, as provided by intelligent light through its university partners program. www.nature.com/scientificreports www.nature.com/scientificreports/ nose). these suggestions were adopted in our standardization of "current use" (cu) protocol for topical sprays. the digital models were inclined forward by an angle of . °, and the vertically upright spray axis was closer to the lateral nasal wall, at one-third of the distance between the lateral side and septal wall. also, the spray bottle was so placed that it penetrated into the airspace by a distance of -mm, inspired by the package recommendations of commercial sprayers for a "shallow" insertion into the nose. refer to fig. (b,c) for the schematics of the cu protocol used in this study. target site identification and proposing an alternate spray use criteria. all sinuses, except sphenoid, drain into the ostiomeatal complex (omc), it being the main mucociliary drainage pathway and airflow exchange corridor between the nasal airway and the adjoining sinus cavities. to ensure that as many drug particulates reach the sinus chambers and their vicinity as would be possible, we hypothesize that the spray axis should be directed straight toward the omc . this is supported by our observation of the effect of airflow physics on droplet trajectories. if the spray axis hits the omc directly, the likelihood that the larger droplets will deposit there is higher. we refer to this usage protocol as "line of sight" (los). like the cu protocol, the los protocol also had the sprayer inserted at a depth of -mm into the nasal airspace. representative los orientation is shown in fig. . tspd percentage at the omc and the sinuses was evaluated as = × (m target /m spray ); with m target being the spray mass of the particulate droplets deposited at the omc and inside the sinus cavities, and m spray being the mass of one spray shot. to establish the robustness of the tspd predictions for the cu and los protocols, we also tracked droplet transport and deposition when the spray directions were slightly perturbed. such perturbed peripheral directions for cu initiated mm away on the nostril plane and were parallel to the cu's vertically upright true direction. for los, the perturbed peripheral directions were obtained by connecting the base of the true los direction on the nostril plane with points that radially lie mm away from a point on the los; this specific point being mm away along the los from the base of the los direction on the nostril plane (e.g. see bottom panel of fig. for an illustrative example). parameters for the simulated spray shot. over-the-counter nasacort (triamcinolone acetonide), a commonly prescribed and commercially available nasal spray, was selected for this study. four units of nasacort were tested at next breath, llc (baltimore, md, usa) to characterize the in vitro spray performance. corresponding plume geometry was analysed through a sprayview nosp, which is a non-impaction laser sheet-based instrument. averaged spray half-cone angle was estimated at . °, and the droplet sizes in a spray shot followed a log-normal distribution. with the droplet diameter as x, the droplet size distribution can be framed as a probability density function of the form : here, x = . μ is the mass median diameter (alternatively, the geometric mean diameter ) and σ g = . is the geometric standard deviation. the latter quantifies the span of the droplet size data. measurements were www.nature.com/scientificreports www.nature.com/scientificreports/ also made with and without the saline additive in the sprayer, and the tests returned similar droplet size distribution. note that a saline additive was used during the physical recording of the sprayed deposits. also, as per earlier findings in literature , the mean spray exit velocity from the nozzle approximates at . m/s, based on phase doppler anemometry-based measurements. for the test spray units (at next breath), the actuation forces were found to range between . - . kg-force. considering an actuation area of approximately cm , the force measurements agree well with earlier values in literature [ ] [ ] [ ] and hence the resultant pressure exerted on the droplets in our physical experiments was assumed to maintain a similar droplet size distribution, as was determined in the test cases by next breath. the droplets contained in one spray shot in the numerical simulations followed the same size distribution. while simulating the droplet trajectories, we assumed typical solid-cone injections and tracked the transport for -mg spray shot while comparing the tspd trends from the cfd predictions with the corresponding experimental drug delivery patterns. on the other hand, . mg (which is one shot of nasacort, as quantified by next breath, llc) of spray mass transport was simulated while comparing the cfd-based tspd numbers for the los and cu protocols in each model. comparison between cu and los spray usage protocols. los was found to be consistently superior in comparison to the cu spray placement protocol, while targeting the omc and the sinus cavities for drug delivery. table lists the deposition fraction percentages for each spray release condition in the five airway models (npm -npm ). for a graphical interpretation, we have plotted the same information on fig. . overall, the deposition fraction for the los was on an average . -fold higher than the cu deposition fraction, with the corresponding subject-specific improvement range being . - . folds for the five test models. the improvement www.nature.com/scientificreports www.nature.com/scientificreports/ does decay when the perturbed peripheral spray directions are compared, to assess the robustness of the los protocol's advantage over cu. considering the varying peripheral directions around the true los and cu, the los set registered an average . -fold increase in tspd, with the corresponding subject-specific improvement range being . - . folds. statistical tests -on improvements achieved by the revised spray use strategy. los was compared to cu through a paired study design on the data from five test models. table lays out the computed numbers. for each model, the outcome comprised the percentage of deposition in omc and the sinuses for both cu and los spray usage. null hypothesis considered for this statistical test assumed that the tspd would be same for cu and los in an . panel (f) compares the tspd for peripheral directions in a . -mm perturbation (on the left) with respect to a -mm perturbation (on the right) from the true los orientation, both in npm . as expected from the overall findings, the tspd increased for the perturbed spray directions that were closer to the true los. panel (g) depicts the spatial perturbation parameters for the los spray axis orientation in npm . www.nature.com/scientificreports www.nature.com/scientificreports/ airway model. the deposition percentage corresponding to cu and los protocols in the same nostril were treated as paired observations for a paired t-test to check the null hypothesis. owing to a relatively small study cohort, paired wilcoxon signed rank test was also used for robustness check. in order to study how spatial variation might affect the difference between cu and los, three different ways of calculating the percentage of deposition were implemented. the first strategy considered the average deposition from the true los and cu directions. the www.nature.com/scientificreports www.nature.com/scientificreports/ second strategy compared the tspd averaged from the true cu and los directions, along with the deposition data for spray release parameters obtained by perturbing the respective true directions. the third strategy used tspd averaged exclusively from the deposition data corresponding to the perturbed spray release parameters. this allowed us to assess the robustness of any probable improvement from using los, while still accounting for slight spatial variations of the spray direction. the first comparison method demonstrates an average deposition increase of . percentage points for los ( . -% for los vis-à-vis . % for cu). this difference is significant at the . level with a p-value from the paired t-test of . . the paired wilcoxon signed-rank test has a p-value of . , which was the lowest possible p-value for the wilcoxon signed-rank test given only five pairs of data. in the second comparison scheme, los has an increased deposition of . percentage points relative to cu ( . % vis-à-vis . %). the p-value for this difference is . using the paired t-test and . using the wilcoxon signed rank test. finally, for the third comparison method, los registered an increased deposition of . percentage points relative to cu ( . % vis-à-vis . %). the p-value for this difference is . using the paired t-test and . using the wilcoxon signed rank test. this provides a strong evidence that los leads to higher percentage of deposition in the omc and sinuses. the estimated difference is largest when using just the true directions, but the difference is still statistically significant even when using the spray release points obtained by perturbing the true directions. the p-value from the paired t-test is actually lower when the tspd from just the perturbed points are considered, owing to the reduced variance for the estimated difference. for all three ways of estimating the percentage of deposition, the paired wilcoxon signed-rank test returns a p-value of . . with only five pairs of data, this suggests that the use of los does result in statistically significant higher deposition for all five nostril models. comparison of the simulated tspd predictions with physical experiments. figure compares the numerical tspd predictions with corresponding gamma scintigraphy-based experimental recordings in npm and npm . while the compartmental deposits visibly presented a congruous trend in the sagittal columns, sagittal rows, and frontal columns; we conducted additional statistical tests to verify the homogeneity between the two sets of data so as to establish the reliability of the computational findings. table gives the pearson and kendall's correlation between the numerical and experimental models for the average deposition fractions in npm and npm for the los protocol. the confidence intervals are based on bootstrap samples, instead of asymptotic approximations, because of the relatively small sample size. based on the output, we can see that the pearson correlation is consistently very high while the kendall's correlation is somewhat lower. however, while the kendall's correlation is frequently thought to be more robust to outliers, particularly for small sample sizes like this data-set; in this particular instance the pearson correlation is likely more illustrative. this is because the pearson correlation is able to show that, for the most part, the magnitudes of the estimates are similar and comparable between the numerical and experimental models. in general, there is a strong linear relationship between the percent of deposition prediction from the numerical model and the corresponding physical measurements in the experimental model. the lower kendall's correlation (overall mean measure . ) is largely due to regions where both the numerical and experimental models had very low average deposition but the exact rank of these regions changed considerably between the two data-sets. note that this does not necessarily indicate a poor performing numerical model. however, the relatively high pearson correlation (overall mean measure . ) does indicate that the numerical models perform well while predicting the sprayed droplet transport. cfd-guided nasal spray usage defined by the los protocol was found to significantly enhance topical drug delivery at targeted sinonasal sites, when compared to currently used spray administration techniques. with increased sample size, this work can be the catalysis toward prompting personalized instructions and specifications for improved use of topical sprays. the findings, thus, have the potential to substantially upgrade the treatment paradigm for sinonasal ailments through the ability to ascertain los in individual subjects via endoscopic examinations conducted in the clinic, and to help guide treatment decision-making and patient instructions for spray usage. to quantifying the suitability of a person's airway for the los spray protocol, we exploratorily propose a scoring system that is based on how much of the targeted drug delivery sites (omc, sinuses) are visible when inspected clinically from outside of the nostril. the scoring system will also serve to quantify nasal anatomic variability www.nature.com/scientificreports www.nature.com/scientificreports/ among individuals. accordingly, as part of the current study, the los scores (see table ) were first determined observationally, based on the external visibility of the omc site in the in silico sinonasal reconstructions. we fixed a range of scores ∈ [ , ] , with being used when the los direction was easiest to ascertain. subjective as that scoring procedure may be, it is similar to what attending physicians will gauge during a clinic visit to determine if a particular patient has a "line of sight" in her/his nasal anatomy. so, to establish the relevance of the findings from this manuscript toward revisions of the therapeutic protocol for sinonasal care, it is important to assess the comparability of the observational los scores with more objective score determination techniques. this was achieved by calculating the surface area of the nostril plane and the projected area of the omc on the plane of the nostril. we computed the ratio of the projected area to the nostril area, as a percentage. scores of were assigned if the ratio exceeded %, if the ratio exceeded %, if the ratio was more than . %, and if the ratio was greater than %. the two scoring techniques yielded very similar results (as in table ), with the highest and lowest scores respectively going to the same anatomic models. pearson's rank correlation for the two sets of scores was . . while a broader study, involving clinical trials, will be necessary to revise therapeutic protocol for nasal drug delivery, the present results illustrate the easy adaptability of our findings into clinical practice settings. on the comparability of the experimental data with the numerical findings. the computational simulations assumed a laminar framework to mimic steady breathing. however, one may argue that even with resting breathing rates, the airflow often contains transitional features like vortices, emerging from the roll-up of www.nature.com/scientificreports www.nature.com/scientificreports/ shearing fluid layers during flow-structure interactions - at the anatomic bends. some of these nuances are, in fact, difficult to model without proper turbulence simulations , . however, true as that may be, the effect of these flow artifacts on eventual drug delivery in the sinuses has been found to be somewhat nominal while comparing laminar and turbulence simulation results . on the other hand, the in vitro techniques also often pose challenges. for instance, there can be post-deposition run-off as the deposited solution traces undergo translocation along the inner walls of the solid replica. such drip-off dynamics can lead to a flawed estimate of regional deposition. the effect of post-deposition dripping can be conjectured to be most prominent for the signals extracted from the sagittal rows, as the deposited droplets start moving downward along the internal solid walls of the d-printed models, owing to gravitational effects. this is confirmed by the physical and numerically-predicted signals from the sagittal rows demonstrating relatively lower correlation coefficients (when contrasted with the correlations for the signals from the sagittal and front columns) in the two experimental comparisons (e.g. see table ). in the gamma scintigraphy-based method of recording deposits, the radiation signal undergoes some level of scattering and hence in the process of signal extraction from each of the compartments, there is the possibility that signals from one compartment may contaminate the signals at neighboring compartments. to minimize this effect while carrying out the comparisons, the nose (the soft plastic anterior part in the d-printed models), which had a bright radiation signal owing to the relatively large amount of anterior deposits, was excluded from both the experimental and numerical data. finally, while the inhalation airflow rates were same in vitro and in silico, the airflow partitioning on the two sides of the nasal airways was likely affected by the placement of the npd, while administering the spray through hand-actuation. caveats and future implications. readers should note that this was a computational study with validation from spray transport observations in inanimate solid replicas. also, not every patient will have a clear access to the omc, and hence may be without an los. for instance, in the current study, of the six airway sides in the three study subjects, subject 's right-side airway did not exhibit an los. bulk rheology of the spray also affects the droplet size distribution. the spray property measurement tests having been performed in real over-the-counter sprays, we did not separately examine the effect of different droplet viscosities on the spray deposition trends. a different viscosity of the nasal spray can indeed alter the drug deposits, as observed in multiple studies , , . it should however be pointed out that the spray positioning strategies proposed in this study could be conjectured to be generic and should maximize drug delivery to the omc and the sinuses for other sprays as well. it is also critical to note that the flow simulations for evaluating the spray usage strategies were not multiphase; implying that the sprayed droplets were not affected by constituents such as inhaled air moisture and the mucous lining, nor was there any consideration of droplet evaporation. there are, however, earlier findings in literature www.nature.com/scientificreports www.nature.com/scientificreports/ that have looked at some of these nuances; e.g., on the interaction of deposited particulates with mucus and on the phase change of inhaled droplets during their passage through the respiratory tract . the current study simply tracked the motion of inert droplets against the ambient inspiratory airflow and recorded their regional deposition. based on the surfactants in the spray solution, the droplets might also be rendered hydrophilic; but such effects are beyond the scope of this project and the numerical schemes that have been implemented. it is, however, expository to reckon that such hydrophilicity may at times lead to agglomeration of droplet molecules, which can impact the topical drug deposition estimates. this study, its restricted sample size and limitations notwithstanding, is still, to the best of our knowledge, the first-of-its-kind to propose an alternative easy-to-implement strategy that can significantly improve the intra-nasal delivery of topical drugs at the diseased sites. the recommendation for using the "line of sight" is user-friendly, personalized (the physician can instruct the patient on the spray usage technique based on a fast los check in the clinic), and has the potential to be smoothly incorporated into the nasal standard-of-care. for probable revisions to the clinical regimen, we will need a broader study with more subjects, along with a component for clinical trials to track patient response. comparison of the numerical data with in vivo spray performance will also eliminate errors that contaminate the in vitro tspd numbers (e.g. from drip-off of the deposited solution along the inner wall contours of the d-printed models). nevertheless on a larger intriguing perspective, the current study conclusively postulates how relatively simple engineering analysis and mechanistic tools can usher in transformative changes in the prognosis and treatment protocol for ailments such as nasal congestion and respiratory infection. special comments on the significance of the findings in view of the - coronavirus pandemic. with the rapid spread of the novel coronavirus disease (covid- ) worldwide, it is essential that a vaccine or a curative is developed at the earliest. with respiratory mucosa as the initial site in coronavirus infection and transmission; mucosal immunization through targeted intra-nasal vaccine promises to be an effective strategy for prophylaxis, by inducing mucosal and systemic immune responses. as of may , several research groups are working on the possibility of designing intra-nasal vaccines for covid- - , with supporting data from work carried out on earlier strains of coronavirus . in this context, the intra-nasal anatomic targeting strategies (e.g. see fig. ) discussed in the current study can be of significant help to increase the topical delivery. this project has generated both simulated and experimental, quantitative, de-identified data on the regional deposition of aerosolized nasal medication in the form of nasal spray droplets in the sinonasal passages. for readers' convenience, table details the drug delivery numbers, processed from all the numerical runs; and the narrative, included under methods, elucidates the computational software settings for the airflow and droplet transport simulations. the datasets generated during and/or analysed 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healthy humans effect of obesity on ozone-induced changes in airway function, inflammation, and reactivity in adult females the authors declare no competing interests. correspondence and requests for materials should be addressed to s.b. publisher's note springer nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. license, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the creative commons license, and indicate if changes were made. the images or other third party material in this article are included in the article's creative commons license, unless indicated otherwise in a credit line to the material. if material is not included in the article's creative commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. to view a copy of this license, visit http://creativecommons.org/licenses/by/ . /. key: cord- -vll s xq authors: jones, huw as; salib, rami j; harries, philip g title: reducing aerosolised particles and droplet spread in endoscopic sinus surgery during covid‐ date: - - journal: laryngoscope doi: . /lary. sha: doc_id: cord_uid: vll s xq objectives: the presence of high sars‐cov‐ viral loads in the upper airway, including the potential for aerosolised transmission of viral particles, has generated significant concern amongst otolaryngologists worldwide, particularly those performing endoscopic sinus surgery (ess). we evaluated a simple negative pressure mask technique to reduce viral exposure. methods: two models simulating respiratory droplets > ‐ μm and fine respiratory nuclei < μm using fluorescein dye and wood smoke respectively were utilised in a fixed cadaveric study in a controlled environment. using ultra‐violet light, fluorescein droplet spread was assessed during simulated ess with powered microdebrider and powered drilling. wood smoke ejection was used to evaluate fine particulate escape from a negative pressure mask using digital subtraction image processing. results: the use of a negative pressure mask technique resulted in a % reduction in the fine particulate aerosol simulation, and eliminated larger respiratory droplet spread during simulated ess, including during external drill activation. conclusions: as global ent services resume routine elective operating, we demonstrate the potential use of a simple negative pressure mask technique to reduce the risk of viral exposure for the operator and theatre staff during ess. the severe acute respiratory syndrome coronavirus (sars-cov- ) responsible for the coronavirus disease was first reported in wuhan, china in december and has since a spread globally in a few short months . at the time of writing, it has claimed nearly , lives . thought to primarily spread via respiratory droplets from the upper respiratory tract , , the nose and throat have consistently reported high viral loads , . additionally, van doremalen et al demonstrated aerosolised sars-cov- remained viable for at least hours . the who defines respiratory droplets as particles > - µm, and respiratory nuclei < µm . although the primary route of spread is thought to be larger droplets, airborne transmission may be possible during procedures that generate large quantities of aerosolised viral particles . although evidence of transmission to health care workers via aerosolised virus is difficult to prove, and evidence of aerosol transmission still debatable , it would seem prudent for otolaryngologists to take steps to reduce exposure for theatre staff. [ ] [ ] [ ] concern has thus been raised regarding the safety of otolaryngologists and theatre staff performing surgery within the upper airway, particularly when using powered instrumentation. both ent-uk and the american academy of otolaryngology-head and neck surgery recommended restriction of aerosol generating procedures (agp) for this reason , . a few studies have sought to investigate this concern in a simulated setting and have demonstrated significant droplet spread during endoscopic sinus surgery, particularly when using powered drills , . there is therefore an urgent need to develop interventions in order to mitigate these risks. using simulations of both aerosols and larger droplets in a cadaveric model, this study investigates the potential for a simple negative pressure mask technique to reduce the risk of intra-operative aerosol and droplet exposure for theatre staff. this article is protected by copyright. all rights reserved. the fixed specimen used in this study had prior consent for research photography. formal ethical approval for this study was not required as no living specimens were used. two models were utilised: smoke to simulate fine particle aerosolization, and fluorescein staining to simulate respiratory droplet spread. the study was conducted in university hospital southampton's anatomy laboratory on the same cadaveric specimen. we utilised a modified endoscopy mask (vbm medizintechnik gmbh ref - - , unit cost £ ) originally designed for bronchoscopy, connected to a standard operating theatre suction unit operating at mmhg ( figure ). the membrane over the instrumentation port was widened to cm diameter allow the passage of a mm rigid endoscope and powered instruments). a wood smoker was used to generate high volumes of smoke expediently (sage bm ) utilising hickory wood chips. particle sizes produced during wood burning peak at . - . µm and thus simulated respiratory nuclei . the smoke was collected and siphoned into a bag-valve-mask respirator (bvm) (intersurgical uk). a size . endotracheal tube was inserted into the cadaver head's trachea in reverse and the cuff inflated. the mouth was occluded with gauze so that the only point of egress was the nose. the bvm bag was squeezed over seconds until empty. five scenarios were tested: ) a control with no mask, ) mask fitted without suction, ) mask fitted with suction, ) mask fitted with suction, and instrument valve removed, ) mask fitted with suction, instrument valve removed, and rigid endoscope in position. a digital camera with a cmos sensor of . megapixels yielded images of . x pixels during each scenario against a black background, with a noise reference image captured before each scenario. the images were processed in adobe photoshop . a threshold filter was applied to each reference image to eliminate background noise and create an image of only black or white pixels. the image sequence in each scenario was stacked, a threshold filter applied to the same level, and the reference image subtracted to remove any confounding noise. white pixels were counted using imagej (imagej.nih.gov). this article is protected by copyright. all rights reserved. to simulate intra-operative droplet spread, a litre solution of mg/ml fluorescein (alcon eye care uk ltd) was prepared. mls of this was instilled both into the nasal cavity, and via mini frontal trephines into the frontal sinuses. saturation was confirmed endoscopically using a blue filter . the remaining mls was used for microdebrider and drill irrigation. the cadaver was placed in a standard supine operating position and the anatomy lab set up as a simulated operating theatre. the cadaver was covered in a blue, washable, drape and illuminated with an ultra violet led strip (wavelength - nm). the drape was marked cm from the edge of the mask with tape for reference and was washed down between each scenario. a total of three scenarios were tested; ) endoscopic sinus surgery (ess) (uncinectomy, middle meatal antrostomy, anterior & posterior ethmoidectomy, sphenoidotomy) using powered suction mm microdebrider ( minute duration) with suction mask and repeated without, ) powered drilling of the frontal recess and beak using a rpm degree integrated suction cutting burr with suction mask and repeated without, ) drill activation outside cadaver, within the mask aperture for seconds with and without suction applied. all surgical simulations were performed by the same author (pgh). after each scenario the blue drape was inspected under uv light for droplet spread and photographed. in line with results from previous work by khoury , we demonstrated a significant emission of aerosolised particles without a mask. table summarises the white pixel count for the final subtraction image in each scenario. figure demonstrates the image processing involved, with figure depicting each subtraction image. scenario demonstrated a good mask seal with no visible leak around the edge of the mask. applying a suction circuit to the mask resulted in a % reduction in the white pixel count. removal of the instrument valve entirely did not result in elevated aerosolised particles. the image for scenario does demonstrate more smoke at the instrument valve aperture, but these particles were captured by the suction circuit and did not escape into the room. addition of an endoscope to the setup did not alter this. the residual white pixels in scenarios - were produced by motion artefact between image captures as evidenced by a fine white outline around the cadaver/mask. visual inspection of the images confirms no escaped particles. no fluorescein droplets were observed with or without the negative pressure mask during the simulation of powered microdebrider assisted ess. this comprised continuous microdebrider activation for minutes whilst performing uncinectomy, middle meatal antrostomy, anterior and posterior ethmoidectomy, and sphenoidotomy. external droplet spread was observed up to the cm mark during the powered drilling simulation, despite the use of a cutting burr with integrated suction (figure ) . however, when the procedure was repeated with the negative pressure mask, no contamination was observed. accidental external drill activation has been shown to cause gross contamination . in the authors' experience, this most commonly occurs in close proximity to the nares during instrument insertion/removal. to simulate this we this article is protected by copyright. all rights reserved. activated the drill external to the cadaver, but within the mask instrument aperture, both with and without negative pressure. significant contamination was observed within the mask, but none was evident externally. table summarises the results. this article is protected by copyright. all rights reserved. as our understanding of sars-cov- transmission evolves, adequate protection of hospital staff from both contracting the virus, and unwittingly acting as asymptomatic vectors, has become paramount. this is particularly so as the uk resumes elective ent services including aerosol generating endoscopic procedures. this proof of concept study demonstrates that a negative pressure mask can effectively reduce both fine droplet nuclei aerosol and larger droplet spread during endoscopic sinus surgery using powered instruments. additionally we suggest that sealing the mask around the instruments may not be necessary which vastly improves the surgeon's range of movement. the use of a mask with a soft face seal also allows for the accommodation of multiple face shapes without needing to manufacture individualised systems. in recent months, several studies have sought to evaluate droplet spread during endoscopic sinus surgery , , , [ ] [ ] [ ] [ ] , but this model is the first to examine the performance of a negative pressure mask with both respiratory droplet and droplet nuclei simulations. in the only other study to use a smoke simulation of droplet nuclei, khoury et al. used incense joss sticks to generate aerosol particles of diameter of . µm . they also demonstrated that their negative airway pressure respirator (napr) was able to prevent aerosol escape. however, their image analysis differed in that they selected one image two thirds of the way through their scenarios for threshold analysis. in an effort to capture all of the particles emitted over each scenario, we stacked all of the captured images to form a composite. this allowed for greater sensitivity and analysis for any leaks that would be potentially missed by assessing only a single time point. despite this we demonstrated effective capture of aerosolised particles with a similar mask provided a suction circuit was in use. workman et al demonstrated significant fluorescein droplet spread in ess, particularly when using powered drills on the sphenoid rostrum and frontal beak for second intervals . they did not demonstrate external spread with the powered microdebrider and our experience concords with this. in a similar cadaveric study, sharma et al. again showed droplet spread with powered drill use, but also up to cm using a microdebrider for minutes. gross this article is protected by copyright. all rights reserved. contamination up to cm was shown on external burr activation for seconds . we did not feel it necessary to repeat this scenario but were able to demonstrate that drill activation external to the nares, but within the mask instrument aperture, did not result in droplet spread beyond the confines of the mask, regardless of whether the suction circuit was activated. furthermore, helman et al. constructed a bespoke d printed mask using a cut surgical glove placed over the aperture as an instrument port, which successfully reduced fluorescein droplet spread by % when drilling in the anterior nasal cavity . depending on the size of the mask aperture, this study suggests that covering it may not be necessary as no smoke or fluorescein spread were observed when the instrument valve was removed. this study has some limitations. it proved difficult to fully eliminate camera movement in our setup during each smoke scenario resulting in minor motion artefact (manifest as a fine white outline around the cadaver/mask in the subtraction images). this could be reduced with more robust equipment. the mask tested was not sterile, although it could easily be sterilised pre-operatively. we only tested a minute period of powered instrument activation rather than a full duration ess. the smoke model did not allow for real time assessment of droplet nuclei generation during surgical instrumentation with the mask. repeating the experiment using an optical particle sizer would allow assessment of sub µm particles generated during ess, and as such analysis of mask effectiveness at preventing external spread. this article is protected by copyright. all rights reserved. as global elective otolaryngology services resume, managing the risk of aerosolised coronavirus is paramount. this study demonstrates the effectiveness of a simple negative pressure mask in reducing droplets and respiratory nuclei generated during endoscopic sinus surgery, thus reducing potential exposure for both operator and theatre staff. this article is protected by copyright. all rights reserved. a novel coronavirus from patients with pneumonia in china coronavirus disease an overview of their replication and pathogenesis modes of transmission of virus causing covid- : implications for ipc precaution recommendations viral load of sars-cov- in clinical samples. the lancet infectious diseases sars-cov- viral load in upper respiratory specimens of infected patients aerosol and surface stability of sars-cov- as compared with sars-cov- world health organization. natural ventilation for infection control in health-care settings aerosol generating procedures and infective risk to healthcare workers: sars-cov- -the limits of the evidence. the journal of hospital 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environments the authors wish to thank dr david walker & ellen adams of the centre for learning anatomical sciences at university of southampton for their support and specimen preparation. simon charters of the medical photography department at queen alexandra hospital, portsmouth photography dept for his post processing advice. richard towler, hospital sales director freelance surgical ltd for supplying the vbm mask samples. key: cord- -sd hbocg authors: felfeli, tina; batawi, hatim; aldrees, sultan; hatch, wendy; mandelcorn, efrem d. title: utility of patient face masks to limit droplet spread from simulated coughs at the slit lamp date: - - journal: can j ophthalmol doi: . /j.jcjo. . . sha: doc_id: cord_uid: sd hbocg nan with the accelerated spread of the severe acute respiratory syndrome coronavirus leading to coronavirus disease pandemic, there are unprecedented challenges on the medical community. of major concern are the high titres of virus in the oropharynx early in the disease course, and long incubation period ( À days) of asymptomatic shedding of severe acute respiratory syndrome coronavirus . effective use of personal protective equipment (ppe) such as gloves, face masks, goggles, face shields, and gowns is critical to prevent the spread of infection to and from health care workers and patients. this is particularly important to clinicians who work in close proximity with the patient's face such as when performing slit-lamp examinations. accordingly, the american academy of ophthalmology has recommended that patients not speak during slit-lamp examinations as well as the use of commercially available slit-lamp barriers or breath shields as an added measure of protection. however, breath shields may not fully eliminate the spread of droplets. the use of masks by patients has been shown to mitigate the emission of various viruses into the environment and is recommended by the centers for disease control and prevention. herein, we aimed to investigate how various scenarios of masks worn by patients can reduce the spread of respiratory droplets onto the examiner during a slit-lamp examination using a simulated patient cough. in a simulation, an ophthalmologist donned in standard ppe including a face mask and eye protection was positioned looking through the oculars of the slit lamp (bm haag-streit). the slit lamp had a commercially available breath shield hung on oculars measuring at . inches in width and . inches in height (carl zeiss meditec ag). a manikin (vera cardiopulmonary resuscitation model, canadian red cross) was placed at the chin rest of the slit lamp to simulate a patient under examination. to standardize the target distance, the slit lamp was focused on the manikin's right eye. a patient cough was simulated using a small latex balloon that was compressed with oxygen and . ml of washable fluorescent dye that was run through tubing inside the manikin and placed inside the oral cavity. the balloon was inflated until it burst at pound-force per square inch, which has been previously reported as the force for a voluntary cough and laryngeal cough reflex. the simulation was performed under ultraviolet light conditions (light-emitting diode nm ultraviolet flashlight, wjzxtek) in order to visualize emission of fluorescent small particles, which included a mixture of dry and wet particles measuring at À mm for varied particle-size distribution (uv neon fluorescent blacklight paint kit, paint glow). a video of the simulation that is slowed down by a factor of at frames per second is available online (video , available online). these methods have been previously validated for visualization of cough droplets. , the initial simulation was repeated for rounds, and subsequent series of simulations were repeated twice each to confirm consistency of observed findings. a multistep process including use of different colour dyes, thorough cleaning of equipment and manikin, as well as switching the examiner's ppe was done to ensure that no cross-contamination between each simulation interfered with the findings. in the next stage of this initiative, we aimed to identify means of further reducing the droplet spread by focusing on the use of masks for the patient under examination. repeat simulations were conducted with (i) one of the most readily available cloth masks (black cotton face mouth mask); (ii) an ear loop surgical mask (american society for testing materials level , m) positioned incorrectly (loose and covering the mouth only to mimic a commonly encountered circumstance); (iii) an ear loop surgical mask with proper positioning (american society for testing materials level , m); and (iv) an n mask (model , m, not fitted to the manikin). the spread of droplets onto the field of the examiner and the slit lamp was identified under ultraviolet light conditions in each simulation as described above. this simulation demonstrates that the use of slit-lamp breath shields and standard ppe for the examiner may reduce but does not eliminate the projection of droplets onto the examiner's field, chest, shoulders, and arms (fig. ) . the spread of smaller droplets was also identified on the bouffant cap, gloves, and shoes of the examiner. further contamination of the floor, walls, and window covers were identified within the room. in the simulation with a cloth mask, droplets were identified on gloves of the examiner, and on the slit lamp. an inspection of the inside of the mask demonstrated the spread of droplets beyond the outer borders of the mask on the superior, inferior, and lateral edges (fig. ) . in the simulation involving the improperly positioned surgical mask, droplets were identified on the shoulders, arms, and gloves of the examiner as well as the slit lamp, floor, and walls. with the surgical mask properly positioned, the examiner was clear of droplets; however, some droplets were noted on the side bars close to the chin rest of the slit lamp. no droplets were identified on the examiner or the slit lamp in the repeat simulation with the use of the n mask. a view of the inside of the mask also revealed that droplets were contained within the mask. this simulation aimed to visualize the spread of respiratory droplets onto the examiner at the slit lamp. our findings suggest that the use of a properly fitted mask on the patient as an adjunct to the current standard ppe used by the examiner, and the breath shield is essential for limiting droplet dissemination during slit-lamp examinations. cloth masks decrease the spread of respiratory droplets onto the examiner and can be even more effective than a surgical mask that is worn incorrectly. however, spread of some droplets was noted on the hands of the examiner during the slit-lamp examination with cloth masks. this may be owing to the poor design and poor flexibility of the material used to make cloth masks, which can lead to gaps through which respiratory droplets can disseminate easily. if worn correctly, surgical masks greatly reduce the spread of droplets onto the examiner. although shown to be effective in this simulation, the current limited resources q x x of n masks that have not been professionally fitted, for routine clinical encounters is not supported. these findings are consistent with other studies that have demonstrated reduced droplet transmission when wearing a face mask. in addition to decreasing the spread of droplets, surgical masks worn by patients have been found to decrease the emission of different viruses into the environment, including influenza virus and coronavirus. it is important to note that this simulation does not identify the spread of very small particles and droplets. although the bursting pressure for the balloon was adjusted to simulate a voluntary cough, the volume of the cough was overproduced beyond what would be expected in a natural cough in order to account for the potential extent and multidirectional spread of a true cough in various scenarios under one simulated setting. no means of accounting for turbulence of mucosalivary filaments in a simulated cough have been previously reported and thus were not accounted for in this simulation. given that the goal of this simulation was to provide effective means of protecting the examiner, we did not assess the spread of droplets beyond the slit lamp and the examiner with the use of various masks. furthermore, some variations may be noted in repeat simulations. lastly, appropriate ppe for the examiner should be selected on a case-by-case basis for patients who are low risk, suspect, or confirmed positive for coronavirus disease and based on the recommendation of the local health authority. overall, this simulation demonstrates the potential spread of droplets during a slit-lamp examination from a patient cough onto the examiner, equipment, and room. based on this, our recommendations for the use of masks for patients include the following: (i) patients should wear a mask during slit-lamp examinations (including a well-fitted cloth mask if it is the only available option); (ii) correct positioning of the mask is critical, and an improperly fitted mask may provide a false reassurance of protection; (iii) slit lamps should be disinfected between patients to prevent cross-contamination. conflict of interest: no conflicting relationship exists for any author. supplementary material associated with this article can be found in the online version at doi: . /j. jcjo. . . . x x each of the masks used in repeat simulations, spread of droplets, and droplets within the inside of the masks visualized with ultraviolet light. with the properly positioned cloth mask (a ), the examiner had spread of droplets onto gloves (a ). droplets spread beyond the outer borders of the mask (a ). with the improperly positioned surgical mask (b ), the examiner had droplets on the gloves, arm, chest, and shoulders (b ). droplets spread beyond the outer borders of the mask (b ). with a properly positioned surgical mask (c ), the examiner was clear of droplets, but droplets were detected on the side bar of the slit lamp (c ). no droplets spread beyond the outer borders of the mask (c ). with a properly positioned n mask (d ), no droplets were detected on examiner or the slit lamp (d ). no droplets spread beyond the outer borders of the mask (d ). early transmission dynamics in wuhan, china, of novel coronavirusÀinfected pneumonia efficacy of slit lamp breath shields respiratory virus shedding in exhaled breath and efficacy of face masks intra-abdominal pressures during voluntary and reflex cough cough aerosol in healthy participants: fundamental knowledge to optimize droplet-spread infectious respiratory disease management coughing and aerosols barrier enclosure during endotracheal intubation visualizing speech-generated oral fluid droplets with laser light scattering footnotes and disclosure quality improvement grant, department of ophthalmology and vision sciences key: cord- - yug jjx authors: dbouk, talib; drikakis, dimitris title: on coughing and airborne droplet transmission to humans date: - - journal: phys fluids ( ) doi: . / . sha: doc_id: cord_uid: yug jjx our understanding of the mechanisms of airborne transmission of viruses is incomplete. this paper employs computational multiphase fluid dynamics and heat transfer to investigate transport, dispersion, and evaporation of saliva particles arising from a human cough. an ejection process of saliva droplets in air was applied to mimic the real event of a human cough. we employ an advanced three-dimensional model based on fully coupled eulerian–lagrangian techniques that take into account the relative humidity, turbulent dispersion forces, droplet phase-change, evaporation, and breakup in addition to the droplet–droplet and droplet–air interactions. we computationally investigate the effect of wind speed on social distancing. for a mild human cough in air at °c and % relative humidity, we found that human saliva-disease-carrier droplets may travel up to unexpected considerable distances depending on the wind speed. when the wind speed was approximately zero, the saliva droplets did not travel m, which is within the social distancing recommendations. however, at wind speeds varying from km/h to km/h, we found that the saliva droplets can travel up to m with a decrease in the concentration and liquid droplet size in the wind direction. our findings imply that considering the environmental conditions, the m social distance may not be sufficient. further research is required to quantify the influence of parameters such as the environment’s relative humidity and temperature among others. the recent covid- pandemic prompted the need for deeper understanding of the transport of fluids and particles emanating from our respiratory tracts when we cough, sneeze, speak, or breathe. the particles' transport will influence the spread of coronavirus and determine the implementation of guidelines on social distancing, mask wearing, crowded gatherings, as well as everyday practices of social behavior in private, public, and business environments. when sneezing or coughing, larger droplets are formed by saliva and smaller droplets by the mucous coating of the lungs and vocal cords. the smaller droplets are often invisible to the naked eye. past research has shown that most respiratory droplets do not travel independently on their trajectories. instead, droplets in a continuum of sizes are trapped and carried forward within a moist, warm, turbulent cloud of gas. in another study, it was shown that as people raise their voice, they emit more droplets, but the size distribution of the droplets remains the same. furthermore, researchers have shown that even breathing could release potentially infectious aerosols. they have captured the large droplets produced when sneezing and coughing as well as the aerosol droplets produced when sneezing, coughing, breathing, and talking on different surfaces. yan et al. showed that the flu virus exists even in the tiny droplets resulting from breathing or talking alone. although the mechanisms of transmission are still under debate, it is widely accepted that aerosol or respiratory droplet transmission is the critical factor for the rapid spread and continued circulation of influenza a virus in humans. the national academies standing committee on emerging infectious diseases and st century health threats has considered whether the sars-cov- virus could be spread through conversation, in addition to the transmission due to sneeze/cough droplets. as beans reported, the team determined that the current evidence supports the possibility that sars-cov- could spread through aerosolized droplets released via patients' exhalations. however, scitation.org/journal/phf they noted that they cannot yet confirm whether the coronavirus identified in air samples is viable and capable of infecting through the above process. we think that it is likely that the dosage and time of exposure would also determine whether or not infection will finally occur. therefore, it is crucial to decide on the scenarios that will allow the transmission to longer distances. according to pan et al., experimental air sampling technologies that can detect the presence of viruses and determine their distribution in aerosol particles have many limitations and are not accurate enough, e.g., low collection efficiencies. here, we aim at advancing the understanding of the transfer of airborne particle carriers to humans through flow modeling and simulation. the initial modeling configuration of the problem takes into account several parameters that can influence the simulation, including the wind speed in an open environment. an accurate prediction of the transfer of airborne particle carriers to humans from a cough is governed by the following modeling considerations that must be taken into account: . the saliva droplet's initial size distribution at the onset of the coughing event. . the human mouth-print of the cough. . the period of the cough and its intensity (or initial saliva droplet speed). . the numerical modeling approach to capture the complex varying space and time scales, e.g., both heat and mass transfer considerations, modeling of mass and phase changes due to droplet evaporation, coalescence, breakup, and turbulent dispersion in interaction with the bulk flow field. xie et al. conducted experimental measurements and quantified exhaled droplet's mass and size due to talking and coughing. moreover, they corrected the droplet's size distribution near the origin of the ejection, which was underestimated in previous studies. , this correction was conducted based on droplet's dispersion analysis because larger droplets are dispersed into smaller ones gradually while moving away from the mouth jet origin. the size distribution adopted by the authors is shown in fig. . it corresponds to a fit law for the data obtained by ref. , fitted by the rosin-rammler distribution law, also known as weibull distribution. the weibull distribution works well for distributing cloud droplets, including water and water-like droplets. the theoretical background can be found. figure (red curve) shows the weibull's law of probability density function f. the fitting parameters are given by f = n dp ⎛ ⎝ dp dp where dp is the droplet diameter. during a human cough, the mouth-print can take different shapes and sizes depending on each individual's morphology that varies from one person to another. previous studies in the literature simplified the mouth form or shape by assigning a general hydraulic diameter. however, accurate mouth-print quantification is a critical task to capture the transport of the airborne droplet virus carriers accurately. figure illustrates an experimental measurement for a human cough captured via a high-speed camera over . s. one can observe that the maximum human mouth opening at . s has a rectangular-like mouth-print with an aspect ratio of lm/hm = . with lm ≈ cm. the curved form of the mouth-print from fig. is used to create a digital mouth-print model for the saliva droplet injector in order to mimic the real droplet ejection during a human cough. we developed a d computational domain and show a d section in fig. . we generated a mesh comprising hexahedral non-uniform structured elements or cells (≈ . × ). the mesh was well refined at the mouth-print and then gradually coarsened in the streamwise cough flow direction at a multilevel of refinement. the choice of this grid has been taken after conducting a grid convergence study on main local and global flow parameters, e.g., u f and p, following a grid convergence index strategy proposed by celik et al. according to van der reijden et al., saliva could have a negligible dependence on the shear rate, and its viscosity could be close to that of water. however, saliva is, in general, a complex fluid because it depends on each individual and may vary from smokers to nonsmokers and diabetic people. here, we have considered saliva to be a newtonian fluid. we applied a time-varying velocity inlet with particle injection at the mouth boundary to mimic the human cough over . s (fig. ) . the velocity applied at the mouth for . s is ux = . m/s, as measured by scharfman et al. using the mouth hydraulic diameter and the above velocity, the reynolds number is re = . note that if the reynolds number is recalculated using the mouth height, it gives re = , which is similar to the experimental reynolds value of of scharfman et al., where the flow is reported as a turbulent flow. we applied an outlet pressure boundary condition at the outlet (y-z plane at x = l). a no-slip wall boundary condition with wall-functions for the turbulent boundary layer was applied at the ground level (x-y plane at z = ). we treated the remaining boundaries as infinite domain boundaries. for non-zero wind speed cases at t > . s, we applied a constant uniform freestream velocity in the cough flow direction along the x-axis. we investigated three wind speed cases: ≈ km/h, km/h, and km/h. the domain length was l = m for wind speeds ≈ km/h and km/h. we applied a longer domain of l = m for the highest wind speed at km/h. we considered an environment of ○ c for the carrier fluid, % relative humidity, ○ c at the ground, and ○ c for the human mouth. the height from the ground (at z = ) to the mouth is . m corresponding to real human dimensions, with a total h = m and w = m. the initial total mass of the injected saliva into the domain is . mg with droplets. these values are of the same order of magnitude as those reported in the literature by zhu et al. and xie et al. three different phases were initially considered inside the carrier multiphase fluid mixture: ( ) dry air, ( ) water vapor, and ( ) liquid water. the initial mass fraction or phase-type composition of the bulk fluid is imposed as . -air, . -water-vapor, and -liquidwater. these mass fractions correspond to % relative humidity at ambient ○ c and atm. the mass fraction or phase-type of the droplets, ejected from the mouth, is considered as -liquid-water corresponding to pure liquid water-like saliva droplets. for the carrier bulk multiphase fluid mixture, we have employed the compressible multiphase mixture reynolds-averaged navier-stokes equations in conjunction with the k − ω turbulence model in the shear-stress-transport formulation. the governing equations are detailed in many textbooks. , respiratory droplets will interact with the airflow and also the ambient airflow. droplet size and properties will influence the simulation. we know that droplets will become droplet nuclei during their dispersion and that evaporation and turbulence affect the dispersion distance. previous studies also suggested that the size distribution and travel distances of droplet nuclei can significantly influence infection risk indoor. liu et al. showed that the droplet nuclei size, at a relative humidity of % ( ○ c), could be % larger than the same droplet at a relative humidity of less than . % ( ○ c). turbulence also influences the trajectories of respiratory droplets and their wide dispersion. liu et al. found that humidity influences more medium-sized droplets ( μm) than smaller and larger droplets. larger, heavier droplets (> μm) will leave the respiratory jet faster. the size of droplets also varies during the evaporation and dispersion processes. wells' classic study of airborne transmission identified the difference between disease transmission via large droplets and by airborne routes. he suggested that under normal air conditions, droplets smaller than μm in diameter would completely dry out before falling ∼ m to the ground. the who has used wells' finding to establish the theory of droplets and droplet nuclei transmission depending on the size of the infecting droplet. for the nusselt and sherwood numbers, we use the ranz-marshall model, , which we will also use to calculate the reynolds number modification to the quiescent evaporation rate. the subject of droplet evaporation is far from being well understood. nonequilibrium effects become significant for initial droplet diameter scitation.org/journal/phf less than μm, and the models based on the langmuir-knudsen law provide results in closer agreement with the experiments. past studies have shown that detailed knowledge on the breakup of droplets is not required when applying the modified concept of a maximum stable diameter, which estimates the size of the most abundant stable fragments. droplet acceleration is taken into account. the median mass droplet can be estimated from empirical observations that the median mass size is one-half the largest stable size particle. the above approach links together the weber number, total breakup time, and velocity correlations for the accelerating cloud droplet. other essential considerations concern the magnitude of the computational time step, mainly when it is significantly larger than the turbulence correlation time. here, we use o'rourke's approach that involves choosing random velocity and position changes for each droplet from probability distributions that we derive for the turbulent droplet velocity and position changes. we treated the saliva droplets as lagrangian particles such that each droplet is tracked individually throughout the computational domain. for each droplet, we solve differential equation, which describes the evolution of its mass, velocity, temperature, and position. the evolution of the mass droplet is used to calculate the mass source terms of the mixture-components in the bulk carrier fluid phase and to update its pressure equation accordingly. the droplet momentum equation is used to calculate the forces exerted by the particles on the carrier phase required in the momentum equation for the fluid. the evolution of droplet mass mp (of diameter dp) is described by the following conservation equation: in which t is time. sh, sc, τp = ρpd p /( μ), and ξm are the sherwood number, the schmidt number, the particle relaxation time, and the potential function driving the evaporation, respectively; ρp is the particle's density and μ is the dynamic viscosity of the carrier phase. the sherwood number describes the ratio of the convective mass transfer to the mass transfer due to diffusion. the schmidt number represents the ratio between viscous and mass diffusion rates. as mentioned above, the heat transfer droplet model by ranz and marshall , was applied to the evolution of the mass of a single saliva liquid droplet due to evaporation. it describes the heat transfer coefficient as an empirically derived correlation as a function of the nusselt number nu with the diameter droplet dp. moreover, the liquid droplet breakup model by pilch and erdman was applied to predict the droplet's size, and thus, the acceleration induced by the breakup depends on the weber number we. the latter describes the ratio between the carrier fluid inertia forces and the droplet's surface tension forces. the evolution of the droplet's velocity is computed by applying newton's second law of motion, where up is the droplet's velocity and fp(up, u f ) are the forces acting on the droplet (as a function of the droplet velocity up and also the carrier fluid velocity u f interpolated at the droplet position). b represents the external force of gravity. the evolution of the droplet's temperature is obtained by solving the following energy equation based on the enthalpy difference hp: where ap is the droplet's surface area. from the above energy equation, hp evolves over time and is the sum of heat transfer due to convection qconv. and radiation q abs. (gained from the surrounding to the particle), minus the heat transfer emitted as radiation qemm. or losses. the enthalpy equation can be expressed as a function of the particle temperature tp such that where cp is the droplet's specific heat capacity. note that all thermophysical properties (density, heat capacity, viscosity, etc.), for both the carrier fluid and the droplets phases, are temperature-dependent. the carrier fluid is modeled as an ideal gas for its equation of state, and its transport is modeled using sutherland's law for its viscosity based on the kinetic theory of gases, which is suitable for non-reacting gases. the open-source computational fluid dynamics (cfd) code "openfoam" was employed to solve all partial differential equations. we have used the finite volume method to discretize the carrier fluid phase. we applied second-order schemes for both time and space operators. the droplet's lagrangian phase equations were discretized employing semi-implicit numerical schemes at second order. the total computation time of a single case was about . days, run in parallel over intel-xeon processors of ghz frequency. the predicted saliva droplet kinematics at the early period of ejection from a human cough are illustrated in fig. from ms to ms. we observe that during the applied ejection period of ms (fig. ) , the carrier fluid flow is at the maximum velocity of . m/s, which drops down gradually after closure of the mouth. a linear jet profile occurs near the mouth, which then breaks down slowly away from the mouth. in this short time at t > ms, a cloud of saliva droplets is entertained inside (or carried by) the carrier fluid cloud for a short period after closure, which can be explained by the retained momentum of the droplet. at longer times, the cloud settles gradually at different rates accompanied by both dispersion and evaporation. at ms, the shape of the cloud and the cm maximum distance found for a droplet (horizontally away from the mouth) are of similar order of magnitude compared to previous results. during a human cough, fig. shows the kinematics of the saliva droplets between ms and ms accompanied by droplet sizes between ≈ μm and μm. the temperature saliva droplet is illustrated in fig. , showing hot droplets near the mouth that are cooled to lower temperature away from the mouth. this is due to a lower temperature of the surroundings at ○ c. according to several governments, strict recommendations were made for people to keep a distance of at least feet ( m). the saliva droplet cloud kinematics show the diameter of the droplets resulting from a human cough. larger droplets settle more rapidly than smaller ones due to gravitational forces. wind speed ≈ . the total mass of ejected saliva is . mg, with total number of droplets. the environment is at ambient temperature, pressure, and relative humidity of ○ c, atm, and %, respectively, with the ground temperature at ○ c. saliva droplet cloud kinematics show the diameter droplet resulting from a human cough. larger droplets settle more rapidly than smaller ones due to gravity. wind speed ≈ = . the total mass of ejected saliva is . mg, with total number of droplets. the environment is at ambient temperature, pressure, and relative humidity of ○ c, atm, and % with the ground temperature at ○ c. above advice was announced to the public as a safe social distancing to prevent airborne disease transmission (such as covid- ) from one person to another. this study shows m is a safe approximate distance in the case where there is no wind, i.e., at wind speed ≈ km/h, at ○ c, relative humidity of %, and a ground surface temperature of ○ c (fig. ) . the ground surface temperature (gst) of ○ c is somehow arbitrary because, in winter/spring season, the ground surface temperature is lower than the air temperature and the opposite in the summer/autumn season. therefore, we considered gst = tair − ○ c. however, the ○ c may vary from region to region and also depends on the soil properties. we aimed to approximate as much as possible a real situation in winter/spring seasons. further investigation is required to quantify the effects of gst, as well as relative humidity and ambient air temperature. figure shows the evolution of human saliva droplets, taking into account the dispersion, evaporation, breakup, and droplet settling. after s, all droplets did not exceed a horizontal distance of m away from the mouth. at the time of s, some droplets appear at . m above the ground. at the time of s, one can witness the circulation of the droplet cloud, which can be explained by its closeness to the body that plays the role of a stationary wall of no-slip like the ground surface. also critical is that the droplets take about s to fall below the human waist level, which is considered as a safe vertical distance. in the case of no wind, young children will be most vulnerable in the close vicinity of the falling droplet cloud. at km/h wind speed blowing from left to right in the direction of the human cough [see fig. (a) ], the saliva liquid droplets can travel up to m away from the mouth in a period of s. the . a human cough: saliva droplet's disease-carrier particles cannot travel more than m in space at approximately zero wind speed. the environment is at ambient temperature, pressure, and relative humidity of ○ c, atm, and %, respectively, with the ground temperature at ○ c and mouth temperature at ○ c. saliva droplets fly as a cloud of droplets sheared by the wind, which causes the cloud deformation under the turbulent dispersion forces. complex phase change and transport phenomena such as evaporation and droplet breakup occur at different rates depending on the environmental conditions and on the intensity of the cough. after s from the occurrence of cough, the droplet cloud loses mass, and minimum size reduces progressively until total disappearance at a critical time > s. figure (a) enlightens another interesting phenomenon, which is the vertical stretching of the droplet cloud while moving away from the mouth where some droplets nearly reach the ground at about t = s. moreover, at this low wind speed, we observe that the saliva droplet cloud remained below the horizontal line situated . m below the mouth. at the same environmental conditions, but with the wind speed increasing from ≈ km/h to ≈ km/h, we observe a different saliva droplet kinematics [ fig. (b) ]. under this wind speed of km/h, the saliva droplets move away faster and reach m in . s with an accelerating dispersion rate. similarly, evaporation is accompanied by mass reduction in the saliva droplets, which we will discuss quantitatively in sec. iii c. additionally, at a speed of km/h, we observe that the droplet cloud is sheared and stretched along an axis, making an angle of about ○ with the horizontal line situated at . m height. the results for km/h reveal that saliva droplets exist above . m height due to dispersion for all times between approximately . s and . s. the droplet cloud [figs. (a) and (b)] will affect both adults and children of different heights. the . m assumption leaves shorter adults and children at even higher risk. we have also examined the kinematics of airborne diseasecarrier saliva droplets (fig. ). different saliva droplet cloud kinematics may occur at different rates such as elongation, drifting, and rotation. the cloud kinematics is very complex and has several driving forces, which are the wind shearing rate, gravitational acceleration, turbulent dispersion, interaction forces manifested by breakup or coalescence, and stress forces manifested by a droplet's phase change or evaporation. at a low wind speed of km/h [ fig. (a) ], the saliva droplet cloud is advected in the wind direction with an increase in anticlockwise rotation between . s and s. however, at a higher wind speed of km/h [ fig. (b) ], the saliva droplet cloud is advected in the wind direction with an increase in clockwise rotation between . s and . s and a ○ angle with the horizontal line at z = . . the above transport evolution is explained by a reversal of the competition between some of the force ratios, e.g., wind shearing, dispersion, and settling forces. a detailed study of droplet kinematics is underway but is beyond the scope of the present study. we have examined the saliva droplet diameter, which represents % of droplets being smaller than their corresponding initial size, d in fig. . for all environmental conditions including different wind speeds, the d saliva droplet diameter decreases with time but at different rates with all values varying between μm and μm. as the wind speed increases from ≈ km/h to km/h, faster and smaller d occurs. of course, at higher wind speeds, the the environment is at ambient temperature, pressure, and relative humidity of ○ c, atm, and %, respectively, with the ground temperature at ○ c. curve of d might disappear at a certain time because the droplet cloud has reached the outlet of the existing computational domain that is m long along the cough flow direction. the evaporation process mainly causes the reduction in the d saliva droplet diameter but is also accompanied by droplet breakup and coalescence that may occur at different rates and as a function of the wind shearing intensity and the turbulent dispersion force. nevertheless, the quantification of d does not constitute a critical parameter in terms of airborne virus disease transmission compared to the maximum saliva droplet size. bigger droplets may carry smaller virus particles and thus constitute more danger or risk in terms of airborne disease transmission between humans. thus, the maximum saliva droplet diameter was quantified and plotted in fig. as a function of time. the maximum saliva droplet diameter dmax decreased with time from μm to μm at different rates. as the wind speed increases, the dmax reduction is observed to be faster. the latter effect is due to the higher shear rate of the wind, which accelerates droplet evaporation. another important quantifying factor is the liquid penetration distance (fig. ) . it describes the maximum distance traveled by a saliva liquid droplet made of % initial mass. from s to s, at a wind speed of km/h, the saliva droplets do not exceed the safe social distancing of m. however, at higher speeds of km/h and km/h, the droplet penetration distance reaches m in about . s and . s, respectively. we have also examined the total percentage of saliva droplet's mass reduction with reference to the initial mass of . mg saliva ejected from the human cough (fig. ). at km/h, the total mass this study shows that, when a person coughs, the wind speed in an open space environment significantly influences the distance that airborne disease-carrier droplets travel. . without the surrounding wind speed, the droplets will fall to the ground in a short distance from the person exhaling or coughing. the present analysis shows that the range may not exceed m. a tiny number of particles may travel slightly further longer. still, their trajectory beyond m will already be at a height significantly below half a meter dropping toward the ground. thus, these droplets may not constitute a risk regarding facial contact of adults at this distance. . at wind speeds from km/h to km/h, we found that saliva droplets can travel to distances up to m with a decrease in concentrations and liquid droplet size in the wind direction. our findings imply that depending on the environmental conditions, the m social distance may not suffice. further research is required to quantify the influence of other parameters such as the environment relative humidity and temperature among others. . the droplet cloud will affect both adults and children of different heights. shorter adults and children could be at higher risk if they are located within the trajectory of falling droplets. . at a lower wind speed, the total mass reduction occurs more slowly compared to a higher speed, which may prolong the exposure of a human to the droplets if the subject is located within the droplet's envelope. overall, the results show that in open spaces, airborne droplet carriers can travel significantly further than the m recommended distance due to the wind speed. several areas need further investigation to examine the impact of the above findings: • a recent letter discussed the covid- outbreak associated with air conditioning in a restaurant in guangzhou, china. therefore, it would be worth mentioning generalizing the current analysis to an indoor setting. • we need to understand the droplet evaporation more deeply, especially at different environmental conditions. • we should also carry out further research to determine the droplet size at the origin. droplet evaporation depends on the time it takes for the droplet to travel from the mouth to a particular position. • the violent cough of patients with respiratory diseases will affect droplet generation and secretions of fluids on airway surfaces and heighten coughing frequency. these factors need to be further quantified. • further research is also required to assess the probability of viral transmission vs droplet. this study shows that the droplet concentration can be significant up to considerable distances from the origin of the cough. the issues arising from the past and the recent pandemic require a holistic approach to elucidate the open scientific questions and address the practical challenges. such an approach would require closer interaction between bio-medicine, engineering fluid physics, and social sciences. see the supplementary material for the airborne droplet transmission at different wind speeds. turbulent gas clouds and respiratory pathogen emissions aerosol emission and superemission during human speech increase with voice loudness infectious virus in exhaled breath of symptomatic seasonal influenza cases from a college community influenza a viruses are transmitted via the air from the nasal respiratory epithelium of ferrets rapid expert consultation on sars-cov- viral shedding and antibody response for the covid- pandemic fluid dynamics work hints at whether spoken word can spread covid- collection, particle sizing and detection of airborne viruses exhaled droplets due to talking and coughing the numbers and the sites of origin of the droplets expelled during expiratory activities the size and the duration of air-carriage of respiratory droplets and droplet-nuclei the laws governing the fineness of powdered coal a statistical distribution function of wide applicability on the size distribution of cloud droplets the weibull distribution visualization of sneeze ejecta: steps of fluid fragmentation leading to respiratory droplets procedure for estimation and reporting of uncertainty due to discretization in cfd applications shear rate dependent viscoelastic behavior of human glandular salivas study on transport characteristics of saliva droplets produced by coughing in a calm indoor environment two-equation eddy-viscosity turbulence models for engineering applications computational techniques for multi-phase flows high-resolution methods for incompressible and low-speed flows how far droplets can move in indoor environments-revising the wells evaporation-falling curve evaporation and dispersion of respiratory droplets from coughing on air-borne infection: study ii. droplets and droplet nuclei natural ventilation for infection control in health-care settings evaporation from drops. part i evaporation from drops. part ii evaluation of equilibrium and nonequilibrium evaporation models for many-droplet gas-liquid flow simulations use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop statistical properties and numerical implementation of a model for droplet dispersion in a turbulent gas the viscosity of gases and molecular force openfoam: open source cfd in research and industry the finite volume method in computational fluid dynamics: an advanced introduction with openfoam and matlab images in clinical medicine: a sneeze assessment of differences between near-surface air and soil temperatures for reliable detection of highlatitude freeze and thaw states evaporation and drying kinetics of water-nacl droplets via acoustic levitation covid- outbreak associated with air conditioning in restaurant the size distribution of droplets in the exhaled breath of healthy human subjects the authors wish to thank the editor-in-chief and physics of fluids staff for their assistance during the peer-review and publication of the manuscript. the data that support the findings of this study are available on request from the authors. key: cord- - ywu r t authors: sharma, dhruv; rubel, kolin e.; ye, michael j.; campiti, vincent j.; carroll, aaron e.; ting, jonathan y.; illing, elisa a.; burgin, sarah j. title: cadaveric simulation of otologic procedures: an analysis of droplet splatter patterns during the covid- pandemic date: - - journal: otolaryngol head neck surg doi: . / sha: doc_id: cord_uid: ywu r t objective: the otolaryngology community has significant concerns regarding the spread of sars-cov- through droplet contamination and viral aerosolization during head and neck examinations and procedures. the objective of this study was to investigate the droplet and splatter contamination from common otologic procedures. study design: cadaver simulation series. setting: dedicated surgical laboratory. methods: two cadaver heads were prepped via bilateral middle cranial fossa approaches to the tegmen (n = ). fluorescein was instilled through a -mm burr hole drilled into the middle cranial fossa floor, and presence in the middle ear was confirmed via microscopic ear examination. myringotomy with ventilation tube placement and mastoidectomy were performed, and the distribution and distance of resulting droplet splatter patterns were systematically evaluated. results: there were no fluorescein droplets or splatter contamination observed in the measured surgical field in any direction after myringotomy and insertion of ventilation tube. gross contamination from the surgical site to ft was noted after complete mastoidectomy, though, when performed in standard fashion. conclusion: our results show that there is no droplet generation during myringotomy with ventilation tube placement in an operating room setting. mastoidectomy, however, showed gross contamination to ft away in all directions measured. additionally, there was significantly more droplet and splatter generation to the left of the surgeon when measured at and ft as compared with all other measured directions. t he current global pandemic brought about by the novel coronavirus disease (covid- ) has led to sweeping transformative change in the health care sector. us hospitals have essentially ceased all elective, nonurgent surgical cases in accordance with guidelines from the centers for disease control and prevention, and much uncertainty remains on how to resume safely. in the current climate, the safety of otolaryngology procedures is of particular concern, as current evidence suggests elevated risk due to close contact with upper respiratory mucosa, which harbors a high viral load. [ ] [ ] [ ] viral transmission is thought to be primarily via respiratory droplets, which can travel . m and linger on contaminated surfaces for hours, if not days. this has led to significant concern for the transmission of the novel coronavirus due to aerosol-generating procedures. as a result, the american academy of otolaryngology-head and neck surgery has issued a position statement to limit elective procedures requiring interaction with upper airway mucosal surfaces or those with increased risk of aerosolization, which may include otologic procedures such as myringotomy and mastoidectomy. , however, to our knowledge, no published literature exists to guide decision making on the safety of these common otologic procedures. this is an important area of investigation due to the potential for the middle ear and mastoid to harbor respiratory pathogens and for droplet dispersion and aerosol generation with use of high-speed drills. this study seeks to investigate and clarify these risks by evaluating droplet dispersion patterns resulting from otologic procedures in a cadaver-simulated series. the study was exempt from institutional review board because it involved the use of nonliving human cadaveric tissue specimens (irb protocol ) . the experiments in this study were all conducted in a dedicated surgical laboratory on fresh-frozen cadaver head specimens prepared in identical fashion and placed in a standard position for the procedures. with the following technique, a middle cranial fossa (mcf) approach was performed bilaterally on both specimens to expose the floor of the mcf. a posteriorly based trapdoor incision approximately cm was made superior to the auricle down to the calvarium, and then a cm bone flap, centered above the temporal root of the zygoma, was fashioned with a -mm cutting burr. after the mcf floor was completely exposed, a -mm port was drilled into the middle ear through the tegmen. fluorescein solution at a concentration of mg/ml was created by mixing mg of fluorescein ( % [ mg/ml], fluorescein injection, usp; ak-fluor) with ml of sterile saline. the mg/ml fluorescein solution was instilled with a -gauge angiocath through the port into the middle ear space ( figure a) . the presence of fluorescein in the middle ear space was confirmed endoscopically by visualization through the external auditory canal ( figure b ). the following surgical procedures were performed systematically on each head: ( ) left-sided myringotomy with insertion of a ventilation tube; ( ) left-sided complete mastoidectomy, including entry into the mastoid antrum and exposure of the tegmen, sigmoid sinus, and lateral semicircular canal; ( ) right-sided myringotomy with insertion of a ventilation tube; and ( ) right-sided complete mastoidectomy. a stryker s pdrive drill with a -mm multi flute burr was utilized for each mastoidectomy procedure. table summarizes the procedures that were performed on the cadaver heads and the duration. following each surgical procedure, the number and distance of the droplets and splatter on the nonabsorbent blue paper was evaluated and measured by the following technique. transparent grid graphs ( cm) were laid sideby-side at , , and ft from the surgical site. the blue paper on the surgeon's chest was removed and laid flat, and a grid was placed on it as well. the surgeon's face shield was removed and laid flat, and blue paper with an overlying grid was placed underneath it. since fluorescein fluoresces yellow under ultraviolet light and blue paper does not, the evaluators used an ultraviolet light to visualize the droplets and splatter from each experimental condition. the evaluators then counted and recorded the number and distance of any -cm area containing any illuminated fluorescent spot or any gross contamination. fluorescein did not penetrate the bone but was limited to the mucosa. no observable fluorescein droplets were noted in the measured surgical field in any direction after myringotomy and insertion of ventilation tube. visible fluorescein contamination was noted only on surfaces in direct contact with surgical instruments. in contrast, gross contamination was measured ft in all cardinal directions after every mastoidectomy. the number of droplets identified at and ft to the left of the surgeon was significantly greater than the number on the right of the surgeon or across from the surgeon. the right side of the surgeon had significantly more splatter and droplets than across at ft ( table ) . after each mastoidectomy, the surgical field within in, the hands and arms, the face shield, and the chest were grossly contaminated by droplets and splatter. covid- has rapidly disseminated from the hubei province of china across the globe, with over million confirmed cases in countries as of april , . the primary mode of viral transmission of sars-cov- is believed to be through the spread of respiratory droplets, which has led to significant community spread of the disease. the potential for spread through opportunistic aerosolization during aerosol generation procedures is also a concern. since the upper respiratory tract harbors a high viral load, otolaryngologists are vulnerable to sars-cov- transmission while performing head and neck procedures that utilize suction and powered instrumentation, such as the surgical drill, especially if they are doing so without appropriate protective personal equipment. with its connection to the nasopharynx through the eustachian tube, the middle ear can serve as a possible source of transmission for upper respiratory tract pathogens during routine otologic procedures, such as myringotomy and mastoidectomy. with the persistence of sars-cov- in the general population for the foreseeable future, we will need to navigate these risks as we resume elective surgical procedures and perform urgent operations on patients whose sars-cov- status is unknown or positive. in conducting this cadaveric simulation study, we confirmed that performing a myringotomy with insertion of ventilation tube caused no droplet or splatter contamination. the potential for aerosolization remains, however, when suction is used across a mucosal surface. in contrast, a complete mastoidectomy performed in standard fashion resulted in gross contamination up to ft from the surgical site, which was the farthest distance measured. aerosol generation with surgical drills has been established in the orthopedic literature. this is likely secondary to the nature of the operation, which involves high-speed drilling of the temporal bone under irrigation creating visible splatter from bone dust and irrigation droplets. our study also demonstrated that significantly more droplet and splatter occur to the left of the surgeon, which corresponds to the direction of rotation of the drill. those within to ft of the drill are at increased risk of exposure. in teaching institutions where multiple members of the team may be directly adjacent to the primary surgeon, this must be taken into account. while the drill is being operated, all steps should be taken to reduce the number of other people within a -to -ft radius. several limitations to this cadaveric simulation study deserve consideration. these procedures were not conducted in a normal adult clinic setting with an actively respiring patient. with stimulation of the external auditory canal during examination, patients can produce a cough reflex that may cause increased risk of viral transmission. moreover, there was no assessment of aerosolization, either forced (eg, sneezing) or from drilling, in this experimental model. however, we believe that it is still vital to understand the quantity, quality, and range of droplet and splatter contamination involved during these common procedures, as respiratory droplets are considered to be the primary mode of sars-cov- transmission. another limitation is that only droplets and splatter visible to the human eye were measured. furthermore, instead of a complete °assessment, the design model allowed for measurements only in the cardinal directions surrounding the specimen. in the context of the findings from this study, we believe that it is important to devise techniques to limit the spread of gross contamination from mastoid surgery. this will not be easily accomplished, because it is difficult to operate a microscope while wearing a face shield or powered airpurifying respiratory. risks to the rest of the surgical staff and anesthesia team also are present in the operating room, which highlights that additional protective personal equipment is necessary for the surgical team, not just the operating surgeon. carron et al recently published a simple technique involving the use of readily available clear surgical drapes to control droplet and splatter contamination during mastoidectomy. they reported that surgical visualization was not affected. although a good step in the right direction for preventing the spread of gross contaminant, this methodology does not create an air-tight surgical field, and droplet or splatter contamination was not measured in any objective way. further studies should be performed comparing different techniques to determine the extent of prevention of droplet contamination and aerosolization. it is essential to evaluate all procedures that have a risk of disrupting respiratory epithelium and spreading sars-cov- . our results indicate that there is no droplet generation during myringotomy with ventilation tube placement in an operating room setting. for mastoidectomy, however, gross contamination was visualized to ft away in all cardinal directions, and significantly more occurred on the left side of the surgeon when compared with the other sides, corresponding to the direction of drill rotation. it is critical to develop techniques to contain contamination as much as possible. dhruv sharma, substantial contributions to the conception or design of the work; manuscript drafting, editing, and final sign off; kolin e. rubel, substantial contributions to the conception or design of the work; manuscript drafting, editing, and final sign off; michael j. ye, data analysis; manuscript drafting, editing, and final sign off; vincent j. campiti, manuscript drafting, editing, and final sign off; aaron e. carroll, manuscript drafting, editing, and final sign off; jonathan y. ting, manuscript drafting, editing, and final sign off; elisa a. illing, contributions to the conception or design of the work; manuscript drafting, editing, and final sign off; sarah j. burgin, designed the original concept for the project; manuscript drafting, editing, and final sign off. integrated infection control strategy to minimize nosocomial infection of coronavirus disease among ent healthcare workers sars-cov- viral load in upper respiratory specimens of infected patients covid- and the otolaryngologist: preliminary evidencebased review coronaviruses: an overview of their replication and pathogenesis airborne or droplet precautions for health workers treating covid- ? nosocomial transmission of emerging viruses via aerosol-generating medical procedures american academy of otolaryngology-head and neck surgery. otolaryngologists and the covid- pandemic academy supports cms, offers specific nasal policy comprehensive detection of respiratory bacterial and viral pathogens in the middle ear fluid and nasopharynx of pediatric patients with acute otitis media endonasal instrumentation and aerosolization risk in the era of covid- : simulation, literature review, and proposed mitigation strategies. int forum allergy rhinol world health organization. coronavirus disease (covid- ) situation report- bloodcontaining aerosols generated by surgical techniques: a possible infectious hazard a simple technique for droplet control during mastoid surgery competing interests: none. funding source: none. key: cord- -t xw y authors: rodriguez-palacios, alexander; cominelli, fabio; basson, abigail; pizarro, theresa; ilic, sanja title: textile masks and surface covers - a 'universal droplet reduction model' against respiratory pandemics date: - - journal: nan doi: . / . . . sha: doc_id: cord_uid: t xw y the main form of covid- transmission is via oral-respiratory droplet contamination (droplet; very small drop of liquid) produced when individuals talk, sneeze or cough. in hospitals, health-care workers wear facemasks as a minimum medical droplet precaution to protect themselves. due to the shortage of masks during the pandemic, priority is given to hospitals for their distribution. as a result, the availability/use of medical masks is discouraged for the public. however, given that asymptomatic individuals, not wearing masks within the public, can be highly contagious for covid- , prevention of environmental droplet contamination (endc) from coughing/sneezing/speech is fundamental to reducing transmission. as an immediate solution to promote public droplet safety, we assessed household textiles to quantify their potential as effective environmental droplet barriers (edbs). the synchronized implementation of a universal community droplet reduction solution is discussed as a model against covid- . using a bacterial-suspension spray simulation model of droplet ejection (mimicking a sneeze), we quantified the extent by which widely available clothing fabrics reduce the dispersion of droplets onto surfaces within . m, the minimum distance recommended for covid- social distancing. all textiles reduced the number of droplets reaching surfaces, restricting their dispersion to < cm, when used as single layers. when used as double-layers, textiles were as effective as medical mask/surgical-cloth materials, reducing droplet dispersion to < cm, and the area of circumferential contamination to ~ . %. the synchronized implementation of edbs as a community droplet reduction solution (i.e., face covers/scarfs/masks & surface covers) could reduce endc and the risk of transmitting or acquiring infectious respiratory pathogens, including covid- . lactis, streptococcus diacetylactis, and saccharomyces florentinus, ml; x - cfu/ml) in ml pbs (fisher bp- - ) to simulate a cloud of droplets produced by a sneeze. probiotics are bsl- /'generally recognized as safe' by the fda and all experiments were conducted in bsl- hepa-filtered microbiology laboratories. no animal/human subjects were used for experimentation. before testing, spray bottle nozzles were adjusted to produce cloud and jet- propelled droplets that match the visual architecture of droplet formation described by bourouiba el at. . quantification of droplets landing over a surface was performed at the time of spray using seven mm-petri dishes containing tryptic soy agar ( . cm surface area/dish) with % defibrinated sheep blood, placed on a need droplets to facilitate their expulsion, transmission and endc , we first validated a rapid spray-simulation model of droplets (mimicking a sneeze) using a bacterial-suspension to quantify the extent by which widely-available household textiles reduced the ejection/long-distance flight of . cc-by-nc-nd . international license it is made available under a author/funder, who has granted medrxiv a license to display the preprint in perpetuity. is the (which was not peer-reviewed) the copyright holder for this preprint . https://doi.org/ . / . . . doi: medrxiv preprint droplets. to facilitate the enumeration of macro-droplets and invisible micro-droplets, spray- simulations were conducted over nutritious-media agar surfaces, incubated for h to enable colony-forming-droplet-unit (cfdu) formation. based on simulations conducted in two institutions, a cloud of bacteria-carrying droplets travel distances reaching > cm, particularly for large droplets (figure a) , consistent with reported dynamics during sneezing . of relevance to sneezing behavior, simulations illustrate that upward inclination of the central-spray angle allows macro-droplets to reach longer distances (simulation /dispersion equations; figure b -e). although macro-droplets frequently reached cm, most micro-droplets landed on surfaces within cm, with spray air-turbulence carrying micro-droplets into areas not reached due to gravity alone. thus, social distancing of . m, without edb-mask protection, as currently recommended, is insufficient to prevent droplet exposure, particularly where essential-service workers congregate during pandemics (transportation, supermarkets/food displays). therein, wearing edb-masks together with inclining downward the head/body during sneezing could minimize the spatial range of endc. household textiles retain liquid droplets, particularly if double layered to quantify the droplet retention potential of textiles as edbs, we next used the same bacterial-spray-simulation model to quantify non-visualizable micro-droplets that could cross/escape the textile-edb and cause microbial-surface agar contamination (textile/thread details in remarkably, spray experiments with 'two-layers' (of %-combed cotton, common in t- shirts; and % polyester, in sports jerseys) completely prevented the ejection of large macro- droplets ( % endc prevention), and drastically reduced the ejection of micro-droplets by a factor of . log , which is equivalent to a . % droplet reduction (p< . vs. single-layers, figure c and supplementary figures - ) . importantly, the least-effective textile as single-layer (most-'breathable', %-cotton homespun- material) achieved a - . % droplet retention improvement when used as two-layers ( %ci= . - . log ). lastly, all textiles were equally effective at absorbing the humidity from -sprays compared to medical mask/surgical cloth materials, which condensate after -spray ( figure d ). together, experiments indicate that two- layers of household textiles are as effective as medical masks preventing endc, and that more breathable materials in ≥ -layers could be effectively used if individuals deem two-layer, 'denser' textiles too air-restrictive. . cc-by-nc-nd . international license it is made available under a author/funder, who has granted medrxiv a license to display the preprint in perpetuity. is the (which was not peer-reviewed) the copyright holder for this preprint increase daily, and the fabrication of edb by centralized organizations could take weeks to reach entire 'lockdown' communities, we suggest, based on the cotton/polyester endc effectiveness, and a homemade edb-mask fabrication trial (supplementary figure ) , that, from one piece of clothing, every individual could make (without sewing machine) two -layer-edb masks as an immediate, synchronized contribution to reduce covid- endc. from a surface perspective, if everyone were encouraged to wear edbs, the collective area contaminated with droplets would be miniaturized to . - . % (two-layers/single-layers), compared to the potential contamination within cm ( . m ). even suboptimal edbs, effective for cm radius, could mathematically reduce the endc area by . % (figure e ). our findings and surface estimations are conservative as they are based on simulations using a (non-viscous) liquid solution, assuming stationary individuals. however, the impact of edb is predictably greater since real/large viscous secretions (figure a) , which also travel long distances (> cm) would be easier to contain by edb, as communities mobilize. to further lower the risk of fomite (plastic/metal surface) transmission from/by non-edb-wearers, edb-textiles used as covers, when relevant, could reduce endc by - % (t-test p= . , figure b ). finally, to illustrate, in volumetric terms, that edbs are even more effective preventing endc, we conducted a scoping review of literature to conduct analyses of droplet fluid-carrying capacity. although published droplet sizes vary with study method (supplementary will also prevent small-size droplet aerosolization by trapping such droplets immediately after production. an overview of a 'universal textile droplet reduction action-model' against pandemics is illustrated in figure c . . cc-by-nc-nd . international license it is made available under a author/funder, who has granted medrxiv a license to display the preprint in perpetuity. is the (which was not peer-reviewed) the copyright holder for this preprint . https://doi.org/ . / . . . doi: medrxiv preprint despite widespread dissemination of information to curtail the rapid spread of covid- outside of china (which affects - -year-old adults, % of hospitalizations in the usa ), little attention has been devoted to endc and prevention strategies for droplet movement from infected to non-infected individuals within the same community. more concerningly, is that following mandatory 'stay-in-home' quarantine orders, people may return to work unprotected, unaware if they are infected/shedders. this is particularly critical for 'essential pandemic workers', who face different levels of risk (health-care vs. electric/transport/food services), and who can contaminate environmental surfaces as they transit through the community between work (i.e., hospitals) and home, or within their households , without wearing masks. because mass testing is not always possible , especially for novel organisms like covid- , there are growing concerns that asymptomatic and mildly symptomatic citizens will continue to spread and reintroduce the virus to new areas, creating waves of cases, contributing to further economic burden from the outbreak . nonpharmaceutical interventions (npis), also known as community mitigation strategies, are actions that individuals and communities can take in order to slow the spread of illnesses. for pandemics, when medical approaches (hospitalization/treatments) are limited, npis are a critical component to achieve resolution. although ppe, including masks, are scientifically-effective to prevent infectious disease transmission, the use of masks for the general public has not been encouraged by governments , , possibly because demand will deepen the current crisis of mask unavailability for medical staff, or alternatively, because the use of masks to prevent respiratory infections has been misleadingly deemed ineffective, despite earlier clinical studies indicating that masks could be beneficial in households during pandemics , , . although masks have been extensively studied to determine whether individuals are clinically protected from infections , , and to confirm that wearing a mask promotes desirable hygiene practices (handwashing, 'avoiding crowds') , , , masks have not been examined for their potential to prevent environmental contamination. masks work, if worn properly; however, individuals (~ %) often fail to wear masks regularly, and properly , . despite low compliance, meta-analyses indicate that masks lower the odds of having (sars)-respiratory infections by % (or= . ), compared to the odds of having an infection 'not wearing a mask' . herein, we propose, that in addition to seeking the classical/clinical 'prevention of infection', npis could be universally based on 'droplet reduction models' such as edb to mitigate endc. not only for the prevention of respiratory diseases, but also to prevent widespread environmental dispersion of the virus, which could reach water sources or affect domestic animals, as has been shown for other viruses, including pandemic influenza . the world is in short supply of masks since the international 'lockdown' affected production , with health-care workers experiencing high morbidity/mortality due to reduced protection . governments are seeking private support to increase mask supplies; however, such strategy could take weeks/months, and infection rates would not improve if supplies were still not available to 'lockdown' communities. increased community transmission leads to higher demand for medical services, unless transmission is halted. using household textiles is a potentially life- . cc-by-nc-nd . international license it is made available under a author/funder, who has granted medrxiv a license to display the preprint in perpetuity. is the (which was not peer-reviewed) the copyright holder for this preprint cfdus on agar plates illustrating ability of cloud micro-droplets to move around spaces driven by cloud turbulence (left images, agar plates were partially covered with lid at moment of spray), concurrent contamination with macro-and micro-droplets. e) number of cfdu/plate ( . cm ) for simulations over distance. . cc-by-nc-nd . international license it is made available under a author/funder, who has granted medrxiv a license to display the preprint in perpetuity. edbs in reducing circumferential endc. . cc-by-nc-nd . international license it is made available under a author/funder, who has granted medrxiv a license to display the preprint in perpetuity. . cc-by-nc-nd . international license it is made available under a author/funder, who has granted medrxiv a license to display the preprint in perpetuity. is the (which was not peer-reviewed) the copyright holder for this preprint . https://doi.org/ . / . . . doi: medrxiv preprint health experts are telling healthy people not to wear face masks for human coronaviruses: insights into environmental resistance and its influence on the development of new antiseptic strategies history and recent advances in coronavirus discovery the first case of novel coronavirus pneumonia imported into korea from wuhan, china: implication for infection prevention and control measures acton: new symptoms of covid- include gi issues, fatigue, no fever aerosol and surface stability of sars-cov- as compared with sars-cov- detection of sars-cov and rna on aerosol samples from sars- patients admitted to hospital controversy around airborne versus droplet transmission of respiratory viruses: implication for infection prevention aerodynamic characteristics and rna concentration of sars-cov- aerosol in wuhan hospitals during covid- outbreak recognition of aerosol transmission of infectious agents: a commentary the infection evidence of sars-cov- in ocular surface. a single-center cross-sectional study indirect virus transmission in cluster of covid- cases natural ventilation for infection control in health-care settings. annex c respiratory droplets. geneva: world health organization characterizations of particle size distribution of the droplets exhaled by sneeze exhaled droplets due to talking and coughing severe outcomes among patients with coronavirus disease united states a familial cluster of pneumonia associated with the novel coronavirus indicating person-to-person transmission: a study of a family cluster the state of california on thursday issued a mandatory, stay-at-home order face mask use and control of respiratory virus transmission in households understanding the factors involved in determining the bioburdens of surgical masks cluster randomised controlled trial to examine medical mask use as source control for people with respiratory illness a cluster randomised trial of cloth masks compared with medical masks in healthcare workers wearing face masks in public during the influenza season may reflect other positive hygiene practices in japan facemasks for the prevention of infection in healthcare and community settings respirators against respiratory infections in healthcare workers: a systematic review and meta-analysis pandemic and seasonal human influenza virus infections in domestic cats: prevalence, association with respiratory disease, and seasonality patterns the world needs masks. china makes them but has been hoarding them italy's lombardy asks retired health workers to join coronavirus fight key: cord- -qcctchsk authors: chen, xiaole; zhou, xianguang; xia, xueying; xie, xiaojian; lu, ping; feng, yu title: modeling of the transport, hygroscopic growth, and deposition of multi-component droplets in a simplified airway with realistic thermal boundary conditions date: - - journal: j aerosol sci doi: . /j.jaerosci. . sha: doc_id: cord_uid: qcctchsk accurate predictions of the droplet transport, evolution, and deposition in human airways are critical for the quantitative analysis of the health risks due to the exposure to the airborne pollutant or virus transmission. the droplet/particle-vapor interaction, i.e., the evaporation or condensation of the multi-component droplet/particle, is one of the key mechanisms that need to be precisely modeled. using a validated computational model, the transport, evaporation, hygroscopic growth, and deposition of multi-component droplets were simulated in a simplified airway geometry. a mucus-tissue layer is explicitly modeled in the airway geometry to describe mucus evaporation and heat transfer. pulmonary flow and aerosol dynamics patterns associated with different inhalation flow rates are visualized and compared. investigated variables include temperature distributions, relative humidity (rh) distributions, deposition efficiencies, droplet/particle distributions, and droplet growth ratio distributions. numerical results indicate that the droplet/particle-vapor interaction and the heat and mass transfer of the mucus-tissue layer must be considered in the computational lung aerosol dynamics study, since they can significantly influence the precise predictions of the aerosol transport and deposition. furthermore, the modeling framework in this study is ready to be expanded to predict transport dynamics of cough/sneeze droplets starting from their generation and transmission in the indoor environment to the deposition in the human respiratory system. the interaction between the bio-aerosol and water vapor also has been investigated. zhang et al., ) , we developed and validated a multi-component droplet/particle-vapor interaction model (chen et al., ) . the difference between our predictions and the experimental results (w. li et al., ) for the hygroscopic growth of nacl particle is only ± . % rh (or ± . in growth ratio) (chen, et al., ) . airway wall boundary conditions (chen, et al., ) . asgari et al. ( ) developed experiment, which can maintain the airway surface temperature at °c using d printed casing with a circulated water bath, for exposure studies of hygroscopic particulate matters. however, the system mentioned above still cannot represent the physiologically realistic non-uniform temperature distributions in airways (mcfadden jr et al., ) . the inhalation flow rate affects the deposition of the hygroscopic droplet/particle. more specifically, higher inhalation flow rate increases the deposition of the hygroscopic droplets/particles due to inertial impaction. however, higher inhalation flow rate decreases the average rh-value in the airway when using a boundary condition with constant temperature and rh (chen, et al., ) , which enhances the evaporation of the droplet. if the more realistic thermal boundary (chen, al., ; wu, et al., ) and indoor air conditions (mcfadden jr, et al., ) are considered, higher inhalation flow rate also has a stronger cooling effect on the mucus-tissue layer, which further affects the mucus evaporation. therefore, the transport, hygroscopic growth, and deposition of multi-component droplets have not been investigated under different inhalation flow rate conditions, when employing the more realistic thermal boundary conditions. to address the knowledge gap mentioned above, this study investigates the evaporation, hygroscopic growth, and transport of a representative multi-component stands for the sea salt and other soluble compositions. fluorescein represents the non-evaporable and non-soluble composition, e.g., crustal matter. the validated transition shear stress transport (sst) model and discrete phase model (dpm) were employed for the prediction of the airflow and inhaled droplet/particle transport, respectively. temperature and rh distributions in the mt airway, as well as the deposition of the hygroscopic multi-component droplets are visualized and analyzed. the simplified mouth-throat (mt) airway geometry (see figure ) consists of two parts, i.e., an mt cavity and a mucus-tissue layer surrounding the cavity. the concluded that the simplified mt models with outlet diameters of . and . mm were better in accordance to in vivo experimental data comparing to the models with other outlet diameters and the usp model. therefore, the simplified mt cavity with a diameter of . mm was used as the fluid region in our study. furthermore, the fluid region was covered by a . mm thick mucus-tissue layer. the mucus-tissue layer (the blue cells shown in figure ) contains two sublayers, i.e., a mucus layer with a thickness of μm and a tissue layer with a thickness of μm. this setup ensures an accurate prediction of the temperature distribution in the mucus-tissue layer (chen, et al., ; wu, et al., ) . the structured hexahedral mesh was generated for both the fluid region and the mucus-tissue layer. the mesh was refined in the fluid region and the mucus-tissue layer near the air-mucus interface. the mesh refinement ensured that the non-dimensional distance y + was smaller than . for the first layer of the fluid mesh cells. mesh independence test was carried out following the same procedure that is documented in our previous study (chen, et al., ). the final mesh contained , , cells for the fluid region, and , cells for the mucus-tissue region. figure visualizes the coupling mechanisms of the heat and mass transfer between air and mucus. specifically, the airflow over the air-mucus interface affects the convective heat transfer, and the resultant water vapor flux evaporated from the mucus layer. assuming rh = . % at the air-mucus interface (finlay, ), the latent heat loss due to evaporation contribute to the variations of mucus temperature. the temperature at the air-mucus interface was calculated by the iterations between the mt cavity and the mucus-tissue layer. if the temperature of a given mucus cell t m is known, the airflow simulation determines the heat flux due to convection and and the mass flux of the water vapor, which determines the latent heat loss of the mucus layer. note that the calculations for the airflow and the heat transfer in the mucus-tissue layer are separated. t m is used as the boundary surface temperature for the airflow calculation. in the mucus-tissue layer, the temperature of the same cell t m is is obtained by solving the energy balance equation based on the conduction in the mucus-tissue layer, as well as the convection and latent heat loss due to the evaporation evaporation effect. the latter two are obtained from the calculation in the domain of the mt domain. the iteration continues until t m is equal to t m . to predict the rh distribution in the airway, the transport both the dry air and water vapor were simulated. the transition sst model was employed to simulate the laminar-to-turbulent airflow (chen, et al., ; chen, et al., ) equations ( ) and ( ), i.e., the k and ω equations, are modified based on the sst model (menter, ) using the production term k p % and destruction term k d % of turbulence kinetic energy (tke). k p % and k d % are determined by the intermittency γ (see eq. ( )) and the transition momentum thickness in terms of the reynolds number re t θ % , (see eq. ( )). the scalar transport equation for both the dry air and water vapor is given by (z. where s y and , s m d are the mass fraction and mass diffusion coefficient for species s. where h is the enthalpy of the mixture, c k and tc k are the thermal conductivity and turbulent thermal conductivity, respectively. a lagrangian method was employed in this study to predict the transport, size change, and deposition of the droplets. all governing equations listed in this section were solved using in-house c codes, implemented as user-defined functions (udfs). the droplets and particles are assumed to be spherical in our simulations. the primary deposition mechanisms are inertial impaction, sedimentation, and diffusion. the diffusion could be ignored due to the negligible brownian motion effect on the micron-sized droplets/particles. therefore, the main forces considered are the drag force and gravity. the saffman's lift force is ignored due to limited droplet/particle rotation. the virtual mass force is ignored, considering the large droplet/particle-to-air density ratio. accordingly, the droplet/particle trajectories are determined by the translation equation ( where dd c is the drag coefficient determined by the droplet/particle reynolds number, the d m , d u and d d are the mass, velocity, and diameter of the droplet/particle, respectively. the eddy-droplet/particle interaction, also known as the random walk kleinstreuer, ), which can be given by: where a is the surface areas of the droplet/particle, s n is the surface averaged mass is the mass fraction of component s on the droplet/particle surface, s y is therefore, the mass flux of the evaporable/condensable component changes the mass and volume of the droplet/particle. thus, the density of the droplet/particle may change during the simulation. in addition, the energy balance of the droplet/particle is given by (chen, et where nu is the nusselt number, s l is the latent heat of species s, c k is the thermal the specific heat and temperature of the droplet/particle, respectively. where h, injecting , particles could ensure that the deposition efficiency is independent of the particle number. the droplet/particle-vapor interaction model was also validated (chen, et al., heat transfer between the mucus-tissue layer and the airflow was examined in our recent study (chen, et al., ) . the latent heat transfer occupied . % of the total heat transfer at the air-mucus interface. this is similar to the percentage suggested by if the droplet evaporates completely, the diameter of the solid particle containing nacl and fluorescein only would be . % of its initial droplet. parameter values for setting up the simulations are provided in the supporting information. including ) airway wall had a constant temperature at °c, ) ignoring the latent heat due to water vapor phase change, but including convective heat transfer, and ) the more realistic thermal boundary condition, which is the same condition we used in this study. the simulated velocity distributions were highly similar due to the negligible effects of the temperature and rh on the fluid density (chen, et al., ) . therefore, the velocity field results and discussion were not provided in this study to avoid duplicated analysis. sharply in size with the increase of q in . as shown in figure (b), more than / area at the outlet has a localized rh higher than %,. however, its size reduces when the flow rate increases to l/min. furthermore, the region with rh > % almost disappears and shrinks into a thin layer near the air-mucus interface, when the flow rate continues to increase to l/min (see figure (c)). this suggests that hygroscopic growth of the droplet/particle can barely occur under high q in condition. shown in figure s in the supporting information. conditions remains approximately % for . < stk < . . when q in further increases to l/min, the difference in des remains % for . < stk < . . it is well known that the deposition of the micron particle in the airway may occur via impaction, including secondary airflow convecting particles to the airway walls, and particles were limited (see figure (a)) in the low rh condition (see figure (c)). therefore, the contribution of the hygroscopic growth to the deposition of the droplets would be limited. this observation indicates that the inertial impaction becomes more dominant on the droplet deposition when stk increases. the intensity of indoor human activity is commonly low. the inhalation flow rate for possible medical applications, e.g., inhaler, nebulizer, is even lower. therefore, the focus on the inhalation flow rate should be smaller than l/min, representing the light activity. neglecting the droplet hygroscopicity could underestimate the de up to % for nacl-water droplet at °c (chen et al., ) . besides, a more realistic airway boundary could increase the intensity of secondary flow that enhances the heat and water vapor mass transfer around the mucus-tissue layer. therefore, it can be projected that the differences in de predictions may also increase accordingly. thus, in order to accurately predict the fate of the inhaled hygroscopic droplet/particle, the the hygroscopic growth threshold for nacl, i.e., approximately % (see figure ). escaped hygroscopic droplets/particles decreases with the increase of q in . this is in accordance with the rh distributions discussed above. higher q in decreases the size of rh value higher than % at the l/min condition. thus, the droplets/particles can barely absorb water before deposition when penetrating this thin layer of high rh air. besides, the lower flow rate also leads to a longer time for droplet/particle-vapor interaction. therefore, the simulation has more large droplets at q in = l/min. also, it can be found that the average diameter of the deposited droplets is smaller than that of the escaped ones under the same condition. this observation is related to the droplet/particle trajectory in the airway. the airway mucus gradually humidifies the inhaled air, and result in a higher average rh at the outlet. due to a similar mechanism, the maximum diameter for the deposited droplets is larger than that of escaped ones. there is an interesting increase in the number of droplets having a growth ratio approximately equal to . in figure (b) under l/min condition. this is related to the droplets and particles entrained into the tube center at the outlet (see the red circle in figure (a) and green squares in figure (b) ). the growth ratio distribution of the droplets and particles within the circle indicates that these droplets are relatively large. % of these droplets and particles are within the growth ratio range from . to . . their average growth ratio value is . , which is also higher than that of the droplets and particles at the whole outlet. besides, the droplets and particles can only absorb water vapor in the high rh (> %) region. therefore, these large droplets are drawn into the tube center by the vortices from the airway boundary, considering their spatial distribution (see figure (a)). i.e., heat conduction in the airway tissue and mucus layer, the latent heat loss of mucus evaporation, and heat convection induced by the airflow over the mucus layer. temperature distributions, rh distributions, droplet deposition efficiencies, deposition patterns, and droplet/particle diameter changes are visualized and discussed. major conclusions are as follows: ( ) high inhalation flow rate can substantially decrease the mucus temperature with noticeable temperature gradients in the mucus-tissue layer. ( ) high inhalation flow rate can decrease the rh in the airway, which limits the hygroscopic droplet growth. no obvious hygroscopic growth of the nacl nuclei was airway. more realistic airway geometry or lower inhalation flow rate would increase this difference. therefore, it is necessary to model the mucus-tissue layer to obtain more realistic droplet deposition patterns in airways. numerical models employed in this study, especially the droplet/particle-vapor the present numerical study is subjected to the following simplifications and assumptions: ( ) a small region of the airway system, i.e., the mouth-to throat airway, is selected and simplified; ( ) the mucus-tissue layer is assumed to have a uniform thickness, and heat transfer related properties are assumed to be the same as water; and ( ) the initial droplet components only include water, ethanol, nacl and fluorescein. in light of the limitations of this study, future work will: ( ) use larger and more realistic airway geometry to model the airflow, heat transfer and water vapor mass transfer in the airway; ( ) consider actual drug particle/droplet components and their hygroscopicity to evaluate the deposition efficiency of the drug particle/droplet in lung; and ( ) perform transient simulation to include the breathing waveform, and investigate the effect of the aerosol release time on the deposition efficiencies of the hygroscopic droplets/particles. where the constants a , a and a are determined by the droplet/particle reynolds the energy balance equation of the mucus-tissue layer can be given by: where the source term m s only existed in the mucus layer. m s is defined as: where a m is the surface area of the mucus, t m is the temperature of the mucus surface, t f is the temperature of the air, l w is the latent heat of water, and j w is the mass flux of water at the air-mucus interface. the two terms on the right-hand side of eq. (s- ) are the convective heat transfer term and evaporation heat term. a summary of the parameter values used for the simulations is provided in table s . table s . inlet, boundary, and droplet conditions applied for the simulations viscosity of the air at inlet [kg/m·s] . × - on the effect of anisotropy on the turbulent dispersion and deposition of small particles evaporation and movement of fine droplets in non-uniform temperature and humidity field a numerical study of heat and water vapor transfer in mdct-based human airway models numerical investigation of motion of sulfuric and hydrochloric droplets with phase change in free-falling process airflow and deposition of nano-particles in a human nasal cavity experimental measurement and numerical study of particle deposition in highly idealized mouth-throat models particle deposition measurements and numerical simulation in a highly idealized mouth-throat transient airflow structures and particle transport in a sequentially branching lung airway model species heat and mass transfer in a human upper airway model cyclic micron-size particle inhalation and deposition in a triple bifurcation lung airway model slip correction measurements of spherical solid aerosol particles in an improved millikan apparatus numerical investigation of the interaction, transport and deposition of multicomponent droplets in a simple mouth-throat model effects of thermal airflow and mucus-layer interaction on hygroscopic droplet deposition in a simple mouth-throat model study on gas/solid flow in an obstructed pulmonary airway with transient flow based on cfd-dpm sci improved numerical simulation of aerosol deposition in an idealized mouth-throat an investigation of particle trajectories in two-phase flow systems size-change and deposition of conventional and composite cigarette smoke particles during inhalation in a subject-specific airway model cyclic micron-size particle inhalation and deposition in a triple bifurcation lung airway model ρ is the droplet/particle density. the energy balance of the droplet/particle is given by: key: cord- -dlsas authors: yang, xia; ou, cuiyun; yang, hongyu; liu, li; song, tie; kang, min; lin, hualiang; hang, jian title: transmission of pathogen-laden expiratory droplets in a coach bus date: - - journal: j hazard mater doi: . /j.jhazmat. . sha: doc_id: cord_uid: dlsas abstract droplet dispersion carrying viruses/bacteria in enclosed/crowded buses may induce transmissions of respiratory infectious diseases, but the influencing mechanisms have been rarely investigated. by conducting high-resolution cfd simulations, this paper investigates the evaporation and transport of solid-liquid mixed droplets (initial diameter μm and μm, solid to liquid ratio is : ) exhaled in a coach bus with thermal manikins. five air-conditioning supply directions and ambient relative humidity (rh = % and %) are considered. results show that ventilation effectiveness, rh and initial droplet size significantly influence droplet transmissions in coach bus. μm droplets tend to evaporate completely within . s and s as rh = % and % respectively, while . s or less for μm droplets. thus μm droplets diffuse farther with wider range than μm droplets which tend to deposit more on surfaces. droplet dispersion pattern differs due to various interactions of gravity, ventilation flows and the upward thermal body plume. the fractions of droplets suspended in air, deposited on wall surfaces are quantified. this study implies high rh, backward supply direction and passengers sitting at nonadjacent seats can effectively reduce infection risk of droplet transmission in buses. besides taking masks, regular cleaning is also recommended since %- % of droplets deposit on object surfaces. highlights  droplet evaporation and transport(initial size μm/ μm) in bus are studied by cfd. [ , , ] , hospital isolation rooms [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] or operating rooms [ ] , general indoor environments [ , ] . besides for vehicle indoor environments, a number of studies emphasized indoor transmission in airplane cabins [ ] [ ] [ ] [ ] and high-speed train [ ] . for instance, zhang and li [ ] used cfd (computational fluid dynamics) simulations to study the respiratory particle dispersion process (without droplet evaporation) in four different boundary conditions of air supply and exhausts in a highspeed rail cabin. however, there is a lack of study on ventilation and droplet dispersion in the coach bus. respiratory infectious diseases can be transmitted via three routes, namely contact, airborne and fomite [ ] . similarly, a higher risk of infection is associated with close proximity to the source patient and decrease rapidly with the distance [ ] [ ] [ ] [ ] [ ] [ ] . with the same initial concentration, a larger quantity of mass released may be expected to experience a slower dilution [ , ] . due to the initial velocity, the exhaled gas and particles can travel in the air over a distance which is determined by the ventilation airflow, gravity force related to particle diameters and buoyancy forces of thermal j o u r n a l p r e -p r o o f bodies [ , , , , , [ ] [ ] [ ] . larger particles (> μm) may settle on wall surfaces or floors quickly because the significance of gravity is greater than ventilation. smaller particles ( . - μm) may remain suspended for a sufficient time and lead to disease transmission over larger range [ , , , ] . apart from the initial droplet size, the droplet evaporation and dispersion may be influenced by the relative humidity (rh) in ambient environment as well [ ] . wei and li [ ] discovered that droplet dispersion with the diameter of μm was very sensitive to rh in the jet-like cough airflow. by calculating the droplet lifetimes and droplet size variation with different rh, xie et al. [ ] indicated that the droplet size was dictated by its evaporation and droplets smaller than μm would evaporate before falling to the ground m away. the shrinking aerosols would ultimately form droplet nuclei small enough to suspend in the air for substantial time. accordingly, instead of using pure water droplets for model testing [ ] , test droplets containing nonvolatile content were investigated by liu et al. [ ] and employed in our study too, which would ultimately form droplet nuclei after evaporation. due to the great impact of initial droplet size on disease transmission, many studies were carried out to reveal the size profile information of droplets during different expiratory activities [ , , ] . it is difficult to identify the actual droplet size exhaled from different patients with various human activities. therefore, we first emphasize and adopt the initial droplet diameters of μm and μm as involved in most previous studies. in summary, there are many studies on the diffusion of tracer gases and particulate matter for indoor transmission in hospital ward, airplane cabin and general indoor environment etc. however, it is still a lack of studies on droplet evaporation and dispersion in enclosed bus environments. this paper aims to investigate the effect of rh and indoor airflow pattern with body j o u r n a l p r e -p r o o f thermal plume on the evaporation and dispersion of exhaled droplets with different initial diameters in enclosed bus environment. the enclosed bus model followed the realistic coach bus that went from guangzhou to huizhou in guangdong province p.r. china and carried a korean patient infected by mers (middle east respiratory syndrome) in may , who did not wear a mask and did not give a cough/sneeze or talk with others either. the other thirteen people were isolated for three weeks after this trip and fortunately no one was infected by this source patient. similarly but unfortunately, infectious cases have been found on public transport [ ] , which was identified as airborne transmission. therefore, it is necessary to study the droplet dispersion in this enclosed bus environment. by cooperating with cdc of guangdong province, we adopted the same passenger locations and average ventilation flow rates in the enclosed bus taken by mers patient in cfd model settings. then the impacts of rh, initial droplet diameters and air-conditioning supply directions can be investigated as case studies by cfd simulations. through statistics of the number of droplets trapped, suspended and escaped to predict the chance of infection, this study attempts to provide some recommendations for reducing the risk of droplet transmissions in enclosed bus environments. in this study, ansys fluent [ ] was applied in the validation and following numerical cases study. as displayed in fig. a , based on the experimental data of yin et al. [ ] in an inpatient ward furnished with one patient, one visitor, one bed, a tv set and a piece of medical equipment, cfd validation study was first conducted to verify the ability of cfd in predicting indoor airflow and temperature distribution. according j o u r n a l p r e -p r o o f to the experiment [ ] , air was supplied from a near-floor diffuser with the temperature of . ℃ and ventilation rate of ach ( cfm), and air was exhausted through the bathroom exhaust and main exhaust with the ventilation rate of cfm and cfm respectively. the heat generated by patient, visitor, equipment and tv was watt, watt, watt and watt. more details can be found in yin et al. [ ] . in our cfd simulations, the mesh was generated with the maximum grid size of cm (fine grid, total tetrahedral cells of . million) and cm (coarse grid, total tetrahedral cells of . million) near wall surfaces and finer grids near heating surfaces. as shown in fig. b source and the exhaust where the airflow was unstable, both the particle concentration measured in experiment and cfd display a large fluctuation. the particle concentration on tg , tg , tg is relatively small and has similar profile shape. the results show not very good simulation of concentration values but sufficiently well in predicting the changing shape and magnitude of particle concentration. on the whole, the above results prove that present cfd simulations with rng k- model and grid arrangement with the maximum grid size of cm is effective [ , , , ] and can be adopted in the following simulation of indoor environments. this study aims to figure out the characteristics of droplet evaporation and dispersion in an enclosed long-route coach bus. a realistic coach bus, with a dimension of . m× . m× m (l×w×h), was adopted to investigate the influence of airconditioning supply directions and indoor relative humidity. the detailed descriptions of enclosed bus are summarized in table. was about , , , which was determined by refining the mesh until the flow field solution was grid-independent. zhao et al. [ ] found that the dispersion of exhaled particles was easily affected by the size of particles, body thermal plumes and ventilation airflow patterns. so we investigated the particle dispersion and deposition in terms of various initial sizes of droplets, air condition supply directions and rh. c ) where located in the air condition vents will be illustrated in the discussion section. the fate of droplets, including suspended, deposited and escaped, as well as the number concentration of droplets around and on passengers were calculated to quantify the healthy passengers' risk of infection, which can effectively prevent and control the respiratory infectious diseases. as is well-known, there are two main kinds of airflow patterns in nature, laminar flow and turbulent flow. indoor airflow is usually turbulent which can be simulated by large eddy simulation (les) and reynolds average navier-stokes (rans) turbulence models. however, the application of les model requires longer computational time [ ] [ ] [ ] . the renormalization group (rng) k-ε turbulence model which is one of the most widely-adopted rans models is employed in terms of accuracy, computing efficiency, and robustness for modeling indoor environments j o u r n a l p r e -p r o o f [ , , , [ ] [ ] . thus, we adopted the rng k-ε model to simulate the airflow pattern in the bus. more details about the governing equations and the turbulence parameters of rng k-ε model can be found in the literature [ , ] . the simple algorithm was adopted to decouple pressure and velocity. the second-order upwind scheme was used to discretize the convection and diffusion-convection terms in the governing equation. besides, the boussinesq model was employed to consider the buoyancy effect, in which the air density was regarded as a constant except in the momentum equation of vertical velocity. lagrangian method was used to track respiratory droplets. to simplify the calculation, the following assumptions were used: ( ) the heat and mass transfer between air and droplets were neglected; ( ) the influence of droplets on airflow was also neglected; ( ) no droplet was coagulated in its deposition process; ( ) the droplets were all in ideal sphere shape. this approach calculates the trajectory of each droplet by solving the individual droplet movement equation whose theory is newton's second law: ( ) and eq. ( ) were respectively adopted to describe the drag force and gravity on the droplet in i direction: where is the stoke's drag modification function for large aerosol reynolds number ( ) which is defined in eq. ( ); is the aerosol characteristics response time, which is defined as eq. ( ); and are respectively the density of droplet and air; and are respectively the droplet diameter and the turbulent viscosity (kg·m - ·s -model was adopted [ ] . the droplets evaporate till their inert content (residue) [ , ] . the droplet vaporization rate is defined as the following equation: where is the molar flux of vapor, kg·mol·m - ·s - , and is related to the gradient of the vapor concentration between the droplet surface and the surrounding air; is the mass transfer coefficient (m/s) that can be obtained using sherwood relationship [ ] ; , and , are respectively the vapor concentration at the droplet surface and in the surrounding air (both in kg·mol·m - ), and can be obtained via the ideal gas relationship and molar fractions of water vapor. droplet evaporation is influenced by rh in terms of , in eq. ( ). all boundary conditions for airflow are summarized in table. . the influences of human breathing and heat flux at body surfaces were taken into account. considering the total heat of w [ ] produced by the sleeping manikin with surface area of . m , the convection heat flux at body surfaces was defined as w/m for passengers assuming they were sedentary and . w/m for the driver. for simplification, the breathing flow was assumed to be exhaled from the human mouth with the temperature of k. the boundary at mouth openings (~ . m ) was set as the mean exhalation velocity of . m/s [ , , ] in the direction paralleling to y-axis.. our cfd simulation considered only mouth exhalation for all manikins. the air-conditioning vents were also set as velocity inlet, and the wind speed was . m/s (air change rate per hour= . h - ) with the air temperature of k. non-slip boundary conditions were applied for all walls where isothermal condition was assumed. table. . for solid walls and seats, the trap condition was applied with the assumption that droplets were deposited as soon as they touch the wall surfaces and the trajectory calculation was terminated. while for the ceiling and luggage carriers, the reflect condition was set due to gravity. escape condition was applied to the exhaust and mouths as well as air-conditioning vents. gravity plays a particularly important role for the movement of large droplets ( μm) [ , , , , , ] . thus, to better reveal the influence of air condition supply wind, the following subsection focuses on the analysis of the μm droplet diffusion in different air condition supply modes as rh = %. there are differences between windnx (fig. c) and windpx (fig. d ) supply modes as passengers will release heat and affect the flow field. the velocity is larger when air condition supply wind blows to the front of the bus (windpy), which has the superposition effect with the exhaust (fig. f) . a vortex is formed between the patient and the front seat, where the upward flow is relatively stronger. in addition, there is also airflow across the seat backs and front. referring to windpy mode, almost half of droplets move forwards across the back of the chair, and leave several droplets sink because of small vertical downward force, and then rise up because the upward airflow continues to float to the right of the carriage (fig. e -e and fig. s c ). in the process of forward diffusion, some droplets are blocked by the seat backs of v l, and a great number of droplets move across v l, sinking at v l and v l due to the obstruction of the seats subsequently. the droplet which isn't trapped in the object keeps on fluttering forwards in higher level. according to the droplet distribution at t= s, there will be droplet aggregation in the front area on the left side of the bus where the patient is located. as previously investigated [ , , , , , [ ] [ ] [ ] ] , the particle/droplet dispersion process is greatly determined by the gravity force. in this study, the impacts of different initial droplet sizes and its evaporation rate are discussed. results show that the diffusion features between μm and μm droplets are of great variation under the same air condition supply wind direction and rh. in contrast to the initial diameter of μm droplets, μm droplets tend to move faster, farther and wider at the same time. hence, the size of droplets determines the dominant force in the diffusion process. the larger the droplets are, the faster the deposition is, the slower the diffusion is, and the lower the risk is to the driver and passengers. relative humidity was proved to be dominant for evaporation time of droplets [ , ] . droplets consisting of liquid (h o) and solid particulate matter (nacl) was j o u r n a l p r e -p r o o f taken consideration, and the processes of evaporation and diffusion were simulated in this study. after released from patient mouth, the change of droplet size with time was counted. according to our statistics, under rh = %, droplets with the initial diameter of μm was evaporated completely within the first . s. for the condition of rh = %, the evaporation time of μm droplets hardly change, since they evaporated too fast to be seen any difference [ ] . as the ratio of water to sodium chloride in the droplet is set to be : , the final diameter for droplets with the initial size of μm and μm is . μm and . μm, respectively. in another word, their volumes have been reduced to one tenth of their original size ultimately. the change of droplet diameter under different rh is shown in fig. . results show that high rh can dramatically postpone the process of droplet evaporation, since air with higher rh has a lower potential in absorbing the water vapor [ ] . the figure reveals that the droplet size decreases to stable at t= . s and s respectively when rh = % and %. the larger the rh is, the more time it takes for droplets to evaporate. therefore, the effect of buoyancy and gravity forces on the diffusion of droplets will be more obvious for rh= %. nevertheless, as the short time of droplet evaporation, its influence on the diffusion of droplets is limited. compared to μm droplets, μm droplets evaporate too quick to be seen any difference in the dispersion, thus μm droplets are used to present to discuss as followed. fig. depicts the distribution of μm droplets at different time under both dry (rh= %) and wet (rh= %) environment in the windny mode. in general, droplets seem to move towards the same direction, and the dispersion range j o u r n a l p r e -p r o o f has no significant variation between them. actually, as a result of the short evaporation time ( . s) in rh= %, droplets shrink quickly to droplet core whose diameter is . μm, and subsequently diffuse fast. it is observed in fig. a , a and fig. b , b that droplets arrive the farther place compared to rh= %. besides, it should be mentioned that the number of droplets in rh= % is fewer than that in rh= %, because more droplets will deposit in the object surface in the diffusion process, leading to less suspension droplets (e.g. windpy, fig. s d-e) , which will be discussed in section . . after released from the patient' mouth, droplets begin to evaporate and spread to every corner of the carriage because of the gravity, buoyancy force and airflow of the air-conditioning. in this paper, droplets composed of liquid and solid elements are employed. the solid elements still travel around in the carriage after the liquid is evaporated. during the diffusion process, some droplets' journey will end up when they deposit on the surface of the seats, human bodies or walls, while the others still suspend till they deposit or escape from the exhaust fan which is set on the front of the roof. in general, there are three final statuses of droplets when the calculation stops, named trapped, suspended and escaped, and the total number of them is , . in addition, when the droplet size increases to μm (orange bars), the effect of wind direction becomes smaller than that for μm droplets. as a result, more than . % of μm droplets will deposit. the proportion of suspended droplets decreases slightly from . - . % ( μm) to . - . % ( μm) due to the greater gravity force on larger droplets. there is an exception that the proportion of suspended droplets increases from . - . % ( μm) to . - . % ( μm) in the mode of windpy where droplets are stopped by the v l seat backs and move towards the aisle with little obstruction. however, the number of escaped droplets is of dramatically reduction, especially in the windny mode, which decreases to . %. as the initial diameter increased, droplets are less removed from the carriage, and most of them still stay in the bus, which is a risk to passengers. when the relative humidity is between % and %, droplets express similarity in their ultimate fate. there is slight distinction of fate for μm droplets in different conditions of supply wind, which is related to the short evaporation time of μm. taking μm droplet as an example, in the mode of windpy, . % and . % of droplets are suspended when rh= % and %, respectively. the relative humidity brings the same function to droplets size. therefore, the influence of rh on dispersion of droplets depends on the initial size of droplets and the supply wind direction. the zone, which is more than μm droplets ( . ‰). droplets mostly suspend above the fifth and sixth row. this result is consistent with the previous droplet diffusion characteristics in subsection . . . passengers whose body surfaces are deposited by droplets exhaled from the source patient are at higher risk to get infected than those whose body surfaces are not diameter is μm compared to μm. more droplets will deposit on the passengers around the patient such as c, b. in terms of driver and passenger c and d, the distance between them and patient is more than . m, which significantly reduce the probability of airborne transmission. finally, we recall the facts that no passengers were infected by the source patient with mers from south korea. several reasons can be the most significant. first, although the source patient did not wear any mask, fortunately he did not cough/sneeze or talk with other people. there were only droplets exhaled by breathing activities. second, it was lucky that there were no passengers in the adjacent seats in front of or behind this source patient as well as beside his seat which were revealed of the highest risk for droplet transmission. for the other seats, the risk of droplet transmission decreased sharply. our study can be further improved in which more processes/parameters are considered. firstly, we only studied the influence of air-conditioning wind direction and relative humidity on the droplet dispersion. however, in real cases, the location of the infection source relative to the exhaust fan is also an important factor on the droplet diffusion, transmission, and elimination, because the only exhaust fan is of great significance on flow pattern in the enclosed bus. secondly, as a start, this study only considered exhaled droplet by breathing. future investigations will consider different respiratory activities (e.g. speaking, coughing, sneezing), which may lead to complex j o u r n a l p r e -p r o o f jet speed and different initial characteristics of droplets (sizes, velocities etc.). thirdly, the final fate and composition of the droplets are of great significance for the evaluation of the infection risk, and the relationship between them deserves further study. the enclosed and crowded indoor environments in long-route coach buses usually experience high infection risk of respiratory diseases due to droplet transmissions. in this study, as a novelty, we built a numerical model according to a real case to investigate the influence of ventilation and evaporation of exhaled droplets on their transport. we employed five air supply directions, two kinds of relative humidities (rh= % and %) and initial droplet sizes ( μm and μm). we summarized the number of droplets/droplet nuclei suspending in different zones and depositing on the body surface of each passenger to show the temporal and spatial characteristics of droplet distributions. some meaningful findings are addressed: ( ) droplets with the initial diameter of μm finish evaporation within the first . s as rh= % and %, while μm droplets evaporate to pure solid droplet nuclei within . s and . s respectively under dry and wet conditions. ( ) followed by the air supply mode and droplet initial size, droplet evaporation related to relative humidity is the third key factor influencing the droplet diffusion and its final state. rh of % tends to attain less risk of droplet transmission than rh of % because droplets evaporate slower in wetter air and deposit more quickly onto j o u r n a l p r e -p r o o f wall surfaces. ( ) in general, small droplets ( μm) diffuse faster, farther and wider compared with large droplets ( μm). %- % of μm droplets are trapped on the surfaces, which is higher than that of μm ( %- %) because of the gravity-force effects. the authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. miss j o u r n a l p r e -p r o o f (a) (b) fig. . the computational domain, human models and the schematic structure in the coach bus. novel coronavirus ( -ncov) situation reports evidence of airborne transmission of the severe acute respiratory syndrome virus defining the sizes of airborne particles that mediate influenza transmission in ferrets modelling short term individual exposure from airborne hazardous releases in urban environments an epidemiological investigation of novel coronavirus diseases through aerosol-borne transmission by public transport analysis of concentration 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of exhaled breathing droplets: a numerical investigation enhanced spread of expiratory droplets by turbulence in a cough jet how far droplets can move in indoor environments-revisiting the wells evaporation-falling curve evaporation and dispersion of respiratory droplets from coughing exhaled droplets due to talking and coughing the size and concentration of droplets generated by coughing in human subjects ansys fluent user's guide, (version . ) experimental study on displacement and mixing ventilation systems for a patient ward potential airborne transmission between two isolation cubicles through a shared anteroom comparison of indoor aerosol particle concentration and deposition in different ventilated rooms by numerical method comparison of different models for indoor airflow computation large eddy simulation and zonal modeling of human-induced contaminant transport. indoor air large-eddy simulation of human-induced contaminant transport in room compartments evaluation of various turbulence models in predicting airflow and turbulence in enclosed environments by cfd: part- : comparison with experimental data from literature experimental and numerical investigation of airflow and contaminant transport in an airliner cabin mockup human pulmonary secretions in health and disease evaporation from drops, part ii research on inhalation rate of chinese adults key: cord- -h zm p authors: carelli, pasquale title: a physicist's approach to covid- transmission via expiratory droplets date: - - journal: med hypotheses doi: . /j.mehy. . sha: doc_id: cord_uid: h zm p in this paper, a physicist's approach is given to support the necessity to wear surgical masks during the covid- pandemics; they have become compulsory in eastern countries, while in western countries they are still an optional. my thesis is supported and described on the basis of a physicist's model which studies the droplets behavior when emitted by the respiratory apparatus of an infected person, symptomatic or not. the intermediate dimensioned droplets are proved to be changed into aerosol, losing their water content and becoming seriously contagious, but in their initial phase they could be easily caught by a simple surgical mask. the actual efficiency of ffp masks has been examined and found to be lower than expected. while the covid- pandemic is spreading around all over the world in a dramatic way, i think it is necessary to state a reference date in order to make any reflections, i chose the rd april . on that date in italy there were , dead people and , infected, the situation was dramatically changing with a number of deaths higher than a day. that rate (mortality) caused by the virus is of · (deaths/population). at the same date in south korea there were dead people and , infected, mortality was of · % with a lethality rate (deaths/infected people) of · %. as the population in south korea has a life expectation very similar to the italian one (even if koreans are younger than italians[ ]), the korean data about lethality is more plausible. one of the reasons of such a serious pandemic in italy and afterwards in many other western countries, could be the following: in asian countries surgical masks have been widely worn for many years as a means to protect other people. this habit, there are non doubts about the fact that expiratory particles transmit the pandemic, but we must make a coarse distinction among droplets and their dynamic evolutions when emitted by infected people. this paper wants to afford the problem from a physical point of view. the airborne disease is caused by violent coughing [ ] and sneezing [ ] , but many infected people were minimally symptomatic or asymptomatic at all [ , , ] and transmission of virus from asymptomatic carriers has been identified [ ] . we always emit a large quantity of droplets[ , ] even just breathing and speaking. whatever is the possible expiratory particle source, i assume that the smallest droplets are more numerous than the bigger ones and i won't distinguish between speaking and any other more violent expiratory events. a single initial very large droplet (r = cm radius, v = · cm volume) containing a large viral load ( virions for milliliters [ ] ) splits in many smaller droplets (the largest droplets having a radius of r = µm ). the model that i propose assumes that the number of fragments with a radius between r and r is given by: where a is a dimensionless constant. a is simply times the cube of ratio between r and r because the volume of the initial droplet must be equal to that of all the smaller droplets; in this specific case a's value is . , their viral load is absolutely negligible. those particles cannot be stopped by a surgical mask, but there is no reason to intercept them because they are just water or mucous. for the aerosol the gravity has a negligible effect, unless it is in an environment with brackish air. the second group (in green in fig. ) , is made of droplets with the biggest size, having a radius larger than µm, they are a bit more than , . they constitute almost the total volume of the initial large droplet and then they contain most of the viral load. they follow a parabolic trajectory and constitute what is called fomite [ ] , which can contaminate surfaces where they settle. the third group (in black in fig. ) is made of droplets with an initial radius between · µm and µm, they are about , . their dynamic is strongly dependent from the stokes law, that states that a spherical droplet of radius r, moving in the air, undergoes a drag force given by: where µ[ ] is the air viscosity. at first they don't behave like the aerosol, because the gravity action has an important role compared with the drag force; anyway at the end the two equal and opposite forces rapidly balance and the droplet reaches a descending speed limit. that movement is slow and it allows the evaporation of water, till the droplet is reduced to its particulate or virus and it has become aerosol. these droplets have a substantial viral load, they are quite numerous, some thousands of them can contain just one single virion each and they are probably the most contagious and dangerous elements[ ]; if not stopped on time, they constitute the real element of airborne infection [ ] . take note that at the starting phase, when they are larger, they could be easily caught by a common surgical mask. the evolution of those droplets has been roughly studied a long time ago by wells [ ] ; more recently it has been deeply analyzed [ ] . of course the distinction of the three different typologies of droplets is purely as an indication, they are not exact measurements. in the fluids dynamics we define fluidodynamical resistance the ratio between the gas flux (usually measured in liter/s) and the pressure difference. in a normal person breathing through the nose, the fluidodynamical resistance is about pa liter/s [ ]. ffp masks [ ] have very specific technical characteristics, they should have a fluidodynamical resistance lower than pa liter/s and filters at least % of airborne particles larger than · µm. we know that virions of sars-cov are about · µm. fig. shows a drawing on scale of a filter (simulating the ffp mask filters) with holes of nm diameter and a particulate with a nm diameter (down, smaller than the canal): i presume that in % of the cases, whatever is the coming direction, it will hit the wall and it will be stopped. the other particulate with a nm diameter, moving on the same direction and angle, goes inside in the same position, but it passes through the canal without being stopped. therefore a filter able to stop particulates of nm diameter in % of cases, can't have the same efficiency for smaller particles. shortage of ffp masks has been considered a very bad event, but i don't believe we need them so much: as a matter of fact, to be an absolutely safe protection they should cling to the face completely, which is impossible, especially when worn by bearded men. success in fighting against a virus depends on how deep is knowledge of its characteristics: to understand how the virus aerosol changes after being emitted from the otorhinolaryngological apparatus is important in order to recommend a widely spread use of surgical masks everywhere people speak, especially indoors. moreover i underline how ffp masks are poorly efficient in preventing infection, considering the nature of infectious aerosol. waiting for a new vaccine we could hope to extirpate the sars-cov- like it happened for smallpox [ ] . a cough aerosol simulator for the study of disease transmission by human cough-generated aerosols violent expiratory events: on coughing and sneezing kin-hang kokn and others, a familial cluster of pneumonia associated with the novel coronavirus indicating person-to-person transmission: a study of a family cluster xingwang li and others, a novel coronavirus from patients with pneumonia in china guangfu jin, and others, clinical characteristics of asymptomatic infections with covid- screened among close contacts in nanjing, china gisela bretzel and others, transmission of -ncov infection from an asymptomatic contact in germany the size and the duration of air-carriage of respiratory droplets and droplets-nuclei the size distribution of droplets in the exhaled breath of healthy human subjects holbrook and others, aerosol and surface stability of sars-cov- as compared with sars-cov- on air-borne infection: study ii. droplets and droplet nuclei how far droplets can move in indoor environments--revisiting the wells evaporation-falling curve zdenek jezek, and others, smallpox and its eradication key: cord- -fiadxpar authors: george, ajith; prince, mark; coulson, chris title: correspondence‐technical note: safe nasoendoscopy assisted procedure in the post covid‐ pandemic era date: - - journal: clin otolaryngol doi: . /coa. sha: doc_id: cord_uid: fiadxpar for centuries it has been humankind's instinct to cover the mouth and nose when coughing or sneezing. common sense would dictate this instinctively reduces the dispersion of aerosol and droplets and thus the spread of contact and airborne infections. mr ajith george (orcid id : - - - ) mr christopher coulson (orcid id : - - - ) article type : technical note correspondence-technical note: for centuries it has been humankind's instinct to cover the mouth and nose when coughing or sneezing. common sense would dictate this instinctively reduces the dispersion of aerosol and droplets and thus the spread of contact and airborne infections. aerosol generating procedures (agps) have become a new byword for procedures that put clinicians at increased risk of contracting covid- . whilst the title suggests the risk is simply in aerosols, the science is much more interesting. droplets and aerosols are different, with the distinction between them based on size. whilst experts disagree on the absolute size when an aerosol becomes a droplet, the general acceptance is that anything bigger than microns ( . mm) is a droplet and those smaller are aerosols. in most contagious respiratory infections, the principal transmission agents are droplets ( ). this is due to the relatively high viral load in a droplet, purely due to its large size, and also the fact that large droplets have weight, and so gravity pulls them down onto surfaces that others can touch -so passing it on. this is why washing hands is so effective against droplet spread. aerosol transmission is thought to be a much less frequent cause of transmission, mainly due to the very small viral load (given the aerosol itself is by definition very small). however, this article is protected by copyright. all rights reserved it is clearly more concerning as these very light particles, can travel large distances.. that said, it is thought to only play a minor role in transmission compared to droplet spread. this observation supports the well-known concept that covering the mouth does indeed reduce droplet production. on impact with smooth surfaces droplets disperse to smaller sizes and can aerosolise. similarly impact onto soft surfaces absorbs droplets reducing their projection as well as the tendency to aerosolise ( ). as the pandemic plateaus in countries across the world various strategies are to be considered to return to a new normal. this would facilitate the resumption of diagnostic services whilst maintaining the protection to healthcare workers. one suggestion is the use of facemasks to help reduce the risk of inadvertent droplet dispersion ( ) . despite the 'soft surface' barrier masks create, in the ent setting, facemasks obscure access to the nasal cavity thus preventing nasoendoscopy. the 'snap' (safe nasoendoscopic airway procedure) developed by endoscope-i ltd (west midlands, uk) is a single-use, valved endoscopic port, retrofitted to any surgical mask ( figure ) , permitting entry of a mm flexible and rigid endoscope to examine the naso and this article is protected by copyright. all rights reserved pharyngolarynx. the valve, a . mm cylindrical tube truncated by two opposing degree inclined membranes microns thick, approaches a point but terminates in a micron thick and micron wide plateau, creating a 'duck bill' formation the valves are formed using a fff (fused filament fabrication) d printing technique with a flashforge creator pro d printer. the plateau atop the valve serves to provide a reference for introducing a slit using a hardened steel razor blade that is microns thin. the blade is mounted in a jig to ensure angle, penetration depth and position are controlled as it is driven through the membrane. these measures ensure that the valve opening is observably consistent and less than microns. once the snap is fitted to a surgical mask, any cough or sneeze generated during the procedure is caught within the mask. the valve is configured such that pressure from the patient side will serve to collapse the walls of the valve membrane thereby further sealing  droplets produced by coughing or sneezing carry a higher viral particle load and can be reduced by wearing a surgical mask in turn helping reducing infection transmission  the snap device is an effective and safe method of providing access to the nasal cavity during nasoendoscopy whilst also providing a barrier of a surgical mask to protect against droplet dispersion  reducing the exposure to pathogens for all healthcare works facilitates a return of guideline for isolation precautions: preventing transmissions for infectious agents in healthcare settings flexible laryngoscopy and covid- its harder to splash on soft solids refining the head and neck cancer referral guidelines: a twocentre analysis of referrals key: cord- - mj gjv authors: chaudhuri, swetaprovo; basu, saptarshi; kabi, prasenjit; unni, vishnu r.; saha, abhishek title: modeling the role of respiratory droplets in covid- type pandemics date: - - journal: phys fluids ( ) doi: . / . sha: doc_id: cord_uid: mj gjv in this paper, we develop a first principles model that connects respiratory droplet physics with the evolution of a pandemic such as the ongoing covid- . the model has two parts. first, we model the growth rate of the infected population based on a reaction mechanism. the advantage of modeling the pandemic using the reaction mechanism is that the rate constants have sound physical interpretation. the infection rate constant is derived using collision rate theory and shown to be a function of the respiratory droplet lifetime. in the second part, we have emulated the respiratory droplets responsible for disease transmission as salt solution droplets and computed their evaporation time, accounting for droplet cooling, heat and mass transfer, and finally, crystallization of the dissolved salt. the model output favourably compares with the experimentally obtained evaporation characteristics of levitated droplets of pure water and salt solution, respectively, ensuring fidelity of the model. the droplet evaporation/desiccation time is, indeed, dependent on ambient temperature and is also a strong function of relative humidity. the multi-scale model thus developed and the firm theoretical underpinning that connects the two scales—macro-scale pandemic dynamics and micro-scale droplet physics—thus could emerge as a powerful tool in elucidating the role of environmental factors on infection spread through respiratory droplets. it has been well established that the sars-cov- virus responsible for the covid- pandemic transmits via respiratory droplets that are exhaled during talking, coughing, or sneezing. each act of expiration corresponds to different droplet sizes and myriad trajectories for the droplets embedded in the corresponding jets. wells , was the first to investigate the role of respiratory droplets in respiratory disease transmission. expelled respiratory droplets from an average human being contain dissolved salt with a mass fraction of about . as well as various proteins and pathogens in varying concentrations. , in this paper, to model the outbreaks, we extensively use the evaporation and settling dynamics of naclwater droplets as a surrogate model of the infectious droplets. stilianakis and drossinos , included respiratory droplets in their epidemiological models. however, they neglected the droplet evaporation dynamics and assumed that characteristic post-evaporation droplet diameters are half of the pre-evaporation droplet diameters based on nicas et al. in the context of the present covid- pandemic, while the role of droplet nuclei and corresponding "aerosol transmission" route are not clear, it is widely accepted that respiratory droplets are definitely a dominant vector in transmitting the sars-cov- virus. this merits a detailed investigation of the evaporation dynamics of respiratory droplets and development of a pandemic model that is explicitly dependent on the respiratory droplet characteristics. as such, the evaporation mechanism of respiratory droplets are laced with complexities stemming from droplet aerodynamics, initial droplet cooling, heat transfer, mass transfer of the solvent and solute, respectively, and finally, crystallization of the solute-a phenomenon known as efflorescence. all these physics of fluids article scitation.org/journal/phf are strongly affected by ambient conditions in which the droplet evaporates. these urgently necessitate a model based on first principles, which connects the detailed evaporation dynamics of respiratory droplets with the pandemic evolution equations. in this paper, a model for the infection rate constant based on collision theory incorporates the evaporation physics of respiratory droplets, ab initio. the droplet evaporation model thus developed is first validated with new experimental results obtained from droplets observed to evaporate in an acoustic levitator. while very interesting insights can be obtained from sessile droplet evaporation, [ ] [ ] [ ] [ ] [ ] after an expiratory event, the floating droplet evaporates in the absence of surface contact. thus, the levitated droplets are similar to the droplets in atmosphere [ ] [ ] [ ] compared to their sessile counterpart. furthermore, the desiccation dynamics necessitates a contact-less environment for the droplet. alongside a droplet evaporation model, a chemical kinetics based reaction mechanism model is developed with final rate equations similar to that yielded by the sir (susceptible, infectious, recovered) model. in general, the resemblance of the equations modeling kinetics to those of population dynamics is well known. however, the rigorous framework (analytical as well as computational) of chemical reaction mechanisms that can at present handle few thousands of species and tens of thousands of elementary reactions seems particularly attractive. this could be utilized toward adding further granularity in the pandemic model, if required large mechanisms can be reduced systematically with mechanism reduction techniques. furthermore, it can be integrated into advectiondiffusion-reaction equations, and their moments could be solved using appropriate moment-closure methods. , however, for any reaction mechanism, the key inputs are the parameters for the reaction rate constant. in our case, one rate constant is shown to be a strong function of the droplet lifetime. therefore, next, the droplet lifetime is evaluated over a wide range of conditions relevant to the ongoing covid- pandemic, and the growth rate exponents (eigenvalues) are presented. the results do not suggest that factors not considered in this paper play a secondary role in determining the outbreak spread. rather, this paper aims to establish the mathematical connection between the pandemic and the respiratory droplet dynamics using a well defined framework rooted in physical sciences. this paper is arranged as follows: first, we provide details of the experiments used to obtain the evaporation characteristics of the water and salt solution droplets. this is followed by the reaction mechanism model that yields the equations for the growth rate and the infection rate constant of the outbreaks. this infection rate constant provides the connection and motivation for modeling the droplet evaporation time scales. next, to evaluate the rate constant, detailed modeling of the droplet evaporation is presented. this is followed by results and discussions. finally, we summarize the approach and findings in sec. vii. the experiments with isolated evaporating droplets were conducted in a contact-less environment of an ultrasonic levitator (tec ) to discount boundary effects, generally present in suspended, pendant, or sessile droplet setups. , the experimental setup with the diagnostics is shown in fig. . a droplet was generated and positioned near one of the stable nodes of the levitator by using a micropipette. the levitated droplet was allowed to evaporate in the ambient condition of the laboratory at ○ c and at about % relative humidity (rh). the transient dynamics of evaporation and precipitation of the evaporating droplet was captured with the shadowgraphy technique using a combination of a ccd camera (nr s , idt vision) fitted with a navitar zoom lens assembly ( . × lens and × extension tube) and a backlit-illumination by a cold led light source (sl , karl storz). a set of ten images at a burst speed of fps is acquired every s for the entire duration of the droplet lifetime. the spatial resolution of the images was ≈ μm/pixel. the temporal evolution of the diameter of the evaporating droplet was extracted from the images using the "analyze particles" plugin in imagej (open source platform for image processing). the final precipitate was carefully collected on carbon tape and observed in the dark-field mode under a reflecting microscope (olympus bx- ). a range of initial droplet diameters varying from μm to μm were investigated in experiments. in this section, we model the infection spread rate using the collision theory of reaction rates, well known in chemical kinetics. the connection between droplets and the outbreak will be established later. in this model, we adopt the following nomenclature: p represents a covid- positive person infecting a healthy person(s) susceptible to infection. the healthy person is denoted by h (who is initially covid- negative), and r represents a person who has recovered from covid- infection and hence assumed to be immune from further infection, while x represents a person who dies due to covid- infection. we consider one-dimensional head on collisions, and the schematic of a collision volume is shown in fig. . here, one healthy person denoted by h with the effective diameter σh is approached by a covid- positive person p of the same effective diameter with an average relative velocity ⃗ vdh. σh can be considered as the diameter of the hemispherical volume of air that is drawn by h during each act of inhalation, which comes out to be approximately . m. it is widely believed that covid- spreads by respiratory droplets resulting from breathing, coughing, sneezing, or talking. thus, we assume that a volume in front of p is surrounded by a cloud of infectious droplets exhaled by p. the droplet cloud is denoted by d, and the maximum cloud diameter is given by σd. clearly, σd should be determined by the smaller of evaporation or settling time of the droplets ejected by p, the horizontal component of the velocity with which the droplets traverse, as well as the dispersion characteristics. in each such cloud, we assume that there are numerous droplets containing the active covid- virus. the velocity of this droplet cloud relative to h is given by ⃗ vdh. in such a scenario, we assume that in a unit volume, there are np infected persons and nh healthy persons. for a collision to be possible, the maximum separation distance between the centers of d (the droplet cloud) and h is given by the collision volume-the volume of the cylinder within which a collision between the droplet cloud of p and air collection volume of h should lie for the collision to occur in a unit time-is given by πσ dh vdh. thus, the number of collisions between h and the droplet cloud d of p, per unit time per unit volume, that will trigger infections, is given by where np and nh represent the number of p and h, respectively. now, given that each collision between p (basically, its droplet cloud d) and h results in conversion of the healthy individual to the infected individual, we can write now, we can define [p] = np/n total and [h] = nh/n total , whereas n total is the total number of people those who are capable of transmitting the infection, as well as accepting the infection per unit volume, in that given volume. this implies where k = n total πσ dh vdh. here, ω is the reaction rate. furthermore, if we assume that the mortality rate is about % for the ongoing covid- pandemic, we can convert the kinetics of infection spread to a complete reaction mechanism given by the following: it is to be recognized that h does not become p immediately on contact with the droplet cloud. the virus must proliferate for a finite time after contact to render a person infectious. a person who has just come in contact with the virus and does not have the capability to infect others yet is denoted by p * . k , k , and k are the rate constants of reactions [r ], [r ], and [r ], respectively. all rate constants must have dimensions of [t] − (inverse of time). clearly, k > k for the rapid outbreak to occur. it is to be recognized that this framework implies that k , the rate constant of the second order elementary reaction [r ] resulting from collisions between the droplet cloud from an infectious individual and healthy individual, is purely controlled by physical effects. the rate constants k and k of the other two first order elementary reactions [r ] and [r ] are essentially decay rates emerging from the time by which the respective concentrations reach e − levels of the initial concentration for the respective reactions. thus, k and k are purely determined by interaction between the virus and the human body. we know that the approximate recovery time from the covid- disease is about days. thus, we can assume k = / day − . we also assume the latency period (not incubation period) to be day; hence, k = day − . given the importance of k in determining the outbreak characteristics, we will refer to k as the infection rate constant. the major contribution of this work is imparting a rigorous physical interpretation to k and calculating it. using eq. ( ), we can write the system of odes for d[p]/dt and d[p * ]/dt as in this paper, we are interested in modeling the initial phases of the outbreaks where [h] ≫ [p]. hence, we can safely assume [h] ≈ [h] , i.e., the concentration of healthy people remains approximately constant during the early phase of the outbreak and is equal to the initial concentration, which is very close to unity at t = , i.e., at the onset of the outbreak. the time of the beginning of the outbreak denoted by t = for a particular location can be assumed to be the day when the number of covid- positive persons equaled . [p] is [p] at t = . then, [p] can be solved as an eigenvalue problem and is given by c and c are constants to be determined from the eigenvectors and the initial conditions [p] and [p * ] . λ , are the eigenvalues. these can be termed growth parameters and are given by by eq. ( ), k = n total πσ dh vdh. as mentioned before, k = day − and k = / day − , which yields λ , = − . ± √ . + k . if k → ∞, i.e., a healthy person becomes infectious immediately on contact with an infectious person, clearly, this model does not yet account for the preventive measures such as "social distancing," "quarantining" after contact tracing, and population wide usage of masks. we will call this "social enforcement." however, it can be included by accounting for the time variation in [h] . social enforcement measures reduce the concentration of healthy, susceptible individuals from [h ] to [hse] where the concentration of healthy population susceptible to infection after implementing strict social distancing (at time t = tse) [hse] < [h ]. in the case of social enforcement, [p] will be given by here, [p] = [p]se at t = tse and λ ,se , λ ,se are the eigenvalues from eq. ( ) with [h] = [hse]. k , the infection rate constant, remains to be completely determined. it is to be recognized that two of the key inputs of k are σdh and vdh since k ∝ vdhσ dh by eq. ( ). as already mentioned, σh is the diameter of the hemisphere from which breathable air is inhaled. σd is the diameter of the droplet cloud. the aerodynamics of the respiratory droplets needs to be analyzed to evaluate these quantities. the droplets ejected during respiratory events, such as sneezing and coughing, co-follow the volume of air exhaled during the event. studies have confirmed that due to entrainment, the exhaled air volume grows in diameter, while its kinetic energy decays with time. specifically, bourouiba et al. showed that initially, for a short duration, the droplets evolve inside a turbulent jet, while in later stages, the jet transitions to a puff. recognizing that the ejected droplets during the respiratory event is surrounded by this dynamically evolving air volume and that the motion of the droplets will be strongly coupled due to the aerodynamic drag, we first model the surrounding air in two parts using the analytical results of the turbulent jet and puff, respectively. the axial location, axial velocity, and radial spread of a transient turbulent jet and puff can be expressed, respectively, as , and where subscripts j and pf denote the jet and puff, respectively. r and u are the radius and axial velocities at a distance x . k is a characteristic constant for the turbulent jet and is reported to be . . at the inception of the respiratory event (t = ), the jet is assumed to have a velocity uj , = m/s and a radius rj , = mm-the average radius of human mouth. the characteristic constants for a puff are a ≈ . and m = (xp , a)/( rp , ). since the continuous ejection of air from the mouth lasts only for the duration of a single respiratory event, the jet behavior persists only for this period and beyond which the puff behavior is observed. the average duration of such events is roughly s. hence, the velocity and the radial spread of the air surrounding the exhaled droplets will be the horizontal displacement (xp) of the exhaled droplet and its instantaneous velocity (up) due to the drag can be solved with where rs is instantaneous radius of the droplet, ρv and ρ l are gas phase and liquid phase densities, μg is gas phase dynamic viscosity, and cd is the drag coefficient, which can be taken as /rep for the gas phase reynolds number, rep = ( ρv|ug − up|rs)/μg < . as it will be stated later, rep for the respiratory droplets were found to be mostly less than . . by solving eqs. ( )-( ) over the droplet lifetime, τ, the axial distance traveled by the droplets, xp, can be evaluated. the average velocity of the droplet cloud relative to p is vd,p = xp/τ. the diameter of the droplet cloud ejected by p can be approximated as twice the radial spread of the exhaled air, σd = rg(t = τ). it is to be recognized that while the above equations are analytically tractable, given the complexities of the associated turbulent jet/puff, a detailed description of the motion of the droplets necessitates time resolved computational fluid dynamics (cfd) simulations in three dimensions. this has been recently reported in ref. , which simulated dispersion of water droplets using a fully coupled eulerian-lagrangian technique including the wind effects. in this paper, we worked with salt solution droplets, accounting for salt crystallization, but did not include wind effects to retain analytical tractability. nevertheless, the results presented in subsection vi b are qualitatively consistent with the cfd results. due to evaporation or settling, the droplet is present only for a short time τ after it has been ejected. therefore, the steady state k can be defined as just like in collision theory, not all molecules are energetic enough to effect reactions; in our case, the droplet cloud is not always present. the last fraction (τ/tc) is the probability that the droplet cloud with the average diameter σd is present. tc is the average time period between two vigorous expiratory events. vdh = (vd,p + vp) + vh. we can assume vp = vh. it is thus apparent that τ appears in σdh, vdh, and in the last fraction in eq. ( ), thereby emerging as a critical parameter of the entire pandemic dynamics. hence, τ merits a detailed physical understanding. given the composition of the respiratory droplets, modeling τ is highly non-trivial and is taken up in sec. v. it is well documented in the literature that an average human exhales droplets (consisting of water, salt, proteins, and virus/bacteria) in the range of μm- μm. , , in this section, we offer a detailed exposition of the evaporation dynamics of such droplets as ejected during the course of breathing, talking, sneezing, or coughing. the small droplets (< μm- μm) have a very short evaporation timescale. this implies that these droplets evaporate quickly (< s) after being ejected. however, the same conclusion does not hold for slightly larger droplets ejected in the form of cloud (> μm). these droplets exhibit longer evaporation time, leading to increased chances of transmission of the droplet laden viruses. in particular, when inhaled, these droplets enable quick and effective transport of the virus directly to the lungs airways causing a higher probability of infection. in general, the smaller droplets (< μm) have low stokes number, thereby allowing them to float in ambient air without the propensity to settle down. for larger droplets (> μm), the settling timescale is very small (∼ . s). in effect, based on the diameter of the exhaled droplets, there are three distinct possibilities: • small droplets (< μm) evaporate within a fraction of second. • large droplets (> μm) settle within a small time frame (< . s), limiting the radius of infection. • intermediate droplets (∼ μm) show the highest probability of infection due to a slightly longer evaporation lifetime and low stokes number. in this work, we particularly focus our attention to the modeling of droplets over a large range of diameters from μm to μm. based on the available literature, we assume that the droplets exhaled during breathing are at an initial temperature of ○ c. the ambient condition, however, vary strongly with geographical and seasonal changes, etc. hence, in the following, we conduct a parametric study to determine the droplet lifetime across a large variation of temperature and relative humidity conditions. the droplet evaporation physics is complicated by the presence of non-volatile salts (predominantly nacl) as present in our saliva. we would also look into simultaneous desiccation of the solvent and crystallization of such salts subsections v a and v b. once exhaled and encountering ambience, the droplet will evaporate as it undergoes simultaneous heat and mass transfer. for the modeling purpose, the exhaled droplets are assumed to evaporate in a quiescent environment at a fixed ambient temperature and relative humidity. in reality, during coughing, talking, or sneezing, the droplets are exhaled in a turbulent jet/puff. however, as shown in eqs. ( ) and ( ), the puff rapidly decelerates due to entrainment and lack of sustained momentum source, rendering the average vd,p to be less than % of the initial velocity. furthermore, since the prandtl number, defined as ratio of kinematic viscosity and thermal diffusivity, is approximately unity (pr = ν/α ≈ . ) for air, we can safely assume that the temperature and relative humidity that the droplets in the puff experience are on average very close to that of the ambient. at the initial stages, the puff will indeed be slightly affected by buoyancy, which will influence droplet cooling and evaporation dynamics. quantifying these effects accurately, merit separate studies, see for e.g., ref. for buoyant clouds. in a higher dimensional model, these could be incorporated. nonetheless, the evaporation rate of the droplet is driven by the transport of water vapor from the droplet surface to the ambient far field. assuming the quasi-steady state condition, the evaporation mass flux can be written asṁ here,ṁ is the rate of change of the droplet water mass due to evaporation, rs is the instantaneous droplet radius, ρv is the density of water vapor, dv is the binary diffusivity of water vapor in air, and αg is the thermal diffusivity of surrounding air. bm = (y ,s − y ,∞ )/( − y ,s ) and b t = cp, l (ts − t∞)/h fg are the spalding mass transfer and heat transfer numbers, respectively. here, y is the mass fraction of water vapor, while subscripts s and ∞ denote the location at the droplet surface and at the far field, respectively. the numerical subscripts , , and will denote water, air, and salt, respectively. cp, l and h fg are the specific heat and specific latent heat of vaporization of the droplet liquid. for the pure water droplet, the vapor at the droplet surface can be assumed to be at the saturated state. however, as indicated earlier, the exhaled droplets during talking, coughing, or sneezing are not necessarily pure water; rather, they contain plethora of dissolved substances. the existence of these dissolved non-volatile substances, henceforth denoted as solute, significantly affects the evaporation of these droplets by suppressing the vapor pressure at the droplet surface. the modified vapor pressure at the droplet surface for binary solution can be expressed by raoult's law, pvap(ts, χ ,s ) = χ ,s psat(ts), where χ ,s is the mole-fraction of the evaporating solvent (here water) at the droplet surface in the liquid phase and χ ,s = − χ ,s . the far field vapor concentration, on the other hand, is related to the relative humidity of the ambient. considering the effects of raoult's law and relative humidity, the vapor concentrations at the droplet surface and at the far field can be expressed as m and m denote the molecular weights of water and air, respectively. for evaporation, the droplet requires latent heat, which is provided by the droplet's internal energy and surrounding ambient. it has been verified that the thermal gradient in the liquid phase is rather small. therefore, neglecting the internal thermal gradients, the energy balance is given by where ts is instantaneous droplet temperature, m = ( / )πρ l r s and as = πr s are the instantaneous mass and surface area of the droplet, ρ l and e l are the density and specific internal energy of the binary mixture of salt (if present) and water, and kg is the conductivity of gas surrounding the droplet. ∂t ∂r |s is the thermal gradient at the droplet surface and can be approximated as (ts − t∞)/rs, which is identical to convective heat transfer for a sphere with a nusselt number of . as such, including aerodynamic effects, the nusselt number is given by nu = + . re . p pr . . the droplet reynolds number, rep, was observed to be mostly less than . , and as such, the aerodynamic enhancement of the nusselt number, i.e., the second term in the right-hand side, is ignored. evaporative loss of water leads to an increase in the salt concentration in the droplet with time. as shown before, pvap(ts, χ ,s ) is a function of the salt concentration in the droplet, which thus must be modeled using the species balance equation, as shown in the following equation: here, y is the dissolved solute (salt) mass fraction in the droplet. m ,out , which represents the rate at which solute (salt) mass leaves the solution due to crystallization, is modeled below. clearly, eq. ( ) shows that as water leaves the droplet, y increases. when y is sufficiently large such that the supersaturation ratio s = y /y ,c exceeds unity, crystallization begins. here, we use y ,c = . based on the efflorescent concentration of g/l reported for nacl-water droplets in ref. . the growth rate of the crystal could be modeled using a simplified rate equation from , here, l is the crystal length. following ref. , for nacl, we find the constant ccr = . × m/s, the activation energy ea = j/mol, and constant gcr = . using this, the rate of change of the crystal mass, which equalsṁ ,out , is given by we note that while crystallization process could involve complex kinetics of solute, solvent, and ions; a well-studied single-step crystallization kinetics has been used here for tractability. it will be shown that this model is able to predict the experimentally studied droplet lifetime reasonably well. the governing equations [eqs. ( )- ( ) ] manifest that several physical mechanisms are coupled during the evaporation process. for ts , > t∞, the droplet undergoes rapid cooling from its initial value. the droplet temperature, however, should eventually reach a steady state limit (wet bulb). this limit is such that the droplet surface temperature will be lower than the ambient, implying a positive temperature gradient or heat input. the heat subsequently transferred from the ambient to the droplet surface after attaining the wet-bulb limit is used completely for evaporating the drop without any change in sensible enthalpy. for a droplet with pure water, i.e., no dissolved non-volatile content, the mole-fraction of the solvent at the surface remains constant at %, and at the limit of steady state, the droplet evaporation can be written in terms of the well-known d law, , where however, for a droplet with the binary solution, the evaporation becomes strongly dependent on the solvent (or solute) molefraction, which reduces (or increases) with evaporative mass loss. the transient analysis, thus, becomes critically important in determining the evolution of the droplet surface temperature and instantaneous droplet size. during evaporation, the mole-fraction of the solute increases and attains a critical super-saturation limit, which triggers precipitation. the precipitation and accompanied crystallization dynamics, essentially, reduce the solute mass dissolved the in liquid phase, leading to a momentary decrease in its mole-fraction. this, in turn, increases the evaporation rate as mandated by raoult's law, which subsequently increases the solute concentration. these competing mechanisms control evaporation at the latter stages of the droplet lifetime. at a certain point, due to continuous evaporation, the liquid mass completely depletes and evaporation stops. the droplet after complete desiccation consists only of salt crystals, probably encapsulating the viruses and rendering them inactive. if the sars-cov- virus would remain active within the salt crystal, also known as droplet nucleus or aerosol, covid- could spread by aerosol transmission in addition to that by droplets. in this paper, we focus on infection spread exclusive by respiratory droplets since the role of aerosols is not clear for transmission of covid- . to validate the model, few targeted experiments were conducted to observe isolated levitated droplets evaporating in a fixed ambient condition. particularly, the droplets with ( % w/w) nacl solution vaporized to shrink to % of its initial diameter during the first stage of evaporation, as shown in fig. . hereafter, a plateaulike stage is approached due to increased solute accumulation near the droplet's surface, which inhibits the diameter from shrinking rapidly. however, as shown in fig. , shrinkage does occur (until ds/ds , ≈ . ) as the droplet undergoes a sol-gel transformation. the final shape of the precipitate is better observed from the micrographs presented in fig. . figure shows the final precipitate morphology for the desiccated droplets. the precipitates display a cuboid shaped crystalline formation, which is consistent with the structure of the nacl crystal. the size and crystallite structure does show some variation, which could be linked with the initial size of the droplet. only precipitates from larger droplets could be collected since smaller sized precipitates tend to de-stabilize and fly-off the levitator post-desiccation. while the precipitate from larger sized droplets tend to yield larger and less number of crystals, smaller droplets seem to degenerate into even smaller crystallites. however, this work does not investigate the dynamics of morphological changes of crystallization in levitated droplets. figure also displays the comparison between results obtained from experiments and modeling. experiments were performed with both pure water droplets as well as with droplets of % salt solutions. experiments have been described in sec. ii. for the pure water cases shown in the left panel, simulation results follow the experiments rather closely. in the pure water case, classical d law behavior could be observed. for the salt water droplets, a deviation from the d law behavior occurs, and droplet evaporation is slowed. this is governed by raoult's law where the reduced vapor pressure pvap(ts, χ ,s ) on the droplet surface results from the increasing salt concentration with time. the evaporation rate approaches zero at about ds/ds , for . (experiments) and . (simulations), respectively. however, the salt concentration attained at this stage exceeds the supersaturation s ≥ required for onset of crystallization. thus, the salt crystallizes, reducing its concentration and increasing pvap(ts, χ ,s ) such that evaporation and water mass loss can proceed until nearly all the water has evaporated and only a piece of solid crystal as shown in fig. is left. it can be observed from fig. that in all cases, the final evaporation time is predicted within % of the experimental values. this suggests that despite the model being devoid of complexities (associated with inhomogeneities of temperature and solute mass fraction within the droplet and simple one step reaction to model the crystallization kinetics), it demonstrates reasonably good predictive capability. it is prudent to mention again that although we have done the analysis for the single isolated droplet, in reality, coughing or sneezing involves a whole gamut of droplet sizes in the form of a cloud. humans expel respiratory droplets while sneezing, coughing, or talking loudly. such droplets have a size range from μm to μm, while the dispersion could depend on the severity of the action. for example, while talking, an average human being will expel ∼ droplets in a size range of μm- μm, but this number goes upto ∼ in the case of sneezing. for any given act (sneezing, coughing, or talking), the highest number of droplets fall in the range between μm and μm, while the smaller or larger droplets (than the above) are comparatively fewer in number. nevertheless, the expelled volume of air contains a very small fraction of liquid droplets. to illustrate this point, the droplets are assumed to be in a uniform dispersion. the total volume of air expelled by a human being is estimated to be vg ∼ . m . the total volume of liquid for a given mean droplet size is simply (nvd,s , ), where n is the total number of droplets of size ds , and vd,s , is the volume of such a droplet. the total volume occupied by droplets of different sizes in a given act of coughing or sneezing is ∑ i nivd s, ,i. thus, the volume fraction (ϕ) of liquid droplets during a given act is ∑ i nivd s, ,i/vg . using size distribution, reported in ref. , one can show that ϕ for sneezing, coughing, coughing with covered mouth, and talking loudly is ppm, ppm, ppm, and scitation.org/journal/phf ppm, respectively. these numbers indicate that respiratory spray is rather sparse, implying that collective evaporation of droplet clusters may not be significant. this also justifies the modeling based on an isolated, contact free droplet. next, we set out to use this model to predict the droplet lifetime characteristics over a wide range of ambient conditions. the droplet evaporation time tevap(ds , ) is calculated from the analysis presented in secs. v a and v b. indeed, the droplet evaporation competes with gravitational settling. the settling time t settle (ds , ) is calculated by accounting for the decreasing diameter using the equation for the stokes settling velocity, the settling time is estimated as that time by which the droplet gets out of the radius from which breathable air is collected-already defined as σh/ in sec. iii. mathematically, t settle is obtained by the following equation: clearly, for any condition, while tevap monotonically increases with ds , , t settle monotonically decreases with ds , . in view of this, it is necessary to estimate the maximum time an exhaled droplet can remain within the collection volume without being evaporated or settled. such a time can be estimated by defining a characteristic droplet lifetime τ, where τ = min{ tevap | tevap ≥ t settle ∀d s, }. ( ) τ is essentially the time where the two curves tevap, tevap as a function of ds , intersect and represents the maximum time a liquid droplet of any size can exist before it is removed either by evaporation or gravity. for a given ambience specified by the ordered pair (t∞, rh∞), ds , corresponding to τ can be defined as dcrit. droplets with ds , > dcrit settle due to gravity, while ds , ≤ dcrit evaporate, earlier than the droplets with ds , = dcrit. while droplets with ds , ≠ dcrit can certainly transmit the disease, those with dcrit establishes the boundaries in terms of the lifetime, cloud diameter, and maximum distance traversed. dcrit is dependent on ambient conditions, i.e., temperature and relative humidity. the distribution of dcrit over a wide range of relevant ambient conditions is shown in fig. (a) . interestingly, at high t∞ and low rh∞, where the evaporation rate is very fast, even a large droplet rapidly shrinks before it can settle. by the same argument at low t∞ and high rh∞, a relatively smaller droplet cannot evaporate quickly; therefore, tevap = t settle is attained for smaller droplet sizes. this explains why we observe large dcrit at high t∞, low rh∞, and small dcrit at low t∞ and high rh∞. the evaporation time of the droplet of diameter dcrit, which has been established as the characteristic lifetime τ of the droplet set, is shown in fig. (b) . despite the different initial sizes, we find that τ is minimum at high t∞ and low rh∞ conditions, whereas it is maximum at low t∞ and high rh∞. at the same time, longer lifetime, i.e., large τ, allows the droplet cloud to travel a longer distance axially (xp) and disperse radially (σd). thus, xp and σd are (d) . this also shows how the minimum required "social distance" represented by xp is not constant but depends on ambient conditions. combining these results, it can be concluded that the size, lifetime, distance traveled, and the radial dispersion of the longest surviving droplet is not constant and is a strong function of ambient conditions. in particular, low temperature and high rh enhance the droplet lifetime significantly. relative humidity strongly affects the droplet lifetime compared to temperature. an increase in droplet lifetime also implies that such droplets stay in the ambient for longer periods and hence travel longer distances as reflected by xp. this implies that such droplets can lead to higher infection propensities. the critical size, droplet lifetime, distance traveled, or size of the droplet cloud for any practical condition are readily obtainable from figs. (a)- (d), respectively. in fig. , we look into the evolution of the normalized mass and temperature of the droplets for two cases named as case a and case b, also identified with black dots in fig. . for case a, (t∞, rh∞) = ( , ), while for case b, (t∞, rh∞) = ( , ). the unit of t∞ is ○ c and that of rh is %. these conditions have been specifically chosen to loosely represent the spring weather in north america and south east asia, respectively, for the early days of the covid- pandemic at both these locations. figure clearly explains why τa > τb. indeed, higher rh at case b implies that the temporary hiatus in evaporation due to reduced vapor pressure is reached at a higher water mass load of the droplet than at the case a condition. in both cases, this occurs at about s. however, the higher temperature in b results in faster crystallization kinetics due to the arrhenius nature of the equation given by eq. ( ) , which causes an eventual faster crystallization rate than at a. figure clearly shows that although the knee in the solvent depletion profiles are attained at the same time, it is the crystallization and simultaneous desiccation dynamics that governs the eventual difference in lifetime of the droplets at two conditions. it remains to be seen whether this result holds for a detailed crystallization reaction mechanism. the temperature evolution plots shown in the right panel of fig. also reveals how the droplet initially exhaled at ○ c rapidly cools to the corresponding wet-bulb temperature to subsequently allow heat transfer into the droplet leading to evaporation. however, as the salt concentration reduces due to crystallization, the temperature rises subsequently above the corresponding wet-bulb limits. with the droplet lifetime available over a wide range of conditions, the corresponding infection rate constant and eigenvalues given by eqs. ( ) and ( ) could be evaluated. just to recapitulate, τ determines the infection rate constant k by eq. ( ) . in turn, k affects the exponents of the time dependent infection equation [eq. ( )], the growth parameters-eigenvalues λ , λ through eq. ( ) . the contours of λ , λ , and k as a function of t∞ and rh∞ are shown in figs. (a)- (c), respectively. the direct correspondence between τ and k is immediately apparent upon comparing the respective figs. (b) and (c). the infection rate constant is highest at low t∞ and high rh∞ where the droplet evaporation is slowed due to the slow mass loss rate and enhanced crystallization time. on the other hand, faster droplet evaporation leads to small infection rate constant values at high t∞ and low rh∞. the temperature and relative humidity dependency of the eigenvalues λ and λ are shown in figs. (a) and (b), respectively. the direct correspondence of figs. (a) and (b) with fig. (c) and fig. are established through λ , = − . ± √ . + k given by eq. ( ) . it should, however, be noted that due to the inherent negative sign of λ , its influence on determining the growth rate of the infected population is rather limited. it is λ that primarily drives the growth of the infected population as apparent from eq. ( ). from fig. (a), we observe that for a fixed t∞, λ increases with rh∞, while for a fixed rh∞, λ decreases with t∞. furthermore, we observe that the iso-λ contour lines bend and converge at rh∞ > %. this means that for rh∞ > %, large λ > . is expected over a wider range of temperatures between ○ c < t∞ < ○ c. this is a manifestation of the greatly reduced evaporation potential-the difference between water vapor concentration on the droplet surface and in the ambient at high rh∞ conditions. this is further reflected in the dramatic difference in the rate ratio-the ratio of the cumulative number of positive cases on a particular day to the cumulative number of positive cases seven days before: np/np , in fig. (d) . this figure has been arrived at by assuming the local population density to be km − . furthermore, we calculate tc in eq. ( ) as tc = × /nexp. nexp is the number of infecting expiratory events per person per day and is assumed to be based on the coughing frequency of - in normal subjects. we find that purely based on ambient conditions, implying all other factors have been held constant, the rate ratio can be different by an order of magnitude between (t∞, rh∞) = ( , ) vs ( , ) . practically, such a contrast might be less apparent in real data in which other important factors such as population density, social enforcement, travel patterns, and susceptible supply exert significant influence. respiratory flow ejected by human beings consists of a polydisperse collection of droplets. in this paper, we have presented article scitation.org/journal/phf a model for the early phases of a covid- like pandemic based on the aerodynamics and evaporation characteristics of respiratory droplets. the model and its inter-dependencies on the different physical principles/sub-models are summarized in fig. . to our knowledge, this is the first model that utilizes the structure of a chemical reaction mechanism to connect the pandemic evolution equations with respiratory droplet lifetime by first principles modeling of the reaction rate constant. however, it must be recognized that the model assumes conditions where transmission occurs solely due to inhalation of infected respiratory droplets alongside many other simplifying assumptions. the evolution of the droplets is characterized by a complex interaction of aerodynamics, evaporation thermodynamics, and crystallization kinetics. as such, after being ejected, smaller droplets attain the wet-bulb temperature corresponding to the local ambience and begin to evaporate. however, due to the presence of dissolved salt, the evaporation stops when the size of the droplet reaches about %- % of the initial diameter, but now, the droplet salt concentration has increased to levels that trigger onset of crystallization. of course, these processes compete with settling-the process by which larger droplets fall away before they can evaporate. the smaller of the two, complete evaporation time and settling time, thus dictates the droplet lifetime τ. the infection rate constant derived using collision theory of reaction rates is shown to be a function of the respiratory droplet lifetime (τ), where τ is sensitive to ambient conditions. while the infection rate constant in reality is dependent on numerous parameters, the present approach allows us to compute its exclusive dependence on ambient conditions through respiratory droplet modeling. we find that the respiratory droplets exclusively contribute to the infection growth parameters and infection growth rate, which decrease with ambient temperature and increase with relative humidity. as such, the model could be used for providing fundamental insights into the role of respiratory droplets in covid- type viral disease spread. furthermore, the model could be used, with extreme caution and in 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sars-cov- pandemic the authors thank professor chung k. law the data that support the findings of this study are available from the corresponding authors upon reasonable request. key: cord- -kcjnjq authors: kusunose, kenya; matsunaga, kosuke; yamada, hirotsugu; sata, masataka title: identifying the extent of oral fluid droplets on echocardiographic machine consoles in covid- era date: - - journal: j echocardiogr doi: . /s - - - sha: doc_id: cord_uid: kcjnjq nan covid- is an ongoing pandemic worldwide [ ] . one possible mechanism for the spread of this virus is an aerial transmission via droplets generated during speech. in the setting of echocardiography, the risk of infection is particularly high because observers must be in close proximity to the patient. thus, personal protection is crucial in the covid- era [ ] . an important infection prevention method is equipment care. the machine console is where the observer touches the most, but the extent of where droplets could possibly spread is not well examined. the aim of this study was to identify the extent of oral fluid droplet spread on echocardiographic machine consoles, after observers were speaking in english or japanese. to count the droplets generated during speech on the console, we utilized liquid riboflavin (vitamin b ). adding tablet riboflavin ( mg) to water ( ml) and mixing it created a liquid which emitted bright green light when exposed to handheld ultraviolet lamps ( nm). two observers without surgical masks repeated the words "inhale, exhale, hold" (the words often used during examinations) in english and japanese, in front of echocardiographic machine (eub- , hitachi medical corporation, japan) after ingesting the liquid with volunteers lying on your left side echocardiography. the distance between the observer's face and the echocardiographic machine console was - cm. the surface of the console was divided into equal segments, and droplets were counted in each part. this process was repeated ten times for each observer and the droplets were counted. continuous data are expressed as the mean ± standard deviation. finally, two observers with surgical masks repeated the same words to check the droplets on the surface of the console. we compared the number of droplets between english and japanese using an unpaired student's t-test. all statistical analyses were performed with spss . (ibm corp., armonk, ny, usa) and the figure was made by origin software b (lightstone corp., tokyo, japan). p < . was considered statistically significant. when surgical masks were not worn, the total counts of droplets were for japanese and for english, with no significant difference in the counts of droplets for each segment between the two languages (table all p > . ). figure a shows the examples of droplets with fluorescent lamp and ultraviolet lamp. all droplets were clearly detected by the ultraviolet lamp and many droplets (over counts) were observed after three repetitions of the same speech. figure b shows the distribution map for the droplets on the console of ultrasound machine. the place where most droplets were counted was at the front right side in both languages. the droplets after english speech reached slightly farther than those after japanese. it was also important that no droplets were detected on the console when surgical masks were worn in this setting, although it is unlikely that examinations would be performed with either the sonographer/cardiologist scanning or the patient not wearing a mask in the current covid era. the main findings of this study were ( ) many droplets were spread by speech, with the front right side of the console particularly contaminated; ( ) there was no significant difference for the count of droplets between english and japanese; ( ) mask usage can significantly cut down droplet spreading by speech. to the best of our knowledge, this is the first report to assess the spread of the droplets generated by speech on the surface of an echocardiographic machine using visualized methods. the recent study showed that the "th" sound in the word "healthy" was a significant generator of speech droplets [ ] . in our study, the "ex" sound in the word "exhale" and the "d" sound in the word "hold" easily generate droplets. we may need to pay attention to what or how we speak when performing echocardiographic exams. our model assessed the potential of dispersing viruses by sonographer or echocardiography with covid- in front of the echo machine. we could not assess the droplets generated during speech by patients infected with covid- . although the real object of interest would be droplet reach/distribution emanating from the patient, the actual spread range of the droplets exhaled by the patient remains unclear. we did not assess aerosols because special tools are needed to visually detect micro-sized droplets. considering the existence of smaller droplets and aerosols, the actual reach of droplets can expect to be much wider in the clinical setting. the important thing is that all personnel involved in performing the echocardiogram of a patient with covid- or at risk for having covid- wear masks in addition to other personal protective equipment. when they and the patient are wearing masks, there is reduced risk of the passage of the droplets that our experiment generates. in conclusions, sonographers, physicians, and all other medical staff should strive to decrease their infection risk in the echocardiographic laboratory [ ] . based on our results, it is important to keep the following points in mind when performing echocardiography. conflict of interest kenya kusunose, kosuke matsunaga, hirotsugu yamada, and masataka sata declare that they have no conflict of interest. human rights statement and informed consent all procedures followed were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the helsinki declaration of and later revisions. due to the anonymous nature of the data, the requirement for informed consent was waived by our institutional review board. coronavirus disease (covid- ) information for cardiologists-systematic literature review and additional analysis ase statement on protection of patients and echocardiography service providers during the novel coronavirus outbreak: endorsed by the american college of cardiology visualizing speechgenerated oral fluid droplets with laser light scattering review of the efforts of the japanese society of echocardiography for coronavirus disease (covid- ) during the initial outbreak in japan key: cord- -mtfe uq authors: chao, c.y.h.; wan, m.p.; morawska, l.; johnson, g.r.; ristovski, z.d.; hargreaves, m.; mengersen, k.; corbett, s.; li, y.; xie, x.; katoshevski, d. title: characterization of expiration air jets and droplet size distributions immediately at the mouth opening date: - - journal: j aerosol sci doi: . /j.jaerosci. . . sha: doc_id: cord_uid: mtfe uq size distributions of expiratory droplets expelled during coughing and speaking and the velocities of the expiration air jets of healthy volunteers were measured. droplet size was measured using the interferometric mie imaging (imi) technique while the particle image velocimetry (piv) technique was used for measuring air velocity. these techniques allowed measurements in close proximity to the mouth and avoided air sampling losses. the average expiration air velocity was . m/s for coughing and . m/s for speaking. under the experimental setting, evaporation and condensation effects had negligible impact on the measured droplet size. the geometric mean diameter of droplets from coughing was . μm and it was . μm for speaking (counting – ). the estimated total number of droplets expelled ranged from to per cough and – for speaking. the estimated droplet concentrations for coughing ranged from . to . cm(− ) per cough and . – . cm(− ) for speaking. expiratory droplets are potential carriers of pathogens that cause airborne diseases. expiratory droplets are polydispersed and the size of the droplets has high impact on the disease transmission process. smaller droplets evaporate quickly and becomè droplet nuclei'. droplet nuclei can remain airborne for long periods of time and can be dispersed widely by following the airflow pattern. airborne mode transmission refers to infection via inhalation of these airborne pathogenic particles. larger droplets settle out of the air more quickly but, due to the larger size, a vast majority of expelled pathogens are carried in the large droplets. infection via direct spray of large pathogen-laden droplets onto mucous membranes or conjunctiva is known as droplet mode transmission. droplet size also affects the infectivity of pathogen-laden droplets. although larger droplets have higher pathogen-carrying capacities, their ability to penetrate deep into the respiratory tract is lower than that of smaller droplets. smaller pathogen-laden droplets have higher infectivity (nicas, nazaroff, & hubbard, ) compared to the larger ones for diseases that have the lower respiratory tract as the target infection site (e.g., tuberculosis). droplet size is a key factor for the disease to be transmitted and for the size of the spreading zone. tuberculosis, for example, can be transmitted via the airborne route and, thus, can have a wide spreading zone depending on the airflow conditions. diseases such as influenza and severe acute respiratory syndrome (sars) are primarily transmitted via the droplet mode. persons in close contact with the source patient are considered at high risk (hawkey, bhagani, & gillespie, ) . given the importance of droplet size in disease transmission, size profile information of droplets expelled during expiratory actions is of primary interest. over the past few decades, different methods were employed to measure the size profiles of expiratory droplets and different findings were reported. most early studies (e.g., duguid, ; loudon & roberts, ) used collection media (e.g., glass slides and filters) with subsequent microscopic analysis of the expiratory droplets collected on the media. droplets measured by these methods were mainly in the supermicron size range. sampling-based optical particle counters were employed in some more recent studies (e.g., fairchild & stamper, ; papineni & rosenthal, ) . most of the droplets measured were in the submicron size-range in their studies. another recent study by yang, lee, chen, wu, and yu ( ) , which also employed sampling-based optical particle counters, reported droplet size spectra spanning from about . - m, with the average mode at . m during coughing. though different methods were employed, a common problem of these previous studies was that the expiratory droplets were not measured immediately at the mouth/nose exit. instead, the expiratory droplets went through evaporation, dilution, sampling losses and other influences from the environment before being measured or collected, posing error and limitations in estimating the droplets size profile immediately at the mouth/nose exit (or the`original' size distribution). remote sensing techniques may be possible solutions since they do not require air sampling and the sensing volume can be placed very close to the mouth/nose without disturbing the expiratory flow. jennison ( ) conducted such measurements using high-speed photography. however, this technique requires high magnification to resolve small droplets, restricting the ability to detect small droplets and the size of the field of detection (only droplets of larger than m were detected in the study by jennison, ) . the more recently developed interferometric imaging technique overcomes these shortcomings to a great extent (glover, skippon, & boyle, ) . interferometric imaging uses de-focused images of the droplets instead of focused images to lower down the magnification requirement. scattering properties of droplets under the illumination of coherent optical radiation are analyzed using the mie scattering theory to determine droplet size. this method is sometimes called the imi (interferometric mie imaging) method. this study aimed at measuring the expiration air jet velocities and the size profiles of expiratory droplets during speaking and coughing in close proximity to the mouths with the help of the piv (particle image velocimetry) and the imi method. total droplet counts and number concentrations of the droplets would also be estimated. the experiments were conducted in an expiratory droplet measurement setup at the international laboratory for air quality and health (ilaqh), queensland university of technology (qut). the setup was modified from the expiratory droplet investigation system (edis) developed by qut to fit the installation of the imi and piv instruments. fig. shows the schematic of the setup related to the imi and piv experiments. the setup consisted of a mm diameter ( mm internal diameter)× mm long acrylic glass tube supported on a rack mount and a chair for the volunteers. both ends of the tube were open and there was no mechanically induced background airflow in the tube. a mm wide laser safety shield with a mm× mm opening was installed at one end of the tube. the center of the mm opening was mm above the bottom interior of the tube. the safety shield also helped the volunteers to position their head correctly by leaning their head against the shield and placing their mouths on the opening. the safety shield was made from a -mm thick galvanized steel base plate covered with light-absorbing black-out material (edmunds optics, flock paper # ). the bottom of the tube was also covered with the black-out material to stop the laser sheet and to avoid laser light ray reflection. during the measurements, volunteers were asked to lean their heads on the safety shield and to place their mouths on the mm opening. the chair was mounted on a motorized seat lift to allow the volunteers to adjust the height to the correct position. all volunteers were asked to wear laser safety goggles (od at nm, yamamoto) throughout the measurements. the setup was placed inside an air-conditioned room so that the air temperature and relative humidity (rh) inside the tube remained fairly stable. the air temperature and rh inside the tube were monitored in real-time by a digital thermo-hygrometer. the air temperature and rh averaged from all experiments were . • c and . %, respectively. all the side walls and windows of the room were covered with black cardboard paper with rough surface finishing to avoid refracted light rays. the door of the room was interlocked with the power supply of the laser source. the laser power supply could be switched on only if the door was fully closed. detailed descriptions and derivations of the imi technique and sizing calculation are provided by glover et al. ( ) and glantschnig and chen ( ) . briefly, when there is a laser light ray illuminating a transparent droplet in a flow field, due to refraction and reflection, the incident laser light ray is split into several rays. the reflected and refracted light from the droplet is dominant in the wide-angle forward-scatter region, around - • . at an observation angle in the off-axis alignment, the two components of the scattered light appear to emanate from small spots. the two spots are observed as glare points on the focal plane. on the non-focal plane, the two rays interfere with each other and the regular fringes are easily observed, and their origin can be understood in terms of a simplified geometric theory (glantschnig & chen, ) . the fringe spacing can be related to the droplet diameter by the following equation: when a set of fringes can be observed for individual droplets, they provide a potentially accurate measurement of the droplet diameter. for the imi measurement, the laser light source and the sheet optics with a polarizer were mounted above the tube that produced a laser light sheet to cut downward through the tube diameter, perpendicular to the direction of the expiration jets (cut through the cross section of the expiration jet). the laser light source was a double-pulsed nd:yag laser at nm wavelength (new wave research, solo ii), operated at mj with a pulse width of - ns. the sheet optics produced a laser sheet with an aperture angle of . • . the thickness of the laser sheet was about mm. a ccd camera (lavision, imagerintense) was placed inside the tube at the downstream of the laser sheet. the camera was aligned at an observation angle of • to the laser sheet. the observation angle of the camera was monitored by a direct reading dial inclinometer (empire) attached on the camera. the progressive-scan, dual-frame ccd camera had a resolution of × pixels and a maximum frame rate of /s. the exposure time of each image was s. a macro lens (zeiss makro-planar t * . / ) was mounted on the ccd camera to provide a magnification ratio of : . a circular aperture of mm diameter was mounted in front of the lens to produce de-focused droplet images of about pixels in diameter. the laser source and the camera were synchronized by a pc-based control system (lavision, davis ). the lower size detection limit of the imi system was about m. the front end of the lens was about mm away from the laser sheet. the measurement plane was . mm× . mm (w×h). the center of the measurement plane was aligned with the center of the mouth opening on the laser safety shield. imi measurements were made at two distances, and mm, from the mouth. the imi system could only measure transparent droplets. the disturbance by background aerosol to the measurement was essentially screened out. a measurement of background aerosol by aerodynamic particle sizer (aps) showed that the majority of them were smaller than . m in size with an average concentration of . /cm . they were smaller than the lower size detection limit of the imi system. the same laser source and ccd camera were used for the measurements of the velocity of expiration air jet by piv. for the piv measurements, the laser sheet was twisted by • to align along the direction of the expiration air jet. the laser sheet aperture angle was adjusted to . • to produce a wider laser sheet. the camera was placed at the side of the tube and aligned at a o observation angle to the laser sheet. an objective lens (nikkor mm/f . d) with a nm optical filter was mounted on the camera. the measurement area was mm× mm (w×h), located immediately in front of the mouth opening. the piv images were taken in dual-frame pairs for cross-correlation post-processing. the images were taken at a frequency of pairs/s. at the camera's viewing position, an opening was made on the tube wall and a mm× mm planer acrylic glass window was fitted on the opening to avoid image distortion by the curved surface of the tube. flow seeding was provided by an aerosol generator (lavision, aerosol generator) using saline solution. the experiments with volunteers and the use of the laser setup were approved by the human research ethics committee and the safety office of queensland university of technology. eleven healthy volunteers ( men and women) were recruited via a broadcast email invitation with a small financial reward. the volunteers were university students and postgraduate research students (under years old). smokers, asthma sufferers, people who were experiencing illness, who had recently experienced expiratory problems or were likely to experience discomfort in confined spaces were excluded. every volunteer was asked to cough and to speak following a standard protocol. when the volunteer was seated comfortably in the correct position with his/her mouth placed at the opening of the safety shield, they were asked to speak by counting - times loudly and slowly with a pause after speaking each number. the volunteers produced expiration air jets in the horizontal forward direction with the help of the safety shield. the volunteers were allowed to take a brief rest after finishing every round of speaking - . after rounds of counting - were finished, the volunteers were given a -minute break and they were allowed to drink water. after the break, the volunteers were asked to cough times during the cough test. they were instructed to close their lips before each cough. therefore, the volunteers were well-prepared before each cough and started each cough with same mouth shape. the volunteers were allowed to take a brief rest and drink water whenever they needed to during the cough test. every volunteer was asked to conduct two rounds of tests following this protocol. the first round was for measurement at mm from the mouth opening and the second round was for measurement at mm. a -min break was given to the volunteers after finishing the first round to allow time for the experimenters to move the imi system from the mm to the mm distance and to realign the optical setup. piv measurements were made on two volunteers (one man and one woman). the coughing and speaking protocol was the same as in the imi measurements except that the volunteers were asked to do one round of coughing and one round of speaking only. the maximum expiration air velocity during coughing by the male volunteer was . m/s and that by the female volunteer was . m/s. the average expiration air velocity during coughing was . m/s. during speaking, the maximum expiration air velocity was . m/s for the male and . m/s for the female volunteer, with an average velocity of . m/s. example of the measured air velocity field during coughing and speaking. during coughing, a high velocity core of about mm in diameter was formed at the mouth exit. a significant gradient of air velocity can be seen from the center of the jet towards the outer of the jet envelope. entrainment of the surrounding air by the cough jet could be found along the jet making the jet envelope expand. the high momentum of air expulsion during coughing produced an air jet having a throw even longer than the viewable area of the camera. comparatively, the initial air jet velocity was much lower during speaking so that the throw of the air jet was about mm in the example shown in fig. . air entrainment was also observed in the speaking case. table shows the average count of droplets per person during coughing and speaking at the two distances from the mouth opening. the coughing droplet count was aggregated across coughs while the speaking droplet count was aggregated across times of counting - . the standard deviation of the -volunteer data pool is also shown. the droplets were classified into size classes as adopted from duguid ( ) . narrower size classes were used for smaller sizes of droplets since most of the droplets measured were in the lower size end. during coughing, the size class that has the highest number count was m at the two measurement distances. at the mm distance an average total of droplets were counted in coughs but this average reduced to droplets at the mm distance. the size class that had the highest droplet count for speaking was also m. however, the number of droplets was much smaller with speaking, compared to coughing. an average total of droplets were counted at the mm distance after counting - times. the average total number of droplets per person was reduced to at the mm distance. the observation of having the same size class that had the highest droplet count for coughing and speaking was similar to that reported in duguid ( ) . however, in duguid ( ) , this size was in the - m size class. another study (papineni & rosenthal, ) reported that highest counts were found in the size class of less than . m for both talking and coughing. the measured droplet size profiles are presented in terms of df n /d ln d p and are fitted by the log-normal distribution as shown in fig. a and b. the geometric mean (gm) diameters are also shown for comparison. although the droplet size peaked at m for both speaking and coughing, the gm diameter was larger for speaking compared to that of coughing ( . m vs . m at the mm distance). this suggests that the expulsion of air at higher velocity during coughing might promote the production of smaller droplets compared to the lower expiration velocity experienced during speaking. the results reported by duguid ( ) and loudon and roberts ( ) are also plotted on fig. for comparison. it shows that the gm diameters obtained in the current study were fairly close to that reported by duguid ( ) but differed rather significantly from that reported by loudon and roberts ( ) . fig. a and b also show that the gm diameter reduced modestly at the mm distance when compared to the mm distance. the reduction in the gm diameter might be caused by the shrinkage of the droplets by evaporation but this hypothesis is questionable since the traveling time might be very short considering the high velocity of the expiration jets. the rh of the surrounding air might still be high under the influence of the expiration jet. another reason could be that the droplets became more widely dispersed at the mm distance. the chance for capturing the large droplets by the camera became even less compared to the mm distance. expiratory droplets experience evaporation/condensation once they are produced and introduced into the air, leading to changes in droplet size. in the current study, droplet measurements were made at and mm from the mouth. the effects of evaporation/condensation on the droplet size at these two distances were estimated to access if the current results are representative of the`original' size profile. for such estimation, information about the surrounding air temperature and rh along the trajectory of the droplets is essential. numerical simulations were performed for the coughing and speaking cases. a twodimensional numerical geometry with dimensions adopted from the expiratory droplet investigation setup ( mm× mm) was used. an opening of mm in diameter was created at the position corresponding to the mouth position in the experimental setup. one mm hexahedral meshing was generally used in the geometry with grid adaptations near the tube walls to keep the y + value of the first layer of mesh within - . the standard log-law wall function was adopted for the turbulence near-wall treatment. the numerical geometry was constructed and meshed using the gambit (version . ) pre-processor. conservation equations of mass, momentum and energy plus the species transport equation for water vapor were solved using the simple algorithm and the second-order upwind solution scheme by fluent (version . ). the density of the air-water vapor mixture was set to follow a second-order polynomial function of temperature to capture the buoyancy effect. inputs of the numerical simulations are summarized in table . the profiles for the predicted horizontal air velocity along the center-line of the mouth opening up to the mm distance are shown in fig. a . the figure shows that the changes in horizontal air velocities at the two measurement distances were very modest compared to that at the mouth opening. this suggests that the two droplet measurement distances, and mm, were essentially within the core zone (or zone in the classical jet theory, rajaratnam, ) where the center-line velocity is the same as the jet's initial velocity. fig. b shows the numerically predicted air temperature and rh at horizontal distances of up to mm from the mouth opening. the figure shows that, at the mm distance, the air temperature and rh were the same as at the mouth exit ( • c and %, respectively) for both coughing and speaking. the rh was reduced by about . % at the mm distance for coughing but, for speaking, the air became slightly supersaturated (rh > %) at this distance. this happened because the warm and saturated air front of the exhalation air jet met with the cooler surrounding air. in reality, this may trigger the nucleated condensation of water droplets and may lower the rh back to the saturation state but modeling this rather complex phenomenon was not the intention of the current simulations. considering that the solutes might lower the vapor saturation pressure on the droplet surface, the droplets were more likely to grow by condensation rather than shrink by evaporation. the evaporation/condensation of droplets was estimated using the model proposed by kukkonen, vesala, and kulmala ( ) with some simplifications. the models for diffusive mass flux of vapor from a droplet surface and droplet temperature were and the effect of forced convection due to the difference in velocity between the droplets and the surrounding air was neglected in this estimation since the initial air velocity was more or less maintained throughout the -mm distance, as shown in fig. a . however, it is worth noting that significant velocity difference between the droplets and the air may develop at longer distances. the convective heat and mass transfers should be considered if a longer traveling distance is concerned. dependence on temperature by the vapor diffusion coefficient was not considered since such a correction would be less than % under atmospheric conditions (kukkonen et al., ) . radiation heat exchange between the droplets and the surroundings was also neglected. the effect of the solute on the saturation vapor pressure on the droplet surface was included using raoult's law: the expiratory fluid was considered as a saline solution with nacl content of mm (nicas et al., ) . this solute content led to about . % drop in the saturation vapor pressure on the surface of freshly produced expiratory droplets. the effect of other non-volatile components, e.g., glycoprotein, on the hygroscopic behavior is still uncertain and was ignored in this estimation. the temperature and vapor pressure of the surrounding air along the trajectory of the droplets were taken from the fluent simulation results. the system of equations was numerically solved by the fourth-order runge-kutta method. table shows the average number count per person before and after the evaporation/condensation correction at the mm distance. changes in average number were found only for droplets smaller than m for speaking and m for coughing by the correction. this is because the rate of change in droplet size was inversely proportional to the droplet size as indicated in eq. ( ). the average number for the smallest size class increased while the average number decreased for larger size classes. this indicates that the droplets experienced growth by condensation during their travel. however, the change in size distribution was minor due to the short traveling time and the small difference in vapor pressure between the droplet surface and the surroundings. the traveling time for reaching mm was . ms for coughing and . ms for speaking, as estimated from the expiratory air jet velocity. this estimation suggests that the hygroscopic property of the droplets was not the reason for the reduction in the gm diameter measured at mm compared to mm. droplets falling out of the imi measurement area by gravitation settling was also not likely to be the major reason. this can be seen by a simple estimation of a free falling object. the maximum droplet traveling time to the measurement positions was about ms. the downward distance traveled by a free falling object without air resistance after ms can be calculated by y = ( / )at . with a gravitational acceleration, a, of − mm/s , at ms, y = − . mm, this is shorter than half of the vertical height of the imi measurement area, . mm/ = . mm. the falling distance should be even less in reality due to air resistance. from the above analysis, the change in gm diameter could be caused mainly by the wider dispersion of droplets at the mm distance induced by the expansion of the air jet. the estimated evaporation/condensation did not affect the size distribution at the mm distance since the traveling time was even shorter than that for the mm distance. the traveling time for reaching mm was . and . ms for coughing and speaking, respectively. these results suggest that the size distribution obtained at the mm distance may essentially represent the`original' size distribution at the mouth opening. the measurement volume of the imi system covered a . mm× . mm plane that was mm thick (about mm in volume), which is much smaller than the expiration jet envelope. therefore, the imi measurement results can only give the statistical size distribution. to estimate the total number of droplets produced in each of the activities, two projection methods were used. one method was to divide the total volume of droplets produced by the statistical size profiles obtained by imi. this method requires information about the total volume of droplets produced for the particular expiratory action tested but this information is rare. zhu, kato, and yang ( ) reported that the total mass of expiratory droplets in a cough was . mg but no data for speaking was reported. total expiratory droplet volumes estimated from the droplet size profile reported by duguid ( ) and loudon and roberts ( ) may also be used for this purpose. this is because the methods employed by these two studies were intended to collect all the expiratory droplets using collection media instead of using sampling-based instruments (e.g., papineni & rosenthal, ; yang et al., ) . employing the data from studies using collection media should give better estimations of the expelled fluid volume compared to those using sampling-based instruments. this is because the sampling-based instruments tend to miss the larger droplets but they are the major contributors to the total expelled fluid volume. the speaking activity in duguid's ( ) and loudon and roberts's ( ) studies was also counting from to , as in the current study. the droplet number concentrations in the expiration jets were roughly estimated by assuming that a tidal volume of air ( ≈ . l for adults) was exhaled in a cough. it was also assumed that the air volume exhaled per vocalization during speaking followed the ratio of expiration jet velocity obtained from piv measurements. therefore, for example, an air volume of ( . / . )× . l was exhaled by counting`one'. three times of this volume was exhaled when counting`ninety-four'. table shows the estimated total droplet numbers using the measured size profile at mm. for coughing, the estimated total number ranged from to per cough using different data from the literature. however, due to the large difference in the reported droplet size profiles for speaking between duguid ( ) and loudon and roberts ( ) , the estimated total number differed significantly for using the data from different studies. the estimated droplet number concentrations are shown in table . another estimation method was to divide the total number of droplets captured by the total laser measurement volume. for example, if a total of droplets was captured in a measurement in which imi images were taken, the droplet concentration would be /( × mm ) = . × − mm − . the estimated droplet number concentrations using this laser volume method are shown in table , in the column marked`l.v.'. using the exhalation air volumes defined above, the estimated total number of droplets expelled was per cough and droplets were expelled when counting - . this estimation method does not require information on the total expelled liquid volume (or mass), which is uncertain. however, in determining the total laser measurement volume, the images taken between coughs (or vocalizations) and during pauses were also counted. this could induce uncertainties into the estimation. another possible source of error is that the droplet concentration in the measurement volume did not necessarily represent the droplet concentration in the entire exhalation jet envelope. the maximum droplet concentration found in the current study was . /cm . with a maximum traveling time of around ms, the likelihood of droplet key: d-refers to duguid ( ) ; l&r-refers to loudon and roberts ( ) ; and z-refers to zhu et al. ( ) . key: d-refers to duguid ( ) ; l&r-refers to loudon and roberts ( ) ; z-refers to zhu et al. ( ) ; and l.v.-estimation using laser measurement volume. coalescence, that might subsequently affect the size distribution measurements, was estimated to be insignificant via a simple scale analysis. both of the estimation methods have limitations. the above estimations are by no means comments on the accuracy of droplet number and total expiration droplet volume measurements provided in previous studies. however, our results suggest that further studies are needed for better estimation of total expiratory droplet number during different expiratory activities. this information is important for estimating the amount of pathogens disseminated to the air by the source patient, which is crucial for exposure and infection risk analysis studies. according to eq. ( ), the refractive index of the droplet material and the camera's observation angle are two parameters that can affect the calculation of the final droplet size. in the current study, the refractive index of water (n = . ) was used in the calculation but the presence of solutes in the expiratory fluid may alter the refractive index. using eq. ( ), the effect of shifting the refractive index on the calculated droplet size was estimated. the estimation is shown in fig. for n between . and . . it shows that the difference in the calculated droplet sizes within this range of refractive index compared to the calculated droplet size using n = . are within %. a major change in the solute content due to evaporation/condensation was not likely according to the estimations discussed in section . . using the same method, the difference in the calculated droplet size due to errors in observation angle measurements is estimated and shown in fig. for a range of ± • for the preset observation angle, • . the figure shows that the difference in calculated sizes is within ± . % for this error range of observation angle measurement. it is also worth noting that the lower size detection limit of the imi system was about m. several other studies employing sampling-based instruments reported size peaks that are outside the imi detection limit (e.g., < . m for both coughing and talking by papineni & rosenthal, ) , which suggests that the imi system might not cover the entire size range of expiratory droplets and other size modes exist outside the imi detection limit. another set of measurements using aps conduced in the edis showed that it was the case. the aps measurements found size modes at . m for different expiratory activities. details of the aps measurements are reported in another paper (morawska et al., ) . discrepancies between results obtained by different instruments in the similar measurement setup indicate that instrumentation is still a major limitation in this kind of research. an instrument that is able to cover the entire size range of expiratory droplets with minimal sampling loss is still lacking. the volunteers followed certain protocols when coughing and speaking. although real human subjects were involved, the question of how representative the`artificially produced' expiratory activities in the current study of the real expiratory activities is worth further considering. for example, the volunteers were asked to close their lips before each cough. they were also allowed to drink water any time as they need. from the experimenters' observation, each volunteer drank around - cups (regular foam coffee cup size) of water in each set of experiments. these practices might have an impact on the expiration jet velocity and droplet size distribution, compared to coughs made in other mouth patterns, e.g., coughing several times in a row without closing the lips. this study involved healthy volunteers only. the speaking activity tested in the current study was counting - . different mouth movements can be involved if different speaking patterns are tested. different speech patterns may affect the droplet size distribution and expiration jet velocity as well. on the other hand, a recent study by hersen et al. ( ) indicated that the size distributions of exhaled respiratory aerosols from symptomatic individuals were different from that exhaled by healthy individuals. however, a specific size distribution for symptomatic individuals was not identified in their study and the reason for causing such a difference remains unclear. this also gives rise to the question that the exhalation jet velocity could be different according to health conditions. the size distributions of the droplets expelled during coughing and speaking (counting - ) were measured by a series of experiments involving human subjects. imi method was used to obtain droplet sizing measurements at very close distances from the mouth, i.e., and mm in the current study. the optical remote sensing technique could eliminate the errors induced by air sampling techniques. the average expiration air jet velocity was . m/s for coughing and . m/s for speaking using the piv technique. impacts of the evaporation/condensation effects on the droplet size distributions were estimated by numerical method and the effect of the hygroscopic behavior was found to be negligible on the droplet size distributions at such close distances. our numerical results indicate that the measured droplet size distributions can essentially represent the`original' size distributions immediately in front of the mouth. the geometric mean diameter of the droplets expelled during coughing was . m and it was . m for speaking. it was estimated that - droplets were expelled per cough and - droplets were expelled during speaking. using different estimation methods and literature reference data, the droplet concentrations were found to range from . to . cm − per cough and . - . cm − for speaking. comparison between the results obtained at the two measurement distances ( and mm) suggests that the measured size distributions might be distorted if the measurement was not made as close as possible to the mouth opening. in this particular setup, the distortion was mainly due to wider spread of the droplets following the expansion of the expiration jet, resulting in fewer droplets being detected at the mm location our analysis also suggests that other influential factors, including hygroscopic behavior and droplet falling, would become more significant if the droplet sensing element was placed at further distances. this study is the first one employing the imi technique to measure the original droplet size profiles from human expiratory activities. the droplet size distributions obtained in the current study are more in line with that reported by duguid ( ) , who employed collection media in his study. estimating from duguid's ( ) results, the geometric diameters for coughing and speaking were and m, respectively. the geometric mean diameters reported by loudon and roberts ( ) differed from the current study more significantly compared to duguid ( ) but their measured droplet size ranges (about - m) were also similar to the current study. size peaks in the submicron range were reported by some previous studies using sampling-based instruments (e.g., . m in morawska et al., , less than . m in papineni & rosenthal, and less than . m in fairchild & stamper, ) , indicating that there are expiratory droplets smaller than the detection limit of the imi system. limitations and uncertainties of the imi technique were also addressed in the paper. it seems that instrumentation is still a major limitation for this kind of research and the imi technique can only capture the droplet profiles at the larger size range. the size and the duration of air-carriage of respiratory droplets and droplet-nuclei particle concentration in exhaled breath light scattering from water droplets in the geometrical optics approximation interferometric laser imaging for droplet sizing: a method for droplet-size measurement in sparse spray systems severe acute respiratory syndrome (sars): breathtaking progress impact of health on particle size of exhaled respiratory aerosols: case-control study atomizing of mouth and nose secretions into the air as revealed by high speed photography the interdependence of evaporation and settling for airborne freely falling droplets droplet expulsion from the respiratory tract thermal mapping of the airways in humans droplets expelled during human expiratory activities and their origin toward understanding the risk of secondary airborne infection: emission of respirable pathogens the size distribution of droplets in the exhaled breath of healthy human subjects turbulent jet the size and concentration of droplets generated by coughing in human subjects study on transport characteristics of saliva droplets produced by coughing in a calm indoor environment this research was jointly supported by the australian research council discovery project dp and hong kong rgc grant . the expiratory droplet investigation setup and other related laser safety installations were provided by the international laboratory for air quality and health, queensland university of technology. the imi and piv systems were provided by the hong kong university of science and technology. technical support provided by the mechanical workshop of the faculty of science, queensland university of technology is greatly appreciated. key: cord- - a q ad authors: balachandar, s.; zaleski, s.; soldati, a.; ahmadi, g.; bourouiba, l. title: host-to-host airborne transmission as a multiphase flow problem for science-based social distance guidelines date: - - journal: nan doi: . / . . . sha: doc_id: cord_uid: a q ad covid- pandemic has strikingly demonstrated how important it is to develop fundamental knowledge related to generation, transport and inhalation of pathogen-laden droplets and their subsequent possible fate as airborne particles, or aerosols, in the context of human to human transmission. it is also increasingly clear that airborne transmission is an important contributor to rapid spreading of the disease. in this paper, we discuss the processes of droplet generation by exhalation, their potential transformation into airborne particles by evaporation, transport over long distances by the exhaled puff and by ambient air turbulence, and final inhalation by the receiving host as interconnected multiphase flow processes. a simple model for the time evolution of droplet/aerosol concentration is presented based on a theoretical analysis of the relevant physical processes. the modeling framework along with detailed experiments and simulations can be used to study a wide variety of scenarios involving breathing, talking, coughing and sneezing and in a number of environmental conditions, as humid or dry atmosphere, confined or open environment. although a number of questions remain open on the physics of evaporation and coupling with persistence of the virus, it is clear that with a more reliable understanding of the underlying flow physics of virus transmission one can set the foundation for an improved methodology in designing case-specific social distancing and infection control guidelines. the covid- pandemic has made clear the fundamental role of airborne droplets and aerosols as potential virus carriers. the importance of studying the fluid dynamics of exhalations, starting from the formation of droplets in the respiratory tracts to their evolution and transport as a turbulent cloud, can now be recognized as the key step towards understanding sars-cov- transmission. respiratory droplets are formed and emitted at high speed during a sneeze or cough [ ] , and at a lower speed while talking or breathing. the virus-laden droplets are then initially transported as part of the coherent gas puff of buoyant fluid ejected by the infected host [ ] . the very large drops of o(mm) in size, which are visible to the naked eye, are minimally affected by the puff. they travel semi-ballistically with only minimal drag adjustment, but rapidly falling down due to gravitational pull. they can exit the puff either by overshooting or by falling out of the puff at the early stage of emission (fig. ). smaller droplets ( o( µm)) that remain suspended within the puff are advected forward. as the suspended droplets steadily evaporate within the cloud, the virus takes the form of potentially inhalable droplet nuclei when the evaporation of water is complete. meanwhile, the velocity of the turbulent puff continues to decay both due to entrainment and drag. once the puff slows down sufficiently, and its coherence is lost, the eventual spreading of the virus-laden droplet nuclei becomes dependent on the ambient air currents and turbulence. the isolated respiratory droplet emission framework was introduced by wells [ ] in the s and remains the framework used for guidelines by public health agencies, such as the who, cdc and others. however, it does not consider the role of the turbulent gas puff within which the droplets are embedded. regardless of their size and their initial velocity, the ejected droplets are subject to both gravitational settling and evaporation [ ] . although droplets of all sizes undergo continuous settling, droplets with settling speed smaller than the fluctuating velocity of the surrounding puff can remain trapped longer within the puff (fig. ) . furthermore, the water content of the droplets continuously decreases due to evaporation. when conditions are appropriate for near complete evaporation, the ejected droplets quickly become droplet nuclei of non-volatile biological material. the settling velocity of these droplet nuclei is sufficiently small that they can remain trapped as a cloud and get advected by ambient air currents and dispersed by ambient turbulence. based on the above discussion, we introduce the following terminology that will be consistently used in this paper: • puff: warm, moist air exhaled during breathing, talking, coughing or sneezing, which remains coherent and moves forward during early times after exhalation • cloud: the distribution of ejected droplets that remain suspended even after the puff has lost its coherence. the cloud is advected by the air currents and is dispersed by ambient turbulence • exited droplets: droplets that have either overshot the puff/cloud or settled down due to gravity • airborne (evaporating) droplets: droplets which have not completed evaporation and retained within the puff/cloud • (airborne) droplet nuclei: droplets that remain airborne within the puff/cloud and that have fully evaporated, which will also be termed aerosols. figure : image reproduction showing the semi-ballistic largest drops, visible to the naked eye, and on the order of mm, which can overshoot the puff at its early stage of emission [ , ] . the puff continues to propagate and entrain ambient air as it moves forward, carrying its payload of a continuum of drops [ ] , over distances up to meters for violent exhalations such as sneezes [ ] . present in the same contaminated space at the same time. thus, the indirect route involves respiratory droplets and fully-evaporated droplet nuclei that are released to the surrounding by the infected individual, which remain airborne as the cloud carries them over longer distances [ ] . the settling speeds of the airborne droplets and droplet nuclei are so small, that they remain afloat for longer times [ ] , while being carried by the background turbulent airflow over distances that can span the entire room or even multiple rooms within the building (o( − ) feet). a schematic of the two routes of transmission is shown in fig. and in this paper we will focus on the indirect airborne transmission. another factor of great importance is the possibility of updraft in the region of contamination, due to buoyancy of the virus-laden warm ejected air-mass. these slight updrafts can keep the virusladen droplets suspended in the air and enhance the inhalability of airborne droplets and droplet nuclei by recipients who are located farther away. the advection of airborne droplets and nuclei by the puff and subsequently as a cloud may represent transmission risk for times and distances much longer than otherwise previously estimated, and this is a cause of great concern [ , ] . note that if we ignore the motion of the puff of air carrying the droplets, as in the analysis of wells, the airborne droplets and nuclei would be subjected to such high drag that they could not propagate more than a few cm away from the exhaler, even under conditions of fast ejections, such as in a sneeze. this illustrates the importance of incorporating the correct multiphase flow physics in the modeling of respiratory emissions [ ] , which we shall discuss further here. it has been recently reported that the covid- virus lives in droplets and aerosols for many hours in laboratory experiments [ ] . at the receiving end, an increased concentration of virusladen airborne droplets and nuclei near the breathing zone increases the probability of them settling on the body or, more importantly, being inhaled. depending on its material and sealing properties, the use of a mask by the infected host can help reduce the number of virus-laden droplets ejected into the air, and in a less effective way, the use of a mask or other protective devices by the receiving host may reduce the probability of inhalation of the virus-laden airborne droplets and nuclei. we anticipate the present paper to spawn future research in the context of host-to-host airborne transmission. after presenting the mathematical framework in section , the three different stages of transmission, namely droplet generation, transport and inhalation will be independently analyzed in sections , and . these sections will consider the evolution of the puff of exhaled air and the droplets contained within. section will put together the different models of the puff and droplet evolution described in the previous sections, underline their simplifications, and demonstrate their ability to make useful predictions. finally, conclusions and future perspectives are offered in section . we wish to describe the three main stages involved in the host-to-host transmission of the virus: droplet generation during exhalation, airborne transport, and inhalation by the receiving host. in the generation stage, virus-laden drops are generated throughout the respiratory tract by the exhalation air flow, which carries them through the upper airway toward the mouth where they are ejected along with the turbulent puff of air from the lungs. the ejected puff of air can be characterized with the following four parameters: the volume q pe , the momentum m pe , and the buoyancy b pe of the ejected puff, along with the angle θ e to the horizontal at which the puff is initially ejected. the initial momentum and buoyancy of the puff are given by m pe = ρ pe q pe v pe and b pe = (ρ a − ρ pe )q pe g, where v pe is the initial velocity of ejected puff, ρ pe and ρ a are the initial density of the puff and the ambient, respectively, and g is the gravitational acceleration. the ejected droplets are characterized by their total number n e , size distribution n e (d), droplet velocity distribution v de (d) and droplet temperature distribution t de (d), where d is the diameter of the droplet. to simplify the theoretical formulation, here we assume the velocity and temperature of the ejected droplets to depend only on the diameter and show no other variation. as we shall see in section , this assumption is not very restrictive, since the velocity and temperature of the droplets that remain within the puff very quickly adjust to those of the puff. both the ejected puff of air and the detailed distribution of droplets depend on the nature of the exhalation event (i.e., breathing, talking, coughing or sneezing), and also on the individual. this is followed by the transport stage, where the initially ejected puff of air and droplets are transported away from the source. the volume of the puff of air increases due to entrainment of ambient air. the puff velocity decreases due to both entrainment of ambient air as well as drag. since the temperature and moisture content of the ejected puff of air is typically higher than the ambient, the puff is also subjected to a vertical buoyancy force, which alters its trajectory from a rectilinear motion. the exhaled puff is turbulent, and both the turbulent velocity fluctuations within the puff and the mean forward velocity of the puff decay over time. the time evolution of the puff during the transport stage can then be characterized by the following quantities: the volume q p (t), the momentum m p (t), buoyancy b p (t) of the ejected puff, and ρ p (t) is the density of air within the puff which changes over time due to entrainment and evaporation. the trajectory of the puff is defined in terms of the distance traveled s(t) and the angle to the horizontal θ(t) of its current trajectory. following the work of bourouiba et al. [ ] we have chosen to describe the puff trajectory in terms of s(t) and θ(t). this information can be converted to horizontal and vertical positions of the centroid of the puff as a function time. if we ignore the effects of thermal diffusion and ambient stratification between the puff and the surrounding air, then the buoyancy of the puff remains a constant as b p (t) = b pe . furthermore, as will be seen below, the buoyancy effects are quite weak in the early stages when the puff remains coherent, and thus, the puff to good approximation can be taken to travel along a straight line path, as long as other external flow effects are unimportant. to characterize the time evolution of the virus-laden droplets during the transport stage, we distinguish the droplets that remain within the puff, whose diameter is less than a cutoff (i.e., d < d exit ), from the droplets (i.e., d > d exit ) that escape out of the puff. as will be discussed subsequently in § , the cutoff droplet size d exit decreases with time. thus, the total number of droplets that remain within the puff can be estimated as n (t) = d exit n (d, t) dd. however, the size distribution of droplets at any later time, denoted as n (d, t), is not the same as that at ejection. due to evaporation, size distribution shifts to smaller diameters over time. we introduce the mapping d(d e , t), which gives the current diameter of a droplet initially ejected as a droplet of diameter d e . then, assuming well-mixed condition within the puff, the airborne droplet and nuclei concentration (number per volume) distribution can be expressed as where the inverse mapping d − gives the original ejected diameter of a droplet whose current size is d. the prefactor /q p (t) accounts for the decrease in concentration due to the enlargement of the puff over time. in this model, the airborne droplets and nuclei that remain within the coherent puff are assumed to be in equilibrium with the turbulent flow within the puff. under this assumption, the velocity v d (d, t) and temperature t d (d, t) of the droplets can be estimated with the equilibrium eulerian approximation [ , ] . when the puff's mean and fluctuating velocities fall below those of the ambient, the puff can be taken to lose its coherence. thus, the puff remains coherent and travels farther in a confined relatively quiescent environment, such as an elevator, class room or aircraft cabin, than in an open outdoor environment with cross-wind or in a room with strong ventilation. we define a transition time t tr , below which the puff is taken to be coherent and the above described puff-based transport model applies. for t > t tr , we take the aerosol transport and dilution to be dominated by ambient turbulent dispersion. accordingly, this late-time behavior of total number of airborne droplets and nuclei and their number density distribution are given by the theory of turbulent dispersion. it should be noted that the value of transition time will depend on both the puff properties as well as the level of ambient turbulence (see section . ) . we now consider the final inhalation stage. depending on the location of the recipient host relative to that of the infected host, the recipient may be subjected to either the puff that still remains coherent, carrying a relatively high concentration of virus-laden droplets or nuclei, or to the more dilute dispersion of droplet nuclei, or aerosols. these factors determine the number and size distribution of virus-laden airborne droplets and nuclei the recipient host will be subjected to. the inhalation cycle of the recipient, along with the use of masks and other protective devices, will then dictate the aerosols that reach sensitive areas of the respiratory tract where infection can occur. following the above outlined mathematical framework we will now consider the three stages of generation, transport and inhalation. knowing the droplet sizes, velocities and ejection angles resulting from an exhalation is the key first step in the development of a predictive ability for droplet dispersion and evolution. respiratory droplet size distributions have been the object of a large number of studies, as reviewed in [ ] , and among them, those of duguid [ ] and loudon & roberts [ ] have received particular scrutiny as a basis for studies of disease transmission by nicas, nazaroff & hubbard [ ] . there are substantial differences in the methodologies used for quantification of respiratory emission sprays. few studies have used common instrumentation that have enough overlap to reconstruct the full distribution of sizes. for example, there are important gaps in reporting the total volume or duration of air sampling, in addition there are issues in reporting the effective evaporation rates used to back-compute the initial distribution and in the documentation of assumptions about optical or shape properties of the droplets being sampled. in addition, sensitivity analyses are often missing regarding the role of orientation or calibration of sensing instruments with respect to highly variable emissions from human subjects. finally, regarding direct high-speed imaging methods [ , ] , the tools for precise quantification of complex unsteady fragmentation and atomization processes are only now being developed [ , , ] . there are far fewer studies on the velocities and angles of the droplets produced by atomizing flows. the studies of duguid and loudon & roberts have been performed by allowing the exhaled droplets to impact various sheets or slides, with different procedures being used for droplets smaller than µm. the size of the stains on the sheets was observed and the original droplet size was inferred from the size of the stains. to account for the difference between the droplet and the stain sizes an arbitrary factor is applied and droplets smaller than or microns are processed differently than larger droplets. the whole process makes the determination of the number of droplets smaller than microns less reliable. the data are replotted in fig. . many authors have attempted to fit the data with a log-normal probability distribution function. in that case, the number of droplets between diameter d and d + dd is n e (d) dd, and the frequency . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . https://doi.org/ . / . . . doi: medrxiv preprint of ejected droplet size distribution is given by where dd is a relatively small diameter increment or bin width, b is a normalization constant,μ is the expected value of ln d, also called the geometric mean andσ is the standard deviation of ln d, also called the geometric standard deviation (gsd). on the other hand, there have also been numerous studies of the fragmentation of liquid masses in various physical configurations other than the exhalation of mucosalivary fluid [ , , , ] . these configurations include spray formation on wave crests [ ] , droplet impacts on solids and liquids [ ] , wave impacts on vertical or finite walls/surfaces [ , , ] , and jet atomization [ ] . these studies reveal a number of qualitative similarities between the various processes, which can be best described as a sequence of events. those events include a primary instability of sheared layers in high speed air flows [ ] , and then the nonlinear growth of the perturbation into thin liquid sheets. the sheets themselves may be destabilized by two routes, one involving the formation of taylor-culick end rims [ , ] , and their subsequent deformation into detaching droplets [ ] . the other route to the formation of droplets is the formation of holes in the thin sheets [ , , ] . the holes then expand and form free hanging ligaments, which fragment into droplets through the rayleigh-plateau instability [ ] . considering the apparent universality of the process, one may infer that a universal distribution of droplet sizes may exist. indeed, the log-normal distribution has often been fitted to experimental [ ] and numerical data on jet formation [ , ] , for droplet impacts on solid surfaces [ ] , and for wave impacts on solid walls [ ] . the log-normal distribution is frequently suggested for exhalations [ , ] . the fit of the numerical results of [ ] is shown in fig. . however, this apparent universality of the log-normal distribution is questionable for several reasons. first, many other distributions, such as exponential, poisson, weibull-rosin-rammler, beta, or families of gamma or compound gamma distributions [ , ] capture to some extent the complexity of atomization physics. second, the geometrical standard deviation (gsd) of the log-normal fits to the many experimental measurements is relatively small (of the order of . [ ] or . [ ] ) while the wide range of scales in fig. seems to indicate a much larger gsd. indeed nicas, nazaroff & roberts [ ] obtainσ − . one explanation for the smaller gsd in jet atomization studies, both numerical and experimental, is that the numerical or optical resolution is limited at the small scales. indeed, as grid resolution is increased, the observed gsd also increases [ ] . third, many authors [ , ] observe multimodal or bimodal distributions, that can be obtained for example by the superposition of several physical processes. this would arise in a very simple manner if the taylor-culick rim route produced drops of a markedly different size than the holes-in-film route. the non-newtonian nature of the fluid will also influence the instabilities and thereby the droplet generation process. other less violent processes could lead to the formation of small droplets such as the breakup of small films and menisci described in [ ] without going through the sequence of events described above. in order to elucidate this discrepancy, we take another look at the fit of the duguid data in fig. . we replot the data that was provided in table of duguid. since the data are given as counts n i in bins defined by the interval (d i , d i+ ), we approximate n e (d) at collocation points is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . frequency n e (d) ( /microns) duguid cough data loudon and roberts cough data pareto b/d fit figure : frequency of droplet size distribution, replotted from duguid [ ] and loudon & roberts [ ] . the pareto distribution is also plotted. ( ) appears as a parabola. when one attempts to fit a parabola between and µm, one obtains a log-normal distribution withσ = . andμ = ln( ) (for diameters in microns). however, the data above µm are completely outside this distribution. if instead the whole range from to µm is fit to a log-normal distribution, one obtains a very wide log-normal or alternatively a pareto distribution of power in figs. and , we represent the pareto distribution together with the duguid and loudon & roberts data. it is especially clear from fig. that if one does not trust either data at d < µm then both data sets are well described by the pareto distribution. this, however, does not eliminate the possibility that more data with more statistical power could show deviations from pareto, in particular, as multimodal distributions. nevertheless, the multimodal deviation from the pareto distribution is difficult to characterize and will not be pursued in what follows for the sake of simplicity. it is clear that the pareto distribution cannot be valid at diameters that are either too large or too small. the equivalent diameter of the total mass of liquid being atomized is an obvious upper bound, but it is also very unlikely that droplets with d > h where h is the initial film thickness will be observed. it is reasonable to put this film thickness on the scale of mm, which corresponds to the upper bound on diameters in the data of figs is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . fig. to log-normal and pareto distributions, in the same coordinates as fig. . the fit is adequate only up to µm. as a result, only a fraction of the reliable data fits the log-normal. the pareto distribution is a reasonable capture of the data in the to µm range. in the log-log coordinates, the log-normal distribution appears as a parabola while the pareto distribution is a straight line. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . is much harder to determine. exhalations are highly transient, or unsteady, processes involving complex multiscale geometry [ ] , and thread breakup is a fractal multiscale process with satellite droplets [ , ] . going down in scale, the fractal process repeats itself as long as continuum mechanics remains valid, to around nm. this would not be relevant for viral disease propagation as a lot of the relevant viruses have sizes ranging from o( − nm), with an estimated size for sars-cov- ranging from - nm, for example. if the smallest length scale is the thickness at which the thin liquid sheets will break, then experimental observations in water [ ] suggest a scale of o( ) nm. other fluids, including biological fluids or biologically contaminated fluids such as those investigated in [ , , ] may yield different length scales. based on the above considerations, we take a histogram of droplet sizes that reads where d is set to o( nm) and d to o( mm) for simplicity. the total volume of the droplets is since d is four orders of magnitude smaller than d , the total number of droplets is well approximated by , the number of droplets with diameter smaller than x, is very well approximated by so that f ( d )/n e = % of the droplets are of size less than d µm. in other words, a numerical majority of the droplets are near the lower diameter bound. on the other hand, a majority of the volume of fluid is in the larger droplet diameters. the distribution of velocities and ejection angles has been investigated in the atomization experiments of [ ] , which follow approximately the geometry of a high speed stream peeling by a gas layer. these experiments were qualitatively reproduced in the numerical simulations of [ ] . to cite ref. [ ] , "most of the ejection angles are in the range • to • , however, it occurs occasionally that the drops are ejected with angles as high as • ". on the other hand, there are to our knowledge no experimental data on the velocity of droplets, as they are formed in an atomizing jet, that could be used directly to estimate the ejection speed of droplets in exhalation. there are however numerical studies [ , ] in the limit of very large reynolds and weber numbers. the group velocity of waves formed on a liquid layer below a gas stream has been estimated by dimotakis [ ] as . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . where ρ d is droplet density. in [ , ] it was shown that this was also the vertical velocity of the interface perturbation. it is thus likely that this velocity plays a role at the end of the first instability stage of atomization. after this stage, droplets are detached and immersed in a gas stream of initial ejection velocity v pe . since the density ratio ρ p /ρ d is o( − ), we expect the initial velocity of the ejected droplets at the point of their formation to be small. as we show below, it is interesting to note that the large reynolds number limit may apply at the initial injection stage to a wide range of droplets in the spectrum of sizes found above. indeed the ejection reynolds number of a droplet ejected at a velocity v de in a surrounding air flow of velocity v pe is where ν a is the kinematic viscosity of the ejected puff of air (here taken to be the same as that of the ambient air). the largest reynolds number is obtained for the upper bound of d = mm. for example, if the droplet's initial velocity is set to v de ≈ , and the air flow velocity in some experiments [ ] is as high as m/s, we can estimate the largest ejection reynolds number to be re e ≈ and the reynolds number will stay above unity for droplets down to micron size. but as the puff of air and the droplets move forward, the droplet reynolds number rapidly decreases for the following reasons: (i) as will be seen in section . the puff velocity decreases due to entrainment and drag, (ii) as will be seen in section . . the droplet diameter will decrease rapidly due to evaporation, (iii) as will be seen in section . . the time scale τ v on which the droplet accelerates to the surrounding fluid velocity of the puff is quite small, and (iv) very large droplets quickly fall out of the puff and do not form part of airborne droplets. thus, it can be established that droplets smaller than µm quickly equilibrate with the puff within the first few cm after exhalation. this section will consider the evolution of the puff of hot moist air with the droplets after their initial ejection. first in section . we will present a simple modified model for the evolution of the puff of exhaled air, evaluating the effects of drag and the inertia of the droplets within it. this will enable us, in section . to discuss the evolution of the droplet size spectrum, velocity and temperature distributions, with simple first order models. additionally, section . will discuss the effect of non-volatiles on the droplet evolution and the formation of a fully evaporated droplet nuclei or aerosol particle. late-time turbulent dispersion of the virus-laden droplet nuclei, when the puff of air within which they are contained stops being a coherent entity, is then addressed in section . . for the puff model, we follow the approach of bourouiba et al. [ ] , but include the added effects of drag and the mass of the injected droplets. in addition, a perturbation approach is pursued to obtain a simple solution with all the added effects included. fig. shows the evolution of the puff along with quantities that define the puff [ ] . we define t to be the time elapsed from exhalation and s(t) to be the distance traveled by the puff since exhalation. for analytical considerations we define the virtual origin to be at a distance s e from the real source in the backward direction and t e to be the time it takes for the puff to travel from the virtual origin to the real source. we define . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . t = t + t e to be time from the virtual origin and s = s + s e to the distance traveled from the virtual origin -their introduction simplifies the analysis. from the theory of jets, plumes, puffs and thermals [ ] the volume of the puff exhaled grows by entrainment. bourouiba et al. [ ] defined the puff to be spheroidal in shape with the transverse dimension to evolve in a self-similar manner as r (t ) = αs (t ), where α is related to entrainment coefficient. the volume of the puff is then q p (t ) = ηr (t ) = ηα s (t ) and the projected, or cross-sectional, area of the puff a(t ) = βr (t ) = βα s (t ), where the constants η and β depend on the shape of the spheroid. for a spherical puff η = π/ and β = π. as defined earlier, the ejected puff at the real source (i.e., at t = t e ) is characterized by the volume q pe = ηα s e , momentum m pe = ρ pe q pe v pe , buoyancy b pe = q pe (ρ a − ρ pe )g and ejection angle θ e . from the assumption of self-similar growth, we obtain the virtual origin to be defined as where the constant c depends on the drag coefficient of the puff and will be defined below. if we assume a spherical puff with an entrainment factor α = . [ ] , the distance s e depends only on the ejected volume. experimental measurements suggest q pe to vary over the range . to . m . accordingly, s e can vary from . to . m. similar estimates of t e can be obtained for a spherical puff: as q pe varies from . to . m and as the ejected velocity varies from to m/s the value of t e varies over the range . to . s. the horizontal and vertical momentum balances in dimensional terms are in the above c d is the drag coefficient of the puff and m d is the momentum of droplets within the puff. while the puff velocity decreases rapidly over time, the velocity of the larger droplets will change slowly. note that in the analysis to follow, we take the velocity of those droplets that remain within the puff to be the same as the puff velocity. we use s e and t e as the length and time scales to define nondimensional quantities:s = s /s e andt = t /t e . with this definition the virtual origin becomest = ands = and the real source becomest = ands = . in terms of non-dimensional quantities the governing momentum equations can be rewritten as there are three nondimensional parameters: mass ratio of the initial ejected droplets to the initial air puff: r m = ρ d q de /(ρ p q pe ); the scaled drag coefficient: c = c d β/( ηα); and the buoyancy parameter: a = b pe t e /(ρ pe q pe s e ). in the above equations, r m is defined in terms of the mass of . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . figure : evolution of a typical cloud of respiratory multiphase turbulent droplet-laden air following breathing, talking, coughing and sneezing activities. image adapted from [ ] . the initial ejected droplets. this is an approximation since some of the droplets exit the puff over time. even though the droplet mass decreases due to evaporation, the associated momentum is not lost from the system since it remains within the puff. in any case, soon it will be shown that the value of r m is small and the role of ejected droplets on the momentum balance is negligible. it should also be noted that under boussinesq approximation the small difference in density between the puff and that the ambient is important only in the buoyancy term. for all other purposes, the two will be taken to be the same and as a result the time variation of puff density is not of importance (i.e., ρ p = ρ pe = ρ a ). the importance of inertia of the ejected droplets, drag on the puff and buoyancy effects can now be evaluated in terms of the magnitude of the nondimensional parameters. typical experimental measurements of breathing, talking, coughing and sneezing indicate that the value of r m is smaller than . and often much smaller. furthermore, as droplets fall out continuously [ ] from the turbulent puff, this ratio changes over time. here we will obtain an upper bound on the inertial effect of injected droplets by taking the value of r m to be . . the drag coefficient of a spherical puff of air is also typically small -again as an upper bound we take c d = . , which yields c = . for a spherical puff. the value of the buoyancy parameter a depends on the density difference between the ejected puff of air and the ambient, which in turn depends on the temperature difference. for the entire range of ejected volumes and velocities, the value of a comes to be smaller than . , for temperature differences of the order of ten to twenty degrees between the exhaled puff and the ambient. since all three parameters r m , c and a can be considered as small perturbations, the governing equations can be readily solved in their absence to obtain the following classical expressions for the nondimensional puff location and puff velocity: with the inclusion of the drag term the governing equations become nonlinear. nevertheless, they allow a simple exact solution which can be expressed as . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . thus, as to be expected, the forward propagation of the puff slows down with increasing nondimensional drag parameter c. for small values of c the above can be expanded in taylor series as a comparison of the exact solution with the above asymptotic expansion shows its adequacy for small values of c. for small non-zero values of r m , c and a, the governing equations can be solved using regular perturbation. the result can be expressed as and the above expression is accurate to o(c , r m , a ). although the effect of buoyancy is to curve the trajectory of the puff, the leading order effect of buoyancy is to only alter the speed of rectilinear motion. also, as expected, the effect of non-zero r m is to add to the total inertia and thereby slow down the motion of the puff. on the other hand, the effect of buoyancy is to slow down if the initial ejection is angled down (i.e., if θ e < ) and to speed up if the ejection is angled up, provided the ejected puff is warmer than the ambient. the time evolution of the puff as predicted by the above analytical expression is shown in fig. . note that the point of ejection is given byt = ,s = , and the initial non-dimensional velocitỹ v(t = ) = / . the results for four different combinations of c and r m are shown. the buoyancy parameter has very little effect on the results and, therefore, is not shown. it should be noted that at late stages when the puff velocity slows down the effect of buoyancy can start to play a role as indicated in experiments and simulations. it can be seen that the effect of inertia of the ejected droplets, even with the upper bound of holding their mass constant at the initial value, has negligible effect. only the drag on the puff has a significant effect in reducing the distance traveled by the puff. it can then be taken that the puff evolution to good accuracy can be represented by ( ) . over a time span of nondimensional units the puff has traveled about . s e and the velocity has dropped to about % of the initial velocity. by nondimensional units the puff has traveled about . s e and the velocity has dropped to about . % of the initial velocity. the ejected droplets are made of a complex fluid that is essentially a mixture of oral fluids, including secretions from both the major and minor salivary glands. in addition, it is added up with several constituents of non-salivary origin, such as gingival crevicular fluid, exhalted bronchial and nasal secretions, serum and blood derivatives from oral wounds, bacteria and bacterial products, viruses and fungi, desquamated epithelial cells, other cellular components, and food debris [ ] . therefore, it is not easy to determine precisely the transport properties of the droplet fluid. although surface tension is measured similar to that of water, viscosity can be one or two orders of magnitude larger [ ] making drops less coalescence prone [ , ] . in the present context, viscosity and surface tension might be of importance, because they can influence droplet size distribution specifically by controlling coalescence and breakage. these processes are important only during the ejection stage, and once droplets are in the range below µm, coalescence and break up processes are impeded. due to the dilute dispersed nature of the flow droplet-droplet interaction can be ignored. . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . the ejected swarm of droplets is characterized by its initial size spectrum as given in ( ) . the time evolution of the spectrum of droplets that remain within the puff in terms of droplet size, velocity and temperature is the object of interest in this section. the evolution of the ejected droplets depends on the following four important parameters: the time scale τ v on which the droplet velocity relaxes to the puff fluid velocity (in the absence of other forcings), the time scale τ t on which the droplet temperature relaxes to the puff fluid temperature, the settling velocity w of the droplet within the puff fluid, and the reynolds number re based on settling velocity. these quantities are given by [ , , ] where ρ ≈ is the droplet-to-air density ratio, c r ≈ . is the droplet-to-air specific heat ratio, g is the acceleration due to gravity, ν p and κ p are the kinematic viscosity and thermal diffusivity of the puff. in the above, Φ = + . re . and n u = + . re / p r / are the finite reynolds number drag and heat transfer correction factors, where the later is the well-known ranz-marshall nusselt or sherwood number correlation. both the corrections simplify in the stokes regime for drops smaller than about µm. here we take the prandtl number of air to be p r = . . in the stokes limit, the velocity and thermal time scales, and the settling velocity of the droplet increase as d , while reynolds number scales as d . the value of these four parameters for varying droplet sizes is presented in fig. , where it is clear that the effect of finite re becomes important only for droplets larger than µm. for smaller droplets τ v , τ t (s), w (m/s), and re . . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . the size of the droplets under investigation is sufficiently small, and the swarm is dilute to prevent their coalescence, and the only way in which droplets change their size is via evaporation. according to the analysis of langmuir [ ] , the rate of mass loss due to evaporation of a small sphere depends on the diffusion of the vapor layer away from the sphere surface, and under reasonable hypotheses [ , , , ] , it can be expressed as : where, m is the mass of a droplet of diameter d, d is the diffusion coefficient of the vapor, ρ p is the density of puff air and b m = (y d − y p )/( − y s ) is the spalding mass number, where y d is the mass fraction of water vapor at the droplet surface and y p is the mass fraction of water vapor in the surrounding puff. under the assumption that n u and b m are nearly constant for small droplets, the above equation can be integrated [ ] to obtain the following law (mapping) for the evolution of the droplet: where d e is the initial droplet diameter at ejection and k = dn u ln( + b m )/ρ has units of m /s and thus represent an effective evaporative diffusivity. it is important to observe that ( ) would predict a loss of mass per unit area tending to infinity as the diameter of the drop tends to zero. this implies that the droplet diameter goes to zero in a finite time and we establish the result is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . k . assuming n u = and d = . × − m /s, even for very small values of b m , we obtain the evaporation time for a µm droplet to be less than a second. however, it appears that smaller than a certain critical size, the loss of mass due to evaporation slows down [ ] . this could partly be due to the presence of non-volatiles and other particulate matter within the droplet, whose effects were ignored in the above analysis, and will be addressed in section . . it seems that ( ) can give reliable predictions for droplet diameter down to a few µm with much slower evaporation rates for smaller sizes. irrespective of whether water completely evaporates leaving only the non-volatile droplet nuclei, or the droplet evaporation slows down, the important consequence on the evolution of the droplet size distribution is that it is narrower and potentially centered around micron size. we now consider the motion of the ejected droplets, while they rapidly evaporate. the equation of motion of the droplet is newton's law where e e e z is the unit vector along the vertical direction, m p is the mass of puff displaced by the droplet, v v v d and v v v p are the vector velocity of the droplet and the surrounding puff. provided the droplet time scale τ v is smaller than the time scale of surrounding flow, which is the case for droplets of diameter smaller than µm, the above ode can be perturbatively solved to obtain the following leading order solution [ , , ] according to the above equation, the equilibrium eulerian velocity of the droplet depends on the local fluid velocity plus the still fluid settling velocity w of the droplet plus the third term that arises due to the inertia of the droplet. though at ejection the droplet speed is smaller than the surrounding gas velocity, as argued in section . , the droplets quickly accelerate to approach the puff velocity. in fact, since the puff is decelerating (i.e., |dv v v p /dt| < ), the droplet velocity will soon be larger than the local fluid velocity. as long as the droplet stays within the puff, the velocity and acceleration of the surrounding fluid can be approximated by those of the puff as |v v v p | = ds/dt and |dv v v p /dt| = d s/dt . this allows evaluation of the relative importance of the third term (inertial slip velocity) in terms of the puff motion, which is given in ( ) as [ ] this ratio takes its largest value at the initial time of injection and then decays as /t. using the range of possible values of t e given earlier, this ratio is small for a wide range of initial droplet sizes. we thus confirm that for the most part droplet inertia can be ignored in its motion, and the droplet velocity can be taken to be simply the sum of local fluid velocity and the still fluid settling velocity of the droplet. . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . https://doi.org/ . / . . . doi: medrxiv preprint while the effect of buoyancy on the puff was shown to be small, the same cannot be said of the droplets. the vertical motion of a droplet with respect to the surrounding puff, due to its higher density, is dependent only on the fall velocity w , which scales as d , which in turn decreases as given in ( ) due to evaporation. the droplet's gravitational settling velocity can be integrated over time to obtain the distance over which it falls as a function of time. we now set this fall distance (left hand side) equal to the puff radius (right hand side) to obtain where we have set the droplet diameter at exhalation to be d e,exit , indicating the fact that a droplet of initial diameter equal to d e,exit has fallen by a distance equal to the puff size at time t. thus all larger droplets of size d e > d e,exit have fallen out of the puff by t and we have been referring to these as the exited droplets. it should be pointed out that in the above simple analysis the vertical motion of the particle ignored the vertical component of fluid velocity both from turbulent fluctuations and from the entrainment process. the two critical initial droplet diameters, d e,evap and d e,exit are plotted in fig. a as a function of t. the only other key parameter of importance is k , whose value is varied from − to − m /s. in evaluating d e,exit using ( ), apart from the property values of water and air, we have used the nominal values of α = . , s e = . m and t e = . s (as an example). the solid lines correspond to d e,exit , which decreases with increasing t and for each value of k , there exits a minimum d e below which there is no solution to ( ) since the droplet fully evaporates before falling out of the puff. the dotted lines correspond to d e,evap , which increases with t. the intersection of the two curves is marked by the solid square, which corresponds to the limiting time t lim (k ), beyond which the puff contains only fully-evaporated droplet nuclei containing the viruses. correspondingly we can define a limiting droplet diameter d e,lim (k ). given sufficient time, all initially ejected larger droplets (i.e., d e > d e,lim ) would have fallen out of the puff and all smaller droplets (i.e., d e ≤ d e,lim ) would have evaporated to become droplet nuclei. at times smaller than the limiting time (i.e., for t < t lim ) we have the interesting situation of some droplets falling out of the puff (exited droplets), some still remaining as partially evaporated airborne droplets, and some fully-evaporated to become droplet nuclei. this scenario is depicted in fig. a with an example of t = s for k = − m /s plotted as a dashed line. there can be significant presence of non-volatile material such as mucus, bacteria and bacterial products, viruses and fungi, and food debris in the ejected droplets [ ] . however, the fraction of ejected droplet volume q de that is made up of these non-volatiles varies substantially from person to person. the presence of non-volatiles alters the analysis of the previous sections in two significant ways. first, each ejected droplet, as it evaporates, will reach a final size that is dictated by the amount of non-volatiles that were initially in it. the larger the droplet size at initial ejection, the larger will be its final size after evaporation, since it contains a larger amount of non-volatiles. if ψ is the volume fraction of non-volatiles in the initial droplet, the final diameter of the droplet nuclei after complete evaporation of volatile matter (i.e., water) will be d dr = d e ψ / . . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . this size depends on the initial droplet size and composition. note that even a small, for example %, non-volatile composition results in d dr being around % of the initial ejected droplet size. it has also been noted that the evaporation of water can be partial, depending on local conditions in the cloud or environment. we simply assume the fraction ψ to also account for any residual water retained within the droplet nuclei. the second important effect of non-volatile is to reduce the rate of evaporation. as evaporation occurs at the droplet surface, a fraction of the surface will be occupied by the non-volatiles reducing the rate of evaporation. for small values of ψ, the effect of non-volatiles is quite small only at the beginning. the effect of non-volatiles will increase over time, since the volume fraction of nonvolatiles increases as the volatile matter evaporates. because of this ever decreasing evaporation rate, it may take longer for a droplet to decrease from its ejection diameter of d e to its final droplet nuclei diameter of d dr , than what is predicted by ( ) . it should be noted that intermittency of turbulence and heterogeneity of vapor concentration and droplet distribution within the puff will influence the evaporation rate [ , , ] . nevertheless, for simplicity, and for the purposes of the present first order mathematical framework, we use the d -law given in ( ) , but with a smaller value of effective k to account for the effect of non-volatiles and turbulence intermittency. this approximation is likely to be quite accurate in describing the early evolution of the droplet. only at late stages as the droplet approaches its final diameter d dr , the d -law will be in significant error. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . applying the analysis of the previous sections, taking into account the presence of non-volatiles, we separate the two different time regimes of t ≤ t lim and t ≥ t lim . in the case when t ≤ t lim , we have three types of droplets: (i) exited droplets whose initial size at injection is greater than d e,exit , (ii) droplets of size at ejection smaller than d e,evap that have completely evaporated to become droplet nuclei of size d dr and (iii) intermediate size airborne droplets that are within the puff and still undergoing evaporation. we assume an equation of the form ( ) to approximately apply even in the presence of non-volatiles. with this balance between fall distance of a droplet and the puff radius we obtain the following expression d e,exit = ν a ρg αs e t t + t e t e /( +c) the corresponding limiting diameter of complete evaporation can be obtained from setting d = d e,evap ψ / and d e = d e,evap in ( ) as while the above two estimates are in terms of the droplet diameter at injection, their current diameter at t can be expressed as form the above expressions, we define t lim to be the time when d e,exit = d e,evap , which in terms of current droplet diameter becomes d exit = d evap . beyond this limiting time (i.e., for t > t lim ) the droplets can be separated into only two types: (i) exited droplets whose initial size at injection greater than d e,exit = d e,evap , and (ii) droplets of size at ejection smaller that have become droplet nuclei. the variation of t lim and d e,lim as a function of k is presented in fig. b . it is clear that as k varies over a wide range, t lim ranges from . s to s, and correspondingly d e,lim varies from to µm. we now put together all the above arguments to present a predictive model of the droplet concentration within the puff. the initial condition for the size distribution is set by the ejection process discussed in section , and the simple pareto distribution given in ( ) provides an accurate description. based on the analysis of the previous sections, we separate the two different time regimes of t ≤ t lim and t ≥ t lim . in the case when t ≤ t lim the droplet/aerosol concentration (or the number per unit volume of the puff) can be expressed as . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . where we have recognized the fact that equation ( ) is the mapping d between the current droplet size and its size at injection. due to the turbulent nature of the puff, the distribution of airborne droplets and nuclei is taken to be uniform within the puff. quantities such ass, d evap and d exit are as they have been defined above and the pre-factor /q(t) accounts for the expansion of the puff volume. in the case of t ≥ t lim , the droplet number density spectrum becomes and only droplet nuclei remain within the puff. here, the size of the largest droplet nuclei within the puff is related to its initial unevaporated droplet size as d lim = d e,lim ψ / , and the plot of d e,lim as a function of k for a specific example case of puff and droplet ejection was shown in fig. b . in this subsection we will briefly consider droplet temperature, since it plays a role in determining saturation vapor pressure and the value of k . following pirhadi et al. [ ] we write the thermal equation of the droplet as where c pw is the specific heat of water, k p is the thermal conductivity of the puff air, l is the latent heat of vaporization, t d and t p are the temperatures of the droplet and the surrounding puff. the first term on the right accounts for convective heat transfer from the surrounding air and the second term accounts for heat needed for phase change during evaporation. it can be readily established that the major portion of heat required for droplet evaporation must come from the surrounding air through convective heat transfer. the equilibrium eulerian approach [ ] can again be used to obtain the asymptotic solution of the above thermal equation and the droplet temperature can be explicitly written as where τ t is the thermal time scale of the droplet that was introduced earlier. the second term on the right is negative and thus contributes to the droplet temperature being lower than the surrounding puff. simple calculation with typical values shows that the contribution of the third term is quite small and can be ignored. as a result, the temperature difference between the droplet and the surrounding is largely controlled by the evaporation rate dm/dt, which decreases over time. again, using the properties of water and air, and typical values for n u and b m , we can evaluate the temperature difference t p − t d to be typically a few degrees. thus, the evaporating droplets need to be only a few degrees cooler than the surrounding puff for evaporation to continue. when the puff equilibrates with the surrounding and its velocity falls below the ambient turbulent velocity fluctuation, the subsequent dynamics of the droplet cloud is governed by turbulent is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . dispersion. this late-time evolution of the droplet cloud depends on many factors that characterize the surrounding air. this is where the difference between a small enclosed environment such as an elevator or an aircraft cabin or an open field matters, along with factors such as cross breeze and ventilation. a universal analysis of the late-time evolution of the droplet nuclei cloud is thus not possible, due to problem-specific details. the purpose of this brief discussion is to establish a simple scaling relation to guide when the puff evolution model presented in the above sections gives way to advection and dispersion by ambient turbulence. it should again be emphasized that the temperature difference between the puff fluid containing the droplet nuclei cloud and the ambient air may induce buoyancy effects, which for model simplicity will be taken into account as part of turbulent dispersion. we adopt the classical scaling analysis of richardson [ ] , according to which the radius of a droplet cloud, in the inertial range, will increase as the / power of time as given by where c is a constant, is the dissipation rate, which will be taken to be a constant property of ambient turbulence, and t is the time shift required to match the cloud size at the transition time between the above simple late time model and the puff model. in the above, the subscript lt stands for the late-time behavior of the radius of the droplet-laden cloud. we now make a simple proposal that there exists a transition time t tr , below which the rate of expansion of the puff as given by the puff model is larger than dr lt /dt computed from the above expression. during this early time, ambient dispersion effects can be ignored in favor of the puff model. but for t > t tr droplet-laden cloud's ambient dispersion becomes the dominant effect. the constants t and t tr can be obtained by satisfying the two conditions: (i) the size of the droplet-laden cloud given by ( ) at t tr matches the puff radius at that time given by αs e ((t tr + t e )/t e ) /( +c) , and (ii) the rate of expansion of the droplet-laden cloud by turbulent dispersion matches the rate of puff growth given by the puff model. this latter condition can be expressed as from these two simple conditions, we obtain the final expression for the transition time as given a puff, characterized by its initial ejection length and time scales s e and t e , and the ambient level of turbulence characterized by , the value of transition time can be estimated. if we take entrainment coefficient α = . , the constant c = , and typical values of s e = . m and t e = . s, we can estimate t tr = . s for a dissipation rate of c = − m /s . the transition time t tr increases (or decreases) slowly with decreasing (or increasing) dissipation rate. thus, the early phase of droplet evaporation described by the puff model is valid for o( ) s, before being taken over by ambient turbulent dispersion. however, it must be stressed that the scaling relation of richardson is likely an over-estimation of ambient dispersion, as there are experimental and computational evidences that suggest that the power-law exponent in ( ) is lower than [ ] . but it must be remarked that even with . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . corresponding changes to late-time turbulent dispersion, the impact on transition time can be estimated to be not very large. also, it must be cautioned that according to classical turbulent dispersion theory, during this late-time dispersal, the concentration of virus-laden droplet nuclei within the cloud will not be uniform, but will tend to decay from the central region to the periphery. nevertheless, for sake of simplicity here we assume ( ) to apply and we take the droplet nuclei distribution to be uniform. according to above simple hypothesis, the effect of late-time turbulent dispersion on the number density spectrum is primarily due to the expansion of the could, while the total number of droplet nuclei within the cloud remains the same. thus, the expressions ( ) and ( ) still apply. however, the expression for the volume of the cloud must be appropriately modified as the location of the center of the expanding cloud of droplets is still given by the puff trajectory s(t), which has considerably slowed down during late-time dispersal. the strength of the above model is in its theoretical foundation and analytical simplicity. but, the validity of the approximations and simplifications must be verified in applications to specific scenarios being considered. for example, considering variability in composition, turbulence intermittency, initial conditions of emissions and the state of the ambient, direct observations show that the transition between puff dominated and ambient flow dominated fate of respiratory droplets vary from o( - s) [ ] . this section will mainly survey the existing literature on issues pertaining to what fraction of the droplets and aerosols at any location gets inhaled by the recipient host, and how this is modified by the use of masks. these effects modeled as inhalation and filtration efficiencies will then be incorporated into the puff-cloud model. the pulmonary ventilation (breathing) has a cyclic variation that varies markedly with age and metabolic activities. the intensity of breathing (minute ventilation) is expressed in l/min of inhaled and exhaled air. for the rest condition, the ventilation rate is about - l/min and increases to about - l/min for mild activities. during exercise, ventilation increases significantly depending on age and metabolic needs of the activity. in the majority of earlier studies on airflow and particle transport and deposition in human airways, the transient nature of breathing was ignored for simplification and to reduce the computational cost. haubermann et al. [ ] performed experiments on a nasal cast and found that particle deposition for constant airflow is higher than those for cyclic breathing. shi et al. [ ] performed simulations on nanoparticle depositions in the nasal cavity under cyclic airflow and found that the effects of transient flow are important. grgic et al. [ ] and horschler et al. [ ] performed experimental and numerical studies, respectively, on flow and particle deposition in a human mouth-throat model, and the human nasal cavity. particle deposition in a nasal cavity under cyclic breathing condition was investigated by bahmanzadeh et al. [ ] , naseri et al. [ ] , and kiasadegh et al. [ ] , where the unsteady lagrangian particle tracking was used. they found there are differences in the predicted local deposition for unsteady and equivalent steady flow simulations. . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . in many of these studies, a sinusoidal variation for the volume of air inhaled is used. that is here q max is the maximum flow rate, and t = s is the period of breathing cycle for an adult during rest or mild activity. the period of breathing also changes with age and the level of activity. haghnegahdar et al. [ ] investigated the transport, deposition, and the immune system response of the low-strain influenza a virus iav laden droplets. they noted that the shape of the cyclic breathing is subject dependent and also changes with nose and mouth breathing. they provided an eight-term fourier series for a more accurate description of the breathing cycle. the hygroscopic growth of droplets was also included in their study. analysis of aspiration of particles through the human nose was studied by ogden and birkett [ ] and armbruster and breuer [ ] . accordingly, the aspiration efficiency η a is defined as the ratio of the concentration of inhaled particles to the ambient concentration. using the results of earlier studies and also his works, vincent [ ] proposed a correlation for evaluating the inhalability of particles. that is, the aspiration efficiency η a of particles smaller than µm is given as, here, d is an aerodynamic diameter of particles. while the above correlation provides the general trend that larger particles are more difficult to inhale, it has a number of limitations. it was developed for mouth-breathing with the head oriented towards the airflow direction with speeds in the range of m/s to m/s. the experimental investigation of aerosol inhalability was reported by hsu and swift [ ] , su and vincent [ , ] , aitken et al. [ ] , and kennedy and hinds [ ] . dai et al. [ ] performed in-vivo measurements of inhalability of large aerosol particles in calm air and fitted their data to several correlations. for calm air condition, they suggested, computational modeling of inhalability of aerosol particles were reported by many researchers [ , , , , , ] . interpersonal exposure was studied by [ , ] . the influence of thermal plume was studied by salmanzadeh et al. [ ] . nasiri et al. [ ] performed a series of computational modeling and analyzed the influence of the thermal plume on particle aspiration efficiency when the body temperature is higher or lower than the ambient. their results are reproduced in figure . here the case that the body temperature t b = . • c and the ambient temperature t a = . • c (upward thermal plume) and the case that t b = . • c and t a = . • c (downward thermal plume) are compared with the isothermal case studied by dai et al. [ ] . it is seen that when the body is warmer than the surrounding, the aspiration ratio increases. when the ambient air is at a higher temperature than the body, the inhalability decreases compared to the isothermal case. in light of the results of the previous section, it can be concluded that at a distance of o( ) m the ejected droplets have sufficiently reduced in size that these o( ) µm aerosols have near perfect inhalability. however, recall that this estimation must be adjusted to account for the possible slow down of evaporation due to variability in the initial conditions of emissions and the ambient, intermittency of cloud turbulence and drop concentration. thus, the above conclusion represents a lower bound of timescale and distance of transition to fully evaporated droplet nuclei from the cloud model [ ] . . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . https://doi.org/ . / . . . doi: medrxiv preprint figure : influence of thermal plume on aspiration efficiency [ ] . is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . https://doi.org/ . / . . . doi: medrxiv preprint using a respiratory face mask is a practical approach against exposure to airborne viruses and other pollutants. among the available facepiece respirators, n , and surgical masks are considered to be highly effective [ , ] . n mask has a filtration efficiency of more than % in the absence of face leakage [ , ] . surgical masks are used extensively in the hospital and operating rooms [ ] . nevertheless, there have been concerns regarding their effective filtration of airborne bacteria and viruses [ , , ] . there is often discomfort in wearing respiratory masks for extended durations that increases the risk of spread of infection. the breathing resistance of a mask is directly related to the pressure drop of the filtering material. the efficiency of respiratory masks varies with several factors, including the intensity and frequency of breathing as well as the particle size [ ] . the filtration efficiencies of different masks under normal breathing conditions, as reported by zhang et al. [ ] and feng et al. [ ] , are shown in figure . it is seen that the filtration efficiencies of different masks vary significantly, with n having the best performance, which is followed by the surgical mask. it is also seen that all masks could capture large particles. the n , surgical, and procedure masks remove aerosols larger than a couple of microns. cotton and gauze masks capture a major fraction of particles larger than µm. the capture efficiency of all masks also shows an increasing trend as particle size becomes smaller than nm due to the effect of the brownian motion of nanoparticles. figure also shows that the filtration efficiencies of all respiratory masks drop for the particle sizes in the range of nm to about µm. this is because, in this size range, both the inertia impaction and the brownian diffusion effect are small, and the mask capture efficiency reduces. based on these results, and the earlier finding that most ejected droplets within the cloud have become sub-micron-sized aerosol particles by about o( − ) m distance, it can be stated that only professional masks such as n , surgical, and procedure masks provide reliable reduction in the inhaled particles. hence, the importance for healthcare workers to have access to high-grade respirators upon entering a room or space with infectious patients [ ] . it should be emphasized that the concentration that a receiving host will inhale (φ inhaled ) depends on the local concentration in the breathing zone adjusted by the aspiration efficiency given by equations ( ) and ( ) (or plotted in figure ). when the receiving host wears a mask, an additional important correction is needed by multiplying by a factor ( − η f ), where η f is the filtration efficiency plotted in figure . that is, where φ(d, t) is the droplet nuclei concentration at the breathing zone given in ( ) or ( ) . it is seen that the concentration of inhaled droplets larger than microns significantly decreases when the mask is used. but the exposure to smaller droplets, particularly, in the size range of nm to µm varies with the kind of mask used. the object of this section is to put together the different models of the puff and droplet evolution described in the previous sections, underline their simplifications, and demonstrate their ability to make useful predictions. such results under varying scenarios can then be potentially used for science-based policy making, such as establishing multi-layered social distancing guidelines and other safety measures. in particular, we aim at modeling the evolution of the puff and the . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . concentration of airborne droplets and nuclei that remain within the cloud so that the probability of potential transmission can be estimated. as discussed in section . , the virus-laden droplets exhaled by an infected host will undergo a number of transformations before reaching the next potential host. to prevent transmission, current safety measures impose a safety distance of two meters. furthermore, cloth masks are widely used by the public and their effectiveness has been shown to be questionable for droplets and aerosols of size about a micron. the adequacy of these common recommendations and practices can be evaluated by investigating the concentration of airborne droplets and nuclei at distances larger than one meter and the probability of them being around a micron in diameter, since such an outcome will substantially increase the chances of transmission. in the following we will examine two effects: the presence of small quantities of non-volatile matter in the ejected drops that remain as droplet nuclei after evaporation, and the adequacy of the log-normal or pareto distribution to quantify the number of droplets in the lower diameter classes. let us consider the situation of speaking or coughing, whose initial puff volume and momentum are such that they yield s e . m and t e . s. under this specific condition, as shown in figure the puff travels about m in about s . for this simple example scenario, we will examine our ability to predict airborne droplet and nuclei concentration, as an important step towards estimating the potential for airborne transmission in situations commonly encountered. in most of the countries, current guidelines are based on the work by xie et al. [ ] , who revisited previous guidelines by [ ] with improved evaporation and settling models. they identified the possibility that, due to evaporation, the droplets quickly become aerosolized before reaching a significant distance and thus may represent a minor danger for transmission due to their minimal virus loading. this scenario is shown in figure , where we present the evolution of the drop size spectrum while droplets are transported by the ejected puff. the initial droplet size distribution is taken to be that measured by duguid [ ] modeled with a log-normal distribution, which in the monte-carlo approach is randomly sampled with one million droplets divided into one thousand diameter classes. each droplet is then followed while evaporating and falling. the evaporation model is taken to be ( ) with the effective diffusion coefficient estimated as k · − m /s. this value is computed under the assumption that drops are made of either pure water or a saline solution [ ] and that air has about % humidity. therefore, this is an environment unfavorable to evaporation and consequently drop size reduction happens relatively slowly. however, from the figure it is clear that, even in this extreme case, after few tens of centimeters, and within a second, all droplets have evaporated down to a size below µm. this is in line with the predictions of xie et al. [ ] . naturally, if the air is dryer, the effective evaporation coefficient will be larger (even as large as k − m /s) and the droplet size spectrum will evolve even faster, leaving virtually all droplets to be smaller than µm in the puff. in the model, we set the minimum diameter that all drops can achieve equal to µm (shown by the single point indicated in the figure) so to emphasize this effect of the model. recall that intermittency of turbulence with the puff can create clusters of droplets and concentration of vapor and thereby significantly alter the evaporation rate [ , , ] . hence, our estimate of evaporation time is a lower bound, as governed by the d -law ( ). as discussed in section . there is current consensus that droplets ejected during sneezing or coughing contain, in addition to water, other biological and particulate non-volatile matter. specifically, viruses themselves are just large protein chains of size almost . µm. here we will examine the evolution of droplet size distribution in the presence of non-volatile matter. it will be clear in the following, that in this case, even a small amount of non-volatile matter plays an important role with the evaporation coefficient being a minor factor in deciding how fast the final state is reached. in figure , we show the final distribution of droplets under two scenarios, where the initially ejected droplets contain . % and . % of non-volatile matter. in figure a , the initial drop size distribution is modeled as a log-normal distribution (i.e., as in fig. ), whereas in figure b , the initial drop size distribution is modeled according to the pareto distribution with initial droplet size varying between and µm. this range is smaller than that suggested earlier in section . however, drops that are larger than µm fall out of the cloud and therefore are not important for airborne transmission and droplets initially smaller than µm have much smaller viral load. here "final droplet size distribution" indicates the number of droplets that remain within the puff after all the larger droplets have fallen out and all others have completed their evaporation to become droplet nuclei. this final number of droplet nuclei as a function of size does not vary with time or distance. the size distribution is computed here as in figure , with a random sampling from the initial log-normal or pareto distribution. as before, these computations used an evaporation coefficient of k = − m /s. however, there are two important differences: each droplet is allowed to fall vertically according to its time-dependent settling velocity, w , which decreases over time as the droplet evaporates. integration of the fall velocity over time provides the distance traveled by the droplet relative to the puff. droplets whose fall distance exceeds the size of the puff are removed from consideration. second, each droplet that remains within the puff evaporates to its limiting droplet . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . https://doi.org/ . / . . . doi: medrxiv preprint nuclei size that is dictated by the initial amount of non-volatile matter contained within the droplet. for ψ = . % non-volatile matter, the final aerosol size cannot decrease below % of the initial droplet diameter, whereas for . % of non-volatile matter, the final droplet size cannot decrease below % of the initial diameter. from fig. , it is clear that when evaporation is complete, the drop size distribution rigidly shifts towards smaller diameters, with a cut-off upper diameter due to the settling of large drops. essentially, it is clear that the initial number of viruses that were in droplets of size smaller than d e,exit still remain within the cloud almost unchanged, representing a more dangerous source of transmission than predicted by the conventional assumption of near-full evaporation. again, it is important to note that the final droplet size distribution is established rapidly even with the somewhat lower effective evaporation diffusivity of k = − m /s, and when not accounting for the effect of localized moisture of the cloud in further reducing the rate. figure also illustrates the important difference in the drop size distribution. the pareto distribution will predict a much larger number of drops in the micron and sub-micron range, possibly the most dangerous for both inhalation efficiency and filtration inefficiency. in this section we will demonstrate the efficacy of the simple model presented in ( ) and ( ) for the prediction of droplet/aerosol concentration. in contrast to the monte-carlo approach of the previous subsection, where the evolution of each droplet was accurately integrated, here we will use the analytical prediction along with its simplifying assumptions. the cases considered are identical to those presented in figure for ψ = . % and k = − m /s. the initial droplet size distributions considered are again log-normal and pareto distributions. in this case, however, we underline that the quantity of importance in airborne transmission is not the total number of droplet nuclei, but rather their concentration in the proximity of a susceptible host. accordingly, we plot in figure airborne droplet and nuclei concentration (per liter) of volume as a function of droplet size. here the area under the curve between any two diameters yields the number of droplets within this size range per liter of volume within the cloud. at the early times of t = . and . s, we see that larger droplets above a certain size have fallen out of the cloud, while droplet nuclei smaller than d evap have fully evaporated and their distribution is a rigidly-shifted version of the original distribution. the distribution of intermediate size airborne droplets reflects the fact that they are still undergoing evaporation. unlike in figure , the concentration continues to fall . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . even after t lim . s when the number and size of droplets within the cloud have reached their limiting value. this is simply due to the fact that the volume of the puff continues to increase and this continuously dilutes the aerosol concentration. most importantly, the results of the simple model presented in ( ) and ( ) are in excellent agreement with those obtained from monte-carlo simulation. the increasing size of the contaminated cloud with time can be predicted with ( ) and the centroid is given by the scaling law ( ) . figure : droplet/aerosol concentration evolution as predicted by the analytical model presented in ( ) and ( ) . left frame shows the evolution starting from the log-normal distribution. right frame shows the evolution starting from the pareto distribution. both cases use k = − m s. the primary goal of this paper is to provide a unified theoretical framework that accounts for all the physical processes of importance, from the ejection of droplets by breathing, talking, coughing and sneezing to the inhalation of resulting aerosols by the receiving host. these processes include: (i) forward advection of the exhaled droplets with the puff of air initially ejected; (ii) growth of the puff by entrainment of ambient air and its deceleration due to drag; (iii) gravitational settling of some of the droplets out of the puff; (iv) modeling of droplets evaporation, assuming that the d law prevails; (v) presence of non-volatile compounds which form the droplet nuclei left behind after evaporation; (vi) late-time dispersal of the droplet nuclei-laden cloud due to ambient air turbulent dispersion. despite the complex nature of the physical processes involved, the theoretical framework results in a simple model for the airborne droplet and nuclei concentration within the cloud as a function of droplet diameter and time, which is summarized in equations ( ), ( ) and ( ) . this framework can be used to calculate the concentration of virus-laden nuclei at the location of any receiving host as a function of time. as additional processes, the paper also considers (vii) efficiency of aspiration of the droplet nuclei by the receiving host; and (viii) effectiveness of different kinds of masks in filtering the nuclei of varying size. it must be emphasized that the theoretical framework has been designed to be simple and therefore involves a number of simplifying assumptions. hence, it must be considered as the . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . starting point. by relaxing the approximations and by adding additional physical processes of relevance, more complex theoretical models can be developed. one of the primary advantages of such a simple theoretical framework is that varying scenarios can be considered quite easily: these different scenarios include varying initial puff volume, puff velocity, number of droplets ejected, their size distribution, non-volatile content, ambient temperature, humidity, and ambient turbulence. the present theoretical framework can be, and perhaps must be, improved in several significant ways in order for it to become an important tool for reliable prediction of transmission. (i) accurate quantification of the initially ejected droplets still remains a major challenge. further high-quality experimental measurements and high-fidelity simulations [ ] are required, especially mimicking the actual processes of talking, coughing and sneezing, to fully understand the entire range of droplet sizes produced during the exhalation process. (ii) as demonstrated above, the rate at which an ejected droplet evaporates plays an important role in determining how fast they reach their fully-evaporated state. it is thus important to calculate more precisely the evaporation rate of non-volatile-containing realistic droplets resulting from human exhalation. the precise value of evaporation rate may not be important when droplets evaporate fast, since all droplets remaining within the puff would have completed their evaporation. but under slow evaporation conditions, accurate evaluation of evaporation is important. (iii) the assumption of uniform spatial distribution of droplets within the puff and later within the dispersing cloud is a serious approximation [ ] . the intermittency of turbulence within the initial puff and later within the droplet cloud is important to understand and couple with the evaporation dynamics of the droplets. in addition to the role of intermittency, even the mean concentration of airborne droplets and nuclei may decay from the center to the outer periphery of the puff/cloud. characterization of this inhomogeneous distribution will improve the predictive capability of the model. (iv) the presence of significant ambient mean flow and turbulence either from indoor ventilation or outdoor cross-flow will greatly influence the dispersion of the virus-laden droplets. but accounting for their effects can be challenging even in experimental and computational approaches. detailed experiments and highly-resolved simulations of specific scenarios should be pursued. but it will not be possible to cover all possible scenarios with such an approach. a simpler approach where the above theoretical framework can be extended to include additional models such as random flight model (similar to those pursued in the calculation of atmospheric dispersion of pollutants [ ] ) may be promising approaches. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . https://doi.org/ . / . . . doi: medrxiv preprint . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . https://doi.org/ . / . . . doi: medrxiv preprint . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . https://doi.org/ . / . . . doi: medrxiv preprint . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . https://doi.org/ . / . . . doi: medrxiv preprint aerosol inhalability in low air movement 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facepiece respirators key: cord- - yuzl he authors: woo, myung-heui; hsu, yu-mei; wu, chang-yu; heimbuch, brian; wander, joseph title: method for contamination of filtering facepiece respirators by deposition of ms viral aerosols date: - - journal: journal of aerosol science doi: . /j.jaerosci. . . sha: doc_id: cord_uid: yuzl he abstract a droplet/aerosol loading chamber was designed to deliver uniform droplets/aerosols onto substrates. an ultrasonic nebulizer was used to produce virus-containing droplets from artificial saliva to emulate those from coughing and sneezing. the operating conditions were determined by adjusting various parameters to achieve loading density and uniformity requirements. the count median diameter and mass median diameter were . – and – μm, respectively, around the loading location when % relative humidity was applied. the average loading density was ∼ × plaque-forming units/cm for -min loading time with a virus titer of plaque-forming units/ml. six different filtering facepiece respirators from commercial sources were loaded to evaluate uniform distribution. for each of the six ffrs, the virus loading uniformity within a sample and across numerous samples was . % and . %, respectively. this system supports a standard method for loading viable bioaerosols onto specimen surfaces when different decontamination techniques are to be compared. the public's concern about bioterrorism (e.g., the anthrax attack) and spread of airborne pathogens (e.g., severe acute respiratory syndrome (sars) and avian flu (h n )) through the aerosol route has increased greatly in recent years (tellier, ) . for example, in and , sars caused over illnesses and deaths, and there is still no adequate treatment (yang, lee, chen, wu, & yu, ) . the recent swine flu outbreak due to a new strain of h n influenza a has caused illness in over countries and resulted in deaths worldwide as of july (who, ). on june , , the world health organization (who) raised the pandemic alert level to phase , indicating the onset of a global pandemic (cdc, ) . one effective method for protection against airborne pathogens during pandemic spread through droplet and aerosol transmission is to wear a filtering facepiece respirator (ffr) certified by national institute for occupational safety and health (niosh) . this approach considerably decreases the incidence and severity of infection. the center for disease control and prevention (cdc) has issued guidelines about the use of face masks and respirators to protect against h n transmission in healthcare facilities (cdc, ). however, using medical masks and n ffrs as countermeasures for bioaerosols has not been demonstrated to provide a complete response: ( ) although using surgical masks and n ffrs for tuberculosis has been shown to meet cdc guidelines, the same is not true for viral agents such as the swine flu virus. ( ) there is no experimental basis upon which the ffr's life span in an h n scenario can be estimated. ( ) the stockpile of ffrs will be exhausted in the event of a severe pandemic. cdc estimates that more than million ffrs will be required for healthcare workers in the us if a pandemic influenza event persists for days (cdrf, ) . one possible approach to resolve insufficient supplies of ffrs is to decontaminate the ffrs by applying disinfecting agents/processes, such as microwave irradiation, ultraviolet germicidal irradiation (uvgi), bleach solution, peroxides, etc., and then reusing the decontaminated respirator. to qualify a method to decontaminate an ffr for reuse, one must provide a statistically robust demonstration that the technologies applied do not alter the mechanical properties of the ffr, do not leave any toxic byproduct on the ffr, and achieve at least four-log virucidal efficacy on the materials of construction of the ffr. however, no protocol has been reported for such decontamination testing, a consequence of two main limitations. first, no standard test method has been reported for simulating bioaerosol contamination of the ffrs. second, the unique properties of bioaerosols generated by respiratory secretions can be expected to affect the efficacy of the decontamination process, and the window of operating conditions affording controlled and consistent properties is not known. therefore, development and validation of methods that are representative of human respiratory secretions is a necessary condition before one can realistically evaluate techniques for decontamination. influenza is commonly thought to be transmitted by three mechanisms (droplet, contact, and aerosol (droplet nuclei)) (cdrf, ) . some diseases (e.g., tuberculosis) are known to be mainly transmitted by the droplet nuclei route, whereas droplet transmission is considered by many to be the dominant route for some other diseases (e.g., mumps), although the actual routes are still being debated (fiegel, clarke, & edwards, ; tellier, ; yang et al., ) . salgado, farr, hall, and hayden ( ) suggested different roles in influenza between droplet and aerosol transmission. influenza is mainly spread through droplet transmission by coughing and sneezing from infectious people, while aerosol transmission is important for long-distance and sporadic infection. an infected human can be a source of large droplets generated by coughing and sneezing. during airborne transmission, these droplets will shrink in size with the consequence that both droplets and droplet nuclei contact surfaces. although many researchers have examined the droplet size generated from humans, the actual size is not clear. yang et al. ( ) reported that most droplets from coughing, sneezing, and talking have diameter between and mm, and these droplets may contract depending on the humidity and medium generated. viruses in these droplets can aggregate with each other or be encased by the saliva component, both enhancing persistence of viability. meanwhile, viability of viruses in saliva can be attenuated by an enzyme action (diaz-arnold & marek, ) . therefore, it is important that the transmission medium be factored into the design of the test method. the focus of this study is to develop a method for reproducibly applying fixed amounts of representative viral particles generated from droplets/aerosols onto ffrs for decontamination testing. this study had specific objectives: ( ) to build a droplet/aerosol chamber system that generates droplets/aerosols containing viruses to emulate those from coughing and sneezing, ( ) to deliver the droplets and resultant aerosol onto specimens of six commercially available ffrs, and ( ) to demonstrate uniformity of deposition within a sample and across independent samples by achieving quarter-to-quarter (q-t-q) and sample-to-sample (s-t-s) coefficients of variations (cvs) of less than % and %, respectively. while the focus of this study was ffrs and a biosafety level (bsl)-i virus, the system was designed to be used with bsl-ii microorganisms, which require advanced containment. this fact limited the overall size of the unit, due to the requirement for secondary containment of the test system. the system also has utility outside of ffrs and could be used to load any surface (e.g., a surgical scalpel or glove). ms bacteriophage (ms ; atcc s , -b tm ) was applied as the first challenging bioaerosol, because it requires only a bsl-i facility. ms has a nonenveloped, icosahedral capsid with a nominal diameter of . nm (prescott, harley, & klein, ; valegard, lijas, fridborg, & unge, ) . ms infects only male escherichia coli (e. coli) and is commonly used as a non-pathogenic surrogate for human pathogenic viruses (e.g., poliovirus, influenza a, and rhinovirus), because of its similarity in resistance to antimicrobial agents and ease of preparation and assay (aranha-creado & brandwein, ; brion & silverstein, ; fisher, rengasamy, viscusi, vo, & shaffer, ). freeze-dried ms was suspended in deionized (di) water to a titer of approximately - plaque-forming units (pfu) per ml and stored at c. artificial saliva was used as the nebulization fluid to emulate droplets generated by coughing and sneezing. saliva is a very dilute fluid composed of more than % water, plus electrolytes, proteins, and enzymes (diaz-arnold & marek, ) . a variety of inorganic ions maintain osmotic balance and offer buffering (diaz-arnold & marek, ; dodds, johnson, & yeh, ; humphrey & williamson, ) . the compounds and their corresponding amounts of artificial saliva are listed in table (aps & martens, ; edward et al., ; veerman, van den keybus, vissink, & nieuw amerongen, ; wong & sissions, ) . mucin from porcine stomach (sigma-aldrich, m ) was chosen as the representative mucus stimulant (vingerhoeds, blijdenstein, zoet, & aken, ). six different models of ffrs approved by niosh were employed in this study. three of those models were also approved by the food and drug administration (fda) as surgical devices. each type of ffr has different characteristics, such as number of layers, hydrophilicity, and physical shape. prior to an ffr testing, -mm diameter discs of flat glass-fiber filter (gelman science, ) were used to determine workable operating conditions of virus concentration, flow rate, and loading time. a droplet/aerosol loading system was custom built for this study with the following requirements: ( ) the width and height are less than cm so that it can be placed in a biosafety cabinet; ( ) parts can be easily disassembled for sterilization; ( ) droplets/aerosols can be distributed uniformly onto substrates; ( ) the droplet size distribution is consistent; ( ) environmental conditions that can affect the droplet size, such as relative humidity (rh) and temperature, can be controlled. the schematic design of the loading system is shown in fig. . the system consists of a chamber body, an ultrasonic generator ( t, sonear s , farmingdale, ny) for producing the droplets, a bubbler for generating moisture, compressed cylinder air for controlling rh and diluting virus concentrations, an rh meter for measuring humidity, a sixport manifold for distributing the aerosols, a thermometer for measuring temperature, and six supports to hold the flexible-form ffrs during loading (baron et al., ; feather & chen, ; fisher et al., ) . this system can also include a charge neutralizer (model , tsi inc., shoreview, mn). the chamber body was fabricated from stainless steel sheet with welded seams to withstand the high temperature for sterilization. the turntable and six perforated sample plates were employed to increase uniformity of deposition. the particle size distributions (psds) were measured by an aerodynamic particle sizer (aps; model , tsi inc., shoreview, mn) through a port on the side of the chamber. before and after experiments, the chamber was decontaminated by wiping the interior of the chamber with isopropyl alcohol, then allowing the chamber to set for min. six samples were placed onto the supports on the turntable using sterile forceps. theoretically, a titer of around pfu/ml in the ultrasonic nebulizer with -min loading time should provide sufficient loading density ( pfu/cm ). the titer was prepared by adding . ml virus stock suspension into ml artificial saliva. the droplets from the ultrasonic nebulizer after passing the distributor entered the chamber through six inlets. the size of droplets generated and loaded can be affected by the frequency of the ultrasonic generator and by environmental conditions such as rh and temperature. for this study, the frequency of the generator was . mhz and the environmental conditions were c and %. low rh was chosen because the survivability of ms is high under this condition. after loading, the residual droplets were allowed to clear for min, and the ffr samples were taken out for extraction and assay. various operating parameters were evaluated to determine the conditions that would provide desired droplet characteristics, including loading time ( - min), virus titer ( - pfu/ml), turntable speed ( - rpm), airflow rate ( - lpm), and mucin concentration ( . - . %). the loading density was controlled by adjusting the loading time and the titer of the virus suspension. to evaluate how viability of the virus is influenced by the ultrasonic process, bioaerosols produced at different times were collected by a biosampler and their viability was compared. the turntable speed was varied to determine its relationship with uniformity. flow rate and mucin loading were also varied to investigate their effects on the consistency of delivered droplets. three runs were carried out for each set of conditions. after loading with virus, each filter sample was cut into four equal quarters. each quarter was immersed in ml of extraction medium in a -ml conical tube. a . m glycine solution was applied to extract ms from the quarter sample with agitation by a wrist-action shaker (model , burrell scientific, pittsburgh, pa.) at a angle for min to analyze the loading density (these conditions showed the best extraction efficiency in preliminary testing). the extracted solution was assayed by using the single-layer method (epa, ) to determine the loading density according to eq. ( ) with the where ld is the loading density, v is the volume of extraction solution, v is the volume of sample, d is the diameter of the filter, and n is the number of dilutions (lee et al., ). to visualize the particle loading, scanning electron microscopy (sem, jeol jsm- f, jeol inc.) of the filter was done before and after loading particles. the q-t-q and s-t-s cvs of loading density were obtained to evaluate the uniformity. r . software (cran) and microsoft excel s were used to calculate one-way analysis of variance (anova) and cv, respectively. the impact of ultrasonic nebulization on viability of virus in the nebulizer reservoir was investigated by measuring the viable counts over time. the results present no significant difference in virus viability between and min (p = . ) (data not shown). apparently, the heat shock from ultrasonic vibration did not cause damage to the ms in the reservoir during droplet generation. to determine the effect of ultrasonication on virus during droplet generation, viability of the viruses collected in the biosampler after and min of generation was examined. the theoretical concentration in the biosampler after min of nebulization is  pfu/ml when the virus titer in the reservoir is .  pfu/ml. the -min time-weighted ( - and - min) average concentration of collected viruses in the biosampler was approximately .  pfu/ml, which is similar to the theoretical value. as demonstrated, the ultrasonic nebulizer can be used to produce droplets containing ms virus without adverse effects on viability. fig. a displays the virus loading density as a function of loading time and fig. b shows the loading density as a function of the viral titer. as shown, the loading density had a linear relationship with time and with virus titer in the nebulization medium, as expected based on the initial viability tests. the results show that these two parameters can be adjusted to acquire a desired loading density. it should be noted that in determining the loading density the extracted fraction was assumed to be ; however, different types of ffrs will have different values that depend on the material property and structure. the uniformity tests were conducted with the turntable at various speeds because marple and rubow ( ) observed increased uniformity of cv from . % to . % when they rotated their aerosol chamber at . rpm. fig. shows the cvs from three runs as a function of turntable speed. the variation of the cvs was somewhat larger than marple and rubow ( ) reported due to variability working with a viable system (ms ) vs. a non-viable system (psl and dust). the flow rate ( lpm) of this work is much lower than the rate ( lpm) used by marple and rubow ( ) , and delivers a distribution of droplets that is sufficiently uniform (cvo %) even without the turntable, which appears to provide a moderate decrease in cv with increasing rotation rate. the difference among the six positions was not statistically significant (p = . ) for flat-sheet glass-fiber filters. the reason for this uniformity is likely because settling is the dominant mechanism for large droplets in our system and a six-port distributor delivered the bioaerosols. a straight fog stream was observed through the front window during the loading. therefore, the turntable speed was not an important parameter to meet the uniformity criteria when the flatsheet filter was employed. the deposition of the particles on ffrs after loading for min was also confirmed by an sem. as shown in fig. , particles were randomly distributed on fiber surface without any specific pattern. the criterion for minimum loading density - pfu/cm -was achieved for all conditions tested and could be easily increased if needed. based on these results, the operating conditions to be discussed later were chosen to be -min loading time at a titer of pfu/ml and rpm turntable speed. fig. shows the size distribution of droplets generated by the ultrasonic nebulizer at different flow rates. the size distributions of droplets generated at - lpm were similar, with count median diameters (cmds) and mass median diameters (mmds) of . and mm, respectively. the droplet size distributions at and lpm were slightly shifted to a smaller diameter. bimodal distribution was observed in the mass-based size distribution, with modes at - mm and over mm. the theoretical cmd from the ultrasonic nebulizer can be determined from eq. ( ) (lang, ) where d p is the nebulized droplet size, s is the surface tension of the liquid, r is the density of the liquid, and f is the frequency of the nebulizer. as shown, the droplet size is independent of the flow rate. the gentle airflow within - lpm just carries the aerosol away from the liquid surface. however, at a higher flow rate, the larger volume of dry dilution air promotes evaporation, and therefore results in a smaller droplet size. to generate droplets of other sizes, the frequency can be adjusted. for example, droplets are expected to be . and . times larger, respectively, when lower frequencies of or khz are used instead of . mhz (lang, ) . the mucin concentration also plays an important role in determining the initial droplet size because it affects surface tension and density of the artificial saliva used. mucin at . % was chosen for the artificial saliva in this study to match the protein content in human saliva. increasing the mucin concentration threefold would reduce the median size to % of its original size because of the decrease in surface tension. in summary, the droplet size can be controlled by adjusting the composition of the spray medium, the frequency of the ultrasonic generator, and the flow rate. the droplet size decreases from the point of generation at the ultrasonic nebulizer all the way to the filter surface due to evaporation, and the size deposited depends on the environmental conditions (i.e., temperature and rh). the flow rates of the ultrasonic generator, dilution air, and temperature of the bubbler can be used to control rh, and heating tape (part (b) in fig. ) can be used to adjust the temperature. fig. displays the droplet size distribution generated and loaded at lpm through the aerosol generator plus lpm dry air to provide % rh. for this condition, the cylinder air without a bubbler was applied to achieve the low-rh condition. the mmds for droplets generated and loaded were . and . mm, respectively, with corresponding cmds of . and . mm, which are similar to the droplet size reported in the literature (yang et al., ; morawska et al. ) to have been generated by humans. the droplet's residence time is . s when settling is considered the main mechanism acting in this chamber. the droplet's theoretical lifetime at % rh is around . s, which means that droplets just reaching the ffr are almost completely evaporated. the size of a completely evaporated droplet can be calculated according to eq. ( ) where d p is the diameter of the aerosol particle and f v is the volume fraction of solid material in the suspension in the nebulizer. for . % mucin, the volume fraction is .  À , so d p is calculated to be . mm when d d is . mm. the reason the measured value is higher than the theoretical value is an incomplete evaporation. after running the experiment, we noted that the filter surface was slightly damp, which is consistent with the above interpretation. fig. . the number-and mass-based particle size distribution of generated droplets and loaded droplets at lpm through the aerosol generator plus lpm dry air and -rpm turntable speed. loading density and cvs of q-t-q and s-t-s for six different ffrs (n = , criteria of cv for q-t-q and s-t-s: % and %, respectively). the cvs for uniform deposition of droplets/aerosols onto substrates for six different ffrs were calculated by analyzing the infectivity of viruses extracted from the loaded filter (table ). the flexible nature of the ffrs makes it difficult to achieve deposition on the same spot with the same shape each time. therefore, a holding medium is necessary to achieve low cv values. even for fixed-form ffrs, some inherently cannot produce equal quarters because the shape is not symmetric. operational variation while cutting the sample (e.g., uneven quarters) can also contribute to larger cv values. consequently, the cv for q-t-q was higher than that for s-t-s over all ffrs. it is possible to use circular areas punched from an ffr so that the difference in shape will not influence the results. however, this was outside the scope of the study, which aimed to evaluate decontamination effectiveness using an entire ffr. nevertheless, the average cvs for both q-t-q and s-t-s for all ffrs were lower than the criteria - % and %, respectivelydemonstrating the system's ability to consistently load the test agents. table also displays the results of the loading densities. as shown, all sets had sufficient quantity to meet the threshold criteria. due to differences in surface properties, the loading density of different respirator models can be different even when the same operating conditions are applied. fig. shows the extraction efficiency of three different ffrs at various extraction times. different layer structures and properties of the ffrs are responsible for the differences as discussed. the shape of the ffr is another reason for differences in loading density. the loading density reported in table was calculated based on the ffr's projected area. the ffr, having a duck-bill shape, showed a lower loading density owing to its different curvature. as shown, both factors can affect loading density. nevertheless, the loading density can be easily met in a controlled fashion using the specified conditions, and can be conveniently increased by adjusting the loading time, virus titer, or both. a simple system for producing, delivering, and loading of consistent challenges of droplets/aerosols containing virus onto ffrs has been developed and assessed. the respective cvs for s-t-s and q-t-q for the six niosh-certified ffrs tested were . and . , lower than the criteria - % and %, respectively. the droplet size can be altered by tuning the frequency of the ultrasonic nebulizer, by changing the composition of the dispersion aerosolized, and by adjusting the temperature and rh inside the chamber. droplets emulating bioaerosols released during coughing and sneezing can be produced using specific conditions and the loading density can be achieved by controlling the loading time and the virus titer in the nebulization medium. this system allows for development and validation of a standard method for loading bioaerosol challenges when different decontamination techniques are to be compared. it also has utility for loading surfaces to study fomite transmission and reaerosolization of particles from surfaces. it can be further applied to generate and load droplets and aerosols of different sizes and to load onto materials other than ffrs. valuable comments on the design of the delivery chamber and to the major analytical instrumentation center, department of materials science and engineering at the university of florida for providing the sem. the authors also wish to acknowledge ken reed (tmr, gainesville) for building the chamber for this project. myung-heui woo acknowledges the alumni scholarship from the university of florida for partial financial support. review: the physiology of saliva and transfer of drugs into saliva application of bacteriophages as surrogates for mammalian viruses: a case for use in filter validation based on precedents and current practices in medical and environmental virology development of an aerosol system for uniformly depositing bacillus anthracis spore particles on surfaces iodine disinfection of a model bacteriophage, ms , demonstrating apparent rebound fact sheet: novel h n flu situation update the impact of saliva on patient care: a literature review health benefit of saliva: a review inhaling to mitigate exhaled bioaerosols design and use of a settling chamber for sampler evaluation under calm-air conditions airborne infectious disease and the suppression of pulmonary bioaerosols development of a test system to apply virus containing particles to filtering facepiece respirators for the evaluation of decontamination procedure a review of saliva: normal composition, flow and function ultrasonic atomization of liquid assessment of iodine-treated filter media for removal and inactivation of ms bacteriophage aerosols an aerosol chamber for instrument evaluation and calibration size distribution and sites of origin of droplets expelled from the human respiratory tract during expiratory activities microbiology influenza in the acute hospital setting review of aerosol transmission of influenza the three-dimensional structure of the bacterial virus ms human glandular salivas: their separate collection and analysis emulsion flocculation induced by saliva and mucin a comparison of human dental plaque microcosm biofilms grown in an undefined medium and a chemically defined artificial saliva the size and concentration of droplets generated by coughing in human subjects this research was supported by the air force research laboratory through contract no. fa - -c . the authors are grateful to profs. dale lundgren (university of florida) and virgil marple (university of minnesota) for providing key: cord- -xx w dc authors: ding, yun; choo, jaebum; demello, andrew j. title: from single-molecule detection to next-generation sequencing: microfluidic droplets for high-throughput nucleic acid analysis date: - - journal: microfluid nanofluidics doi: . /s - - - sha: doc_id: cord_uid: xx w dc droplet-based microfluidic technologies have proved themselves to be of significant utility in the performance of high-throughput chemical and biological experiments. by encapsulating and isolating reagents within femtoliter–nanoliter droplet, millions of (bio) chemical reactions can be processed in a parallel fashion and on ultra-short timescales. recent applications of such technologies to genetic analysis have suggested significant utility in low-cost, efficient and rapid workflows for dna amplification, rare mutation detection, antibody screening and next-generation sequencing. to this end, we describe and highlight some of the most interesting recent developments and applications of droplet-based microfluidics in the broad area of nucleic acid analysis. in addition, we also present a cursory description of some of the most essential functional components, which allow the creation of integrated and complex workflows based on flowing streams of droplets. emulsions (or collections of isolated droplets surrounded by a continuous and immiscible carrier fluid) have long been used in chemical and biological experimentation, with the millions of contained droplets serving as isolated vessels in which reactions or assays may be performed ( fig. a ) (griffiths and tawfik ) . the use of bulk shear forces, although efficient in making large numbers of droplets on short timescales, generates polydisperse droplet populations that prohibit quantitative experimentation (huebner et al. ; pekin et al. ; juul et al. ) . conversely, and as will be shown subsequently, flowbased microfluidic systems can be used to generate similarly large numbers of droplets, but with an unprecedented degree of control over droplet size. these features combined with the facility to adjust the chemical or biological payload at will make microfluidic droplets highly promising vehicles for large-scale biological experimentation. an important application of droplet-based microfluidic systems is in the analysis of nucleic acids. indeed, recent developments have seen the establishment of robust and high-throughput genotyping assays and expression analysis at the single-cell level (macosko et al. ; zeng et al. ; turchaninova et al. ; eastburn et al. ) . a key feature in this respect is the ability to perform rapid dna amplification (via the polymerase chain reaction or pcr) within millions of individual droplets in a parallel fashion (tewhey et al. ; markey et al. ; hindson et al. ) . droplet-based pcr involves the partitioning of a large reaction volume into millions of smaller volumes, which statistically will either be empty or will contain a single copy of target dna. subsequent thermal cycling of all droplets within a sample yields signal only in droplets that originally contained dna. accordingly, quantitation is ensured via a simple process of counting. this feature combined with reduced reagent consumption and efficient heat transfer, engenders a range of experiments (such as rare mutation detection and bias-free amplification) that are simply not possible in other formats (kalinina et al. ) . the realisation of formats for droplet-based pcr (griffiths and tawfik ; williams et al. ; nakano et al. ) has had an immense impact on single-molecule pcr (kumaresan et al. ; diehl et al. ) and has already become a critical component of next-generation sequencing technologies (white et al. ; margulies et al. ) . at a basic level, the utility of droplet-based microfluidic systems in biological experimentation stems from the ability to control and manipulate droplets in a passive, reproducible and rapid fashion. indeed, and unsurprisingly, such platforms have also been used to good effect in many other applications, including nanomaterial synthesis (lignos et al. ) , kinetic analysis (lignos et al. ; bui et al. ) , drug delivery (xu et al. ), high-throughput screening (sjostrom et al. ) and single-cell analysis (brouzes et al. ). in the current review, we aim to survey recent developments in the use of droplet-based microfluidics for nucleic acid analysis, first highlighting key areas where such microfluidic tools have had significant effect and secondly proposing related applications where microfluidic technologies may have impact in the short to medium term. we also note that although essential background knowledge, such as the manner in which droplets are formed and manipulated, will be introduced, more detailed and comprehensive analyses of droplet-based microfluidic systems can be found elsewhere (niu and demello ; oh et al. ; choi et al. ; baroud et al. ; kelly et al. ; shembekar et al. ; price and paegel ; collins et al. ) . emulsions formed using bulk shear forces on the macroscale have long been used to good effect in areas such as polymer chemistry (ugelstad et al. ) , cosmetic formulations (linn and west ) and complex food systems (garti ) . despite their utility, the challenges associated with controlling droplet size, composition and size distributions are immense, making their use in quantitative experimentation demanding. conversely, droplets (with volumes ranging from femtoliters to nanoliters) can be generated in a variety of ways within microfluidic systems. critically, passive strategies that leverage geometrical variations of fluidic structures can be used to transform arbitrary volumes of fluid into defined sub-nanoliter droplets at khz to mhz rates (shim et al. ) . at a simple level, the most common strategies for droplet production involve the use of cross-flow structures (t-junctions) (thorsen et al. ) , flow-focusing geometries (anna et al. ) , co-flow structures (umbanhowar et al. ; cramer et al. ) and step emulsification (sugiura et al. ; kobayashi et al. ) . in planar, chip-based systems immiscible aqueous and oil streams confined within microfluidic channels are brought together via external pressure (typically using syringe or pressure pumps), with droplets for the systems described herein, the discrete (droplet) phase is aqueous in nature and surrounded by an immiscible (oil-based) carrier phase. that said, the only requirements for establishing robust droplet flows are that the continuous phase should preferentially wet the channel surface and the surface tension at the fluid/fluid interface should be sufficiently high to avoid destruction of droplets by shear. (or plugs) being formed at the point of confluence. although the droplet generation mechanism is quite different in each these geometries, all involve the establishment of an interface between co-flowing, immiscible fluids, followed by self-segregation of one of the fluids into droplets that are surrounded by the other fluid. interestingly, variations on the above strategies have been used to good effect (ding et al. ; dangla et al. ) . for example, dangla et al. ( ) exploited gradients of confinement to realise highly robust droplet formation (fig. b) . using this method, droplets are formed due to curvature imbalance along the interface, without the need for shear associated with continuous phase flow. this means that droplet size is primarily determined by the gradient geometry and is insensitive to fluid properties. unsurprisingly, such a "pump-free" droplet generation method (fig. b) has wide ranging utility and potential in point-of-care or point-of-use applications. control of droplet size is of obvious importance when performing quantitative experiments; however, the ability to "load" droplets with multiple reagents at user-defined concentrations is even more critical. introduction of the dispersed phase through a branched inlet channel allows for the direct combination of multiple laminar streams just prior to droplet formation (song et al. ) , with the relative concentration of each reagent being defined by the fig. a physical and chemical variables in droplet-based experiments: ( ) temperature can be controlled over wide ranges, enabling pcr in emulsions; ( ) hydrophobic substrates or ligands can be delivered through the oil phase into aqueous droplets; ( ) watersoluble components can be delivered through nanoscale droplets or swollen micelles, allowing the regulation of biochemical processes; ( ) internal ph can be altered, for example, by the delivery of acetic acid; ( ) photocaged substrates and ligands can be introduced into the droplets during emulsification and photoactivated at later times. adapted from ref. (griffiths and tawfik ) with permis-sion, copyright© elsevier. b device geometry and mechanism of drop formation through confinement gradients. such an approach allows high-throughput production of controlled emulsions. images show an emulsion containing droplets with variable payloads but constant size. adapted from ref. (dangla et al. ) with permission, copyright© pnas. c -million droplet array for dpcr contains one droplet generator, splitters and a mm × . mm viewing chamber. adapted from ref. (hatch et al. ) with permission, copyright© rsc associated volumetric flow-rate ratios . notably, this strategy has been effective in creating droplet barcodes, in which co-encapsulation of multiple fluorophores spectrally encodes droplets and yields uniquely identifiable signatures (ji et al. ; gerver et al. ) . the passive production of droplets is simple, quick and efficient, however, limited in its ability to independently manipulate droplets in a dynamic and bespoke manner. in this respect, active methods show clear utility in creating user-defined droplets in a "droplet-on-demand" fashion. common actuating sources for such purposes include pneumatic pressure (unger et al. ; willaime et al. ; zeng et al. ), mechanical forces , electrical fields (link et al. ) , magnetic fields (vekselman et al. ) , acoustic waves (collins et al. ) , optical traps (lorenz et al. ) and thermal gradients (baroud et al. ) . for example, rane et al. ( ) used a pneumatic valve-based architecture to assemble combinational populations of enzyme-substrate droplets. specifically, unique combinations were programmed and generated in a droplet train in a highly reproducible manner. however, it should be remembered that active methods typically produce droplets at low generation frequencies and require the use of complex control equipment. accordingly, the choice of droplet generation method should be made on the basis of the specific experimental requirements. subsequent to their generation, droplets need to be manipulated in ways that mimic the standard analytical procedures used on the bench top. fortunately, a wide range of (both passive and active) functional components have been presented for operations that include droplet merging (niu et al. ; deng et al. ; mazutis and griffiths ; akartuna et al. ) , dilution (niu et al. ; sun and vanapalli ) , dosing (abate et al. ; chen et al. ) , splitting (link et al. ; gao et al. ) , pairing (ahn et al. ; bai et al. ) , sorting (baret et al. ; nam et al. ; cao et al. ) , trapping/releasing korczyk et al. ; courtney et al. ) , counting (boybay et al. ; yesiloz et al. ; ) and incubation (huebner et al. ; wen et al. ). an instructive example in this respect was reported by hatch et al. ( ) , who used successive bifurcations to split single droplets into daughter droplets in a rapid and passive fashion (fig. c ). using such a strategy, over one million droplets (that are either empty or contain one copy of target dna) could be generated in - min. droplet populations formed in this manner could be subsequently packed into on-chip storage chambers and thermally cycled for digital pcr analysis (hatch et al. ) . conversely, eastburn et al. ( ) reported a powerful and robust (active) method, termed picoinjection, which utilises a pressurised microchannel and periodic electric field to inject a controlled volume of reagent into a moving droplet. picoinjection has proved to be immensely useful in a range of complex, droplet-based assays, being compatible with common biological reagents such as nucleic acids and enzymes. the ability to link functional components within integrated and sequential workflows has been a key reason why droplet-based microfluidic systems have proved so advantageous in biological experimentation (brouzes et al. ; pan et al. ; cho et al. ) . put simply, complex chemical and biological assays can be performed in a rapid and efficient manner. in this respect, lan et al. ( ) assembled an elaborate workflow that leverages short-read dna sequencing to obtain long and accurate sequence reads (fig. a) . central to this process was the use of unique barcodes to label long-dna molecules, thus allowing short-reads of breakage fragments to be accurately reassembled. functional operations within such a workflow included droplet generation, thermal cycling, splitting, pairing/merging, incubation, triple-droplet pairing/merging, splitting, pinched-flow size sorting, and secondary thermal cycling. significantly, such an approach enables accurate sequencing up to kb, and opens up new opportunities for the identification of rare mutations inaccessible to conventional sequencing. in most situations, it is desirable that droplets maintain their size and composition over extended periods of time. longterm stability of droplets is almost exclusively facilitated by the use of appropriate surfactants, which act to inhibit droplet coalescence by stabilising the interface between the immiscible phases. surfactant molecules are normally mixed into the continuous phase, and upon contact with the discrete phase self-organise at the interface. an excellent review of droplet surfactants can be found elsewhere (baret ) , providing a comprehensive discussion of surfactant selection. however, in the current context, some key issues are worthy of discussion. first, although many oils and organic solvents can be used as carrier fluids in droplet-based microfluidic systems, when performing nucleic acid assays choices are somewhat restricted due to biocompatibility requirements and the need to exclude biological impurities. mineral oils and perfluorinated oils (such as hfe- , fc- and fc- ) are most two frequently used. when using mineral oils droplets can be efficiently stabilised by span (sorbitan monooleate) and abil em (a non-ionic, silicone-based emulsifier) (williams et al. ; schütze et al. ; bian et al. ) . nevertheless, due to the prevalence of fluorinated oils as carrier fluids (because of their excellent biocompatibility and high gas permeabilities), fluorosurfactants (perfluoropolyethers containing left: schematics and false-coloured images of devices. right: cartoons of molecular processes occurring inside droplets. first stage (top): single templates are encapsulated into droplets by a flowfocusing drop maker. inside each droplet pcr or mda is used to amplify the single template. second stage (middle): a split-merger is used to add transposases and precisely adjust template concentrations. template droplets are injected on the left side, split at junction ( ) so that / th of the droplet continues to pair with a reagent droplet generated on-chip at ( ), with the pair merging at the channel expansion ( ). inside droplets, the transposase reaction fragments templates and adds adaptors to each fragment. third stage (bottom): the device used for attaching barcodes to dna fragments. template droplets ( ) and barcode droplets ( ) are injected into the device where they pair with each other and a large pcr reagent droplet generated on-chip ( ). the three droplets merge at the electrode ( ) and are split into smaller droplets for thermal cycling ( ). inside droplets, barcodes are spliced onto fragments by overlap-extension pcr. scale bars are µm. adapted from ref. (lan et al. ) with permission, copyright© springer nature. b a summary of developments in (next-generation) sequencing. data are based on throughput metrics for the different platforms since their first instrument version came out. results are visualised by plotting throughput in raw bases versus read length. adapted from ref. (nederbragt ) under a cc by license. c principle comparison between two commercial synthetic long-read sequencing platforms. left: illumina's truseq. genomic dna templates are fragmented into - kb pieces. they are then partitioned into a microtitre plate, such that there are around templates in a single well. within the plate, each fragment is sheared to around bp and barcoded with a single barcode per well. the dna can then be pooled and sent through standard shortread pipelines. right: x genomics' emulsion-based sequencing. with as little as ng of starting material, the gemcode can partition arbitrarily large dna fragments, up to ~ kb, into micelles (also called "gems") along with gel beads containing adapter and barcode sequences. the gems typically contain ~ . × copies of the genome and unique barcode out of , . within each gem, the gel bead dissolves and smaller fragments of dna are amplified from the original large fragments, each with a barcode identifying the source gem. after sequencing, the reads are aligned and linked together to form a series of anchored fragments across a span of ~ kb. unlike the illumina system, this approach does not attempt to get full end-to-end coverage of a single dna fragment. instead, the reads from a single gem are dispersed across the original dna fragment and the cumulative coverage is derived from multiple gems with dispersed-but linked-reads. adapted from ref. (goodwin et al. ) with permission, copyright© springer nature hydrophilic head groups), such as perfluoropolyetherpolyethylenoxide triblock copolymers, have proved to offer exceptional long-term stabilisation of droplets in a range of situations. second, droplet size plays a critical role in emulsion stability, with the existence of thermodynamically and kinetically stable regions with respect to droplet radii (kabalnov ) . indeed, although fluorosurfactants can stabilise droplets (with diameters on the tens of microns scale) for weeks at room temperature (holtze et al. ) , unless absolutely essential droplets should be processed and assayed on the shortest appropriate timescales. put simply, when droplets are in close proximity for long periods of time (e.g. when packed in an incubation chamber) undesirable mass transfer between droplets will occur to some extent due to phenomena such as ostwald ripening, phase partitioning, bilayer diffusion or micelle-mediated transport (webster and cates ; calderó et al. ; skhiri et al. ; chen et al. ; gruner et al. ; debon et al. ) . that said, controlled molecular transport between droplets can in fact open up new and unexpected opportunities (gruner et al. ). in the current context, recent studies suggest that additives (such as bovine serum albumin) can decrease diffusion rates by forming barrier layers, and can also maintain high enzymatic activities (when performing droplet pcr) through competitive adsorption on surfactant layers (gruner et al. ; courtois et al. ; zhang and xing ) . it should also be noted that although mineral and fluorinated oils are both compatible with droplet pcr, their physical and chemical differences define particular limitations and advantages. these are compared and summarised in table . finally, it must not be forgotten that control of channel surface properties is critical in ensuring efficient generation and processing of droplets (bashir et al. ) . although more detailed discussions of this issue can be found elsewhere (debon et al. ) , it is necessary for channels made from hydrophilic materials (such as glass) to made hydrophobic through silanisation and typical for naturally hydrophobic surfaces (such as pdms and pmma) to be treated with fluoroalkylsilanes prior to experimentation ). next-generation sequencing (ngs) is a commonly used umbrella term describing ultra-high-throughput sequencing methods (behjati and tarpey ) . such methods allow nucleic acid sequencing at rates of thousands of gigabases per week and at a cost of less than a dollar per gigabase, and have revolutionised genetic and genomic science. several distinct ngs platforms are commercially available (such as those offered by illumina, roche and life technologies). although metrics such as cost per run, cost per base, error rate and throughput are important when evaluating performance, the read length and number of reads per run are perhaps most useful when judging sequencing capacity (levy and myers ) . since , an annual comparison of available sequencing platforms (based on these two factors) has been presented by lex nederbragt at the university of oslo, with data from july illustrated in fig. b (nederbragt ) . currently, illumina's hiseq platforms lead the field in terms of throughput and unsurprisingly dominate the sequencer market share. that said, most mainstream ngs systems make use of short-read lengths, which yields limitations in the resolution of structural mutations and ability to perform de novo sequencing (treangen and salzberg ) . accordingly, ngs technologies capable of long reads (such as those provided by pacific biosciences and oxford nanopore) are becomingly increasingly important, although still in the early stages of development. finally, it should be noted that extended read lengths can be accessed indirectly via synthetic long-read (slr) sequencing methods, which leverage short-read sequencing data to generate synthetic long reads via partitioning, label indexing and remapping techniques (kuleshov et al. ) . slr methods are compatible with existing shortread sequencing platforms and have already shown utility in the recovery of missing sequences, haplotype phasing and transcriptome analysis amini et al. ; tilgner et al. ) . a number of ngs methods make use of microtiter plates to partition samples adey et al. ) . for example, haplotype determination can be achieved by dilution of samples into -well plates prior to sequencing library preparation (fig. c) (kuleshov et al. ) . a key feature of "dilution haplotyping" is the fact that the low concentration of molecules per partition reduces the probability that a contained dna molecule has an overlapping sequence with another. unfortunately, dilution methods based on microtiter plates are instrumentally complex and limited in their partitioning capacity. to address these limitations, researchers from x genomics and stanford university have recently transformed haplotyping analysis (and many other applications) by using droplet-based microfluidics to achieve large-scale partitioning in a rapid and efficient manner (zheng et al. weak intermolecular forces, bringing about the availability of interstitial space (lemal ) chemically inert, immiscible with many organic solvents, widely applied for organic droplets as continuous phase (lemal ) significantly lower solubility for small organic molecules such as fluorescein (gruner et al. ) gases such as oxygen and carbon dioxide are permeable and highly soluble, allowing for droplet cell culture (gruner et al. ) density over flow-rates lead to droplet failure modes: beading, splitting and satellite droplets (debon et al. ) interfacial tension dominates the stress for the moving droplets a reliable manipulation of droplets mainly relies on an efficient surfactant formulation and concentration (gruner et al. ) droplet surface area is nearly minimised by producing spherical ends (baroud et al. ) easy to perform ultra-high-throughput experiments in terms of generation rate and transportation speed page of a). specifically, a double-cross-junction was used to construct phased sequencing libraries from ng inputs of high molecular weight dna. hydrogel beads can then be used as barcode delivery reagents, to allow the controlled loading of individual barcodes into droplet partitions. this core technology platform has since been refined to enable the generation and analysis of more than one million droplet partitions using over four million barcodes and the integrated sequencing of up to (single) cells (fig. c) . the transition from microtiter plate to droplet-based formats has also impacted high-throughput cellular assays. for example, dekosky et al. ( ) recently developed a method able to preserve heavy-chain (vh) and light-chain (vl) antibody pairing information when performing high-throughput immune repertoire sequencing. the authors were able to partition single b cells into spatially isolated compartments, whilst at the same time inserting poly(dt) magnetic beads as barcodes. cells could be lysed, with mrna captured on the magnetic beads and then reverse transcription and emulsion vh-vl linkage pcr performed. after this complex sequence of operations, linked transcripts were finally subjected to ngs. initially, four pdms slides each containing , wells (with each well having a volume of pl) were designed to concurrently accommodate and process , b cells (with a % probability of there being only one cell per well). in each experimental run, over , single b cells could be deposited and analysed. subsequently, the same team replaced the wellbased strategy with a droplet-based microfluidic system (dekosky et al. ). this direct upgrade enabled the high-throughput processing of over one million single b cells per experiment. the schematic procedures for both workflows are shown in fig. . amplification is a prerequisite for the vast majority of nucleic acid assays. the polymerase chain reaction (pcr), the first in vitro nucleic acid amplification technique, was introduced by mullis et al. ( ) over three decades ago, and is still to this day the preferred approach for most amplification-involved procedures. conventional pcr is performed using bulk thermal cyclers, where peltier effect thermoelectric heating is used convert electrical energy into a temperature gradient (bell ) . almost all conventional thermal cyclers possess large thermal masses, which result in high power requirements and relatively slow heating and cooling rates. unsurprisingly, a large number of microfluidic approaches have been developed for pcr over the past years to address these limitations. although, highly successful in allowing amplification to be performed in a rapid and efficient manner (woolley et al. ; kopp et al. ; easley et al. ) , batch and continuous flow approaches do not drastically change how pcr is used by experimentalists to generate biological information. conversely, the adoption of droplet-based formats for pcr over the recent years has begun to transform the application and utility of pcr in complex biological experiments (williams et al. ; diehl et al. ). in addition to obvious advantages, such as reduced reaction times, minimal sample consumption and contamination-free operation, other intriguing features such as massively parallel operation, high amplification sensitivities and reduced amplification bias have begun to fundamentally change how biologists view and use the reaction (tewhey et al. ; white et al. ; nishikawa et al. ) . droplet-based pcr can be carried out in various microfluidic formats, which are broadly categorised as being either on-chip or off-chip (kiss et al. ). for example, early studies by schaerli et al. ( ) used a radial microfluidic device, containing concentric temperature zones, to perform single-copy amplification in pl-volume droplets (fig. a) . batch on-chip microfluidic systems can be created by fabricating integrated chambers that trap or hold large numbers of droplets subsequent to their production. as previously described, hatch et al. ( ) showed an elegant example of such a format, where over a million droplets containing pcr mix were packed into a microfluidic chamber for both thermal cycling and real-time product detection. interestingly, the majority of droplet-based pcr assays have incorporated off-chip amplification, whereby pcr droplets are generated on-chip using standard protocols and then collected and amplified in standard pcr reaction tubes. such an approach is interesting since it leverages the ability of microfluidics to generate large numbers of defined droplets on short timescales and the convenience of using commercial formats or instruments for thermal cycling [rather than more involved approaches to thermal control (sgro et al. ) (hettiarachchi et al. ) ]. the interested reader is directed to table , which summarises fig. a design of a radial pcr device. the device contains an oil inlet (a) that joins two aqueous inlet channels (b and b ) to form droplets at a t-junction (c). the droplets pass through the inner circles ( μm wide channels) in the hot zone (d) to ensure initial denaturation of the template and travel on to the periphery in μm wide channels where primer annealing and template extension occur (e). the droplets then flow back to the centre, where the dna is denatured and a new cycle begins. finally, the droplets exit the device after cycles (f). adapted from ref. (schaerli et al. ) with permission, copyright© asc. b ddpcr enables the absolute quantitation of nucleic acids from a sample in a high-throughput. the process includes three steps: on-chip droplet generation, off-chip droplet incubation and on-chip detection of fluorescence. adapted from ref. (hindson et al. ) with permission, copyright© acs. c workflow of centrifugal step emulsification without associ-ated dead volumes. the system is located on a spinning disc and consists of an inlet chamber (i), a channel (ii) which connects the inlet to a nozzle, and a droplet collection chamber (iii). the inlet chamber is located closer to the centre of rotation than the droplet collection chamber and both chambers are equipped with an air vent. step : the inlet chamber is filled with oil. step : during centrifugation, the oil flows to the radial outer droplet collection chamber. step : a sample is introduced to the inlet. step : the sample is emulsified during centrifugation by step emulsification, and some sample remains in the inlet channel. step : oil is filled into the inlet. step : during centrifugation, the oil flows to the droplet collection chamber pushing the remaining sample through the nozzle which enables the production of droplets with zero dead volume. adapted from ref. (schuler et al. ) with permission, copyright© rsc representative droplet-based pcr studies over the past decade. it should be remembered that nucleic acid amplification is not limited to pcr, with a large number of alternative amplification methods being developed in the intervening years (fakruddin et al. ) . these include the ligase chain reaction (lcr) and isothermal amplification methods such as rolling circle amplification (rca), loop-mediated isothermal amplification (lamp), recombinase polymerase amplification (rpa), helicase-dependent amplification (hda), ramification amplification method (ram), multiple displacement amplification (mda) and nucleic acid sequence-based amplification (nasba). almost all of these basic techniques have been successfully transferred to droplet-based microfluidic formats (zanoli and spoto ) . isothermal amplifications are particularly attractive since they are characterised by short reaction time and require only simple thermal control architectures. these features suggest significant potential for use in point-ofcare diagnostic applications. for example, lamp has been shown to be rapid, accurate, and cost-effective in the diagnosis of infectious diseases such as severe acute respiratory syndrome (sars), malaria and african trypanosomiasis (mori and notomi ; poon et al. ; surabattula et al. ; njiru et al. ) . critically, lamp analysis can be performed simply by visual inspection or through the use of a smartphone camera (tomita et al. ; damhorst et al. ) . recently, rane et al. ( ) demonstrated an integrated device for digital lamp, combining droplet generation, incubation (amplification) and real-time detection. using such an approach, more than one million droplets could be processed in less than h in a continuous manner. droplet digital pcr (ddpcr) is quite possibly the most important microfluidic technology to have been commercialised in recent years (fig. b ) (hindson et al. ) , and refines the concept of digital pcr (dpcr) proposed in the late s (vogelstein and kinzler ) . unlike conventional quantitative pcr (qpcr) methods, dpcr achieves quantitation by portioning a large sample volume into many smaller volumes that statistically contain no more than one copy of target dna. dpcr is particularly robust for the detection of rare nucleic acid samples, the investigation of rare mutations in complex backgrounds and the identification of small differences in expression levels. that said, early embodiments dpcr were limited by the method of sample partitioning, which often involved the use of microtiter plates (vogelstein and kinzler ) , bulk emulsions (using beads, emulsion, amplification and magnetics -beaming) (dressman et al. ) or microfluidic chamber arrays (ottesen et al. ) . hindson et al. ( ) have compared ddpcr with qpcr in the microrna quantification, with results indicating that ddpcr yields significantly greater precision and improved "day-to-day reproducibility" over qpcr. such superior metrics suggest that ddpcr will continue to play an important role in molecular diagnostics of genetic diseases (debrand et al. ) , cancers (mehrian-shai et al. ; watanabe et al. ) , infectious diseases (bian et al. ; trypsteen et al. ) and prenatal diagnosis (orhant et al. ) . for example, epidermal growth factor receptor (egfr) mutation is an important target for many cancer therapies, with the status of the egfr mutation being closely related to the therapeutic effect of egfr inhibitors, such as monoclonal antibodies and tyrosine kinase inhibitor (lièvre et al. ; gazdar ). siravegna et al. ( ) comprehensively combined beaming, ddpcr, ngs and bioinformatics analyses to genotype colorectal cancers and dynamically monitor clonal evolution during treatment with the egfrspecific antibodies cetuximab and panitumumab. results revealed the colorectal tumour genome adapts dynamically to intermittent drug schedules, and provides a molecular explanation for the efficacy of "rechallenge therapies" based on the egfr blockade. such a methodology has significant implications for the development of personalised cancer treatments and the dynamic monitoring of disease progression and response to therapy. put simply, it eliminates the difficulties associated with repeated sample acquisition, and removes temporal and spatial bias in sample selection. ddpcr allows for the simultaneous detection of multiple targets through the use of multi-colour detection schemes, with further expansion of target numbers being achieved by varying parameters that control pcr efficiency (zhong et al. ) . accordingly, in multiplex ddpcr, multiple mutations can be detected in a single experiment; a feature particularly valuable when assaying clinical samples (taly et al. ) . much work has recently focused on improving ddpcr, in terms of detection sensitivity (miotke et al. ) and sample volume limitation (petriv et al. ), but there is little doubt that ddpcr is rapidly becoming a "standard" component in highly sensitive genomic screening. cells are the elementary structural, functional, and biological units in living organisms, with the physiological functions of multicellular organisms being realised through individual cells. it is widely acknowledged that a seemingly homogeneous cell population will differ significantly in terms of size, genetic variants and expression patterns at single-cell level, resulting from the inherent stochasticity of biological processes (elowitz et al. ) and stimulation by the external microenvironment (liberali et al. ) . accordingly, the ability to identify cell-to-cell variations within a given population is critical in understanding clonal evolution in cancer (greaves and maley ) , immune dysfunction (proserpio and mahata ) and somatic mutations (xu et al. ) . in this respect, singlecell genomics aims to enrich our understanding of genetics by engendering the study of genomes at the cellular level. a technical prerequisite for dna or rna sequencing of single cells is the efficient physical isolation of large numbers (> ) of discrete cells, in a manner that allows each cell to be interrogated on an individual basis (gawad et al. ) . normally, cells obtained from blood or solid tissues are processed (via methods such as enzymatic dissociation, density gradient centrifugation and fluorescenceactivated cell sorting) to yield a single-cell suspension, which is then delivered into the microfluidic system. cell isolation in microfluidic systems can be used most easily achieved using traps, droplets or micromechanical valves. for example, the commercially available fluidigm c platform provides an integrated and automated solution for single-cell genomics, leveraging control of pneumatic valves (that deflect under pressure to disrupt fluid flow within a microchannel) to perform single-cell capture, lysis, mrna release, rt-pcr and cdna amplification. such an approach allows the parallel analyse up to cells in an automated fashion. two recent studies describing single-cell rna sequencing methods using droplet-based microfluidics [termed drop-seq (macosko et al. ) and indrop (klein et al. ) ] have attracted significant attention in the biological community due to their ability to barcode rna and analyse mrna transcripts in an efficient, cost-effective and high-throughput fashion (fig. ) . unsurprisingly, these two approaches share much similarity in methodology, since they exploit droplet-based tools developed in the weitz laboratory at harvard university. both utilise microfluidics to load single cells and single microbeads (containing a unique barcode) together with lysis buffer into droplets. subsequently, released mrnas from a given cell are labelled with a unique code prior to droplet breakup and pool amplification. mrnas are converted to cdnas by rt-pcr, followed by library preparation, sequencing and data analysis. critically, all sequencing data, though carried out in batch, can be traced back to its "cell-of-origin" and "gene-of-origin". the drop-seq method uses solid microparticles, with oligonucleotide codes covalently linked to the particle surface, whilst indrop technology uses hydrogel beads, with code release being driven by uv activation. for the interested reader, a more detailed comparison of the biochemical procedures (including transcript coverage) can be found elsewhere (picelli ) . that said, from a technical perspective, some comment on co-encapsulation efficiencies is worthwhile. random (passive) loading of beads, cells and dna molecules into droplets obeys poisson statistics under normal circumstances (collins et al. ) . to ensure a > % probability that a given droplet contains no more than one cell, the average occupancy should not be larger than . cells per droplets. under such conditions, most droplets ( . %) will be empty, with % containing a single cell. accordingly, both drop-seq and indrop utilise dilute cell suspensions to ensure single-cell encapsulation, whilst leveraging the ability of microfluidic droplet generators to make droplets at high speed. interestingly, the indrop method utilises close-packed ordering (abate et al. ) to beat poisson constraints, with almost % droplets receiving gel beads, and over % of cellloaded droplets containing exactly one cell and one bead. this approach involves the use of close packed, deformable particles to allow insertion of a controllable number of particles into every droplet. it should also be noted that the basic drop-seq methodology could in future make use of inertial focusing and ordering to drastically increase the number of droplets containing a single cell and bead (martel and toner ). considering current co-encapsulation efficiencies, the indrop methodology should be well-suited for clinical applications, where cell availability is often limited. interestingly, x genomics have recently tested single-cell rna-seq on their gemcode platform using similar workflows, and reported a cell capture efficiency of ~ % and analysis of eight samples in parallel (zheng et al. b) . besides global single-cell rna-seq, the principle of bead-barcoding and droplet-isolation has also used for targeted transcriptomic sequencing. as noted, dekosky et al. ( dekosky et al. ( , sequenced immune receptor repertoires with the preservation of pairing information (between heavy and light-chain antibodies). these chains contain variable domains and their pairing relationship controls cellular functionality. compared to drop-seq, an additional step of re-emulsifying mrna-captured beads to perform rt-pcr and linkage pcr is necessary. in this respect, the authors have recently published a detailed protocol of the entire workflow (mcdaniel et al. ) . the encapsulation and isolation of single cells in a drop-by-drop fashion has opened up new opportunities for cost-effective and ultra-high-throughput single-cell genetic studies in applications such as whole-genome amplification (fu et al. ) , chromatin profiling and pcr-activated cell sorting (eastburn et al. ) , with microfluidically produced droplets playing a key role. finally, it is worth noting that thermosensitive hydrogel droplets are interesting vehicles for novel experimentation (leng et al. ; kumachev et al. ) . for example, hydrogel droplets can be generated in oil at elevated temperatures and cooled to form gel particles downstream. such gel particles can be washed and handled in aqueous buffer, allowing molecular exchange of substances through diffusion. hence, unlike conventional aqueous droplets that require sophisticated operations to dose or remove reagents, gel droplets may be processed by immersion in appropriate media or dialysate. this innovation has opened up new possibilities for designing highly complex biological workflows in genetic analysis (novak et al. ; zhang et al. ; geng et al. ). over the past decade, the development of droplet-based microfluidic technologies has occurred at a startling pace, with a focus on establishing of functional operational components (for droplet processing) and discovering applications where the features of such systems may be used to the best effect. based on their ability to perform complex experimental workflows in a robust fashion, the next decade will undoubtedly see the commercialisation of many platforms for defined biological applications, delivering microfluidics not only to research laboratories, but also to hospitals, clinics and health ngos. new functions and opportunities will continue to emerge, but research efforts will also continue to focus on improving and integrating existing modules to deliver reliable solutions. to finish, we speculate on two (seemingly dissimilar) developments that may occur over the short-medium term. the demand for rapid, accurate, inexpensive and convenient point-of-care (poc) systems for infectious disease diagnostics and wellness monitoring is significant. ideal diagnostics should be both simple in their structure and portable, whilst ensuring that predefined questions can be answered in a quantitative, low-cost and rapid manner. whilst droplet-based microfluidic systems offer a direct route to such quantitative diagnostics, their implementation for poc nucleic acid analysis is far from simple. for example, fluid manipulation is a key concern in formats, which need to be cheap, robust and small. in this respect, syringe pump-free systems [which utilise manual droplet generation (dangla et al. ) or centrifugal microfluidics (schuler et al. ) ] are particularly interesting. moreover, isothermal amplification methods will be preferable to more traditional thermocycling techniques (zanoli and spoto ) . to this end, schuler et al. ( ) recently demonstrated a system that utilises centrifugal step droplet generation, and is thus pump-and tubing-free (fig. c ). using such an approach, the authors were able to perform isothermal ddpra on-chip and quantify l. monocytogene dna in food samples, reducing the time-to-result by fourfold when compared to the gold-standard tests. moreover, cao et al. ( ) showed a significant enhancement of fluid control in centrifugal microfluidics by introducing a novel two degrees of freedom ( -dof) centrifugal microfluidic platform, which allows complex fluidic control in a direct manner, requiring no external components. such an advance suggests new possibilities for the use of centrifugal microfluidics in poc applications. whilst poc devices provide maximum accessibility to end-users, droplet-based microfluidic technologies have shown their true mettle in addressing comprehensive and complex biological questions. although, and as we have a custom-designed microfluidic device joins two aqueous flows before their compartmentalisation into discrete droplets. one flow contains cells, and the other flow contains barcoded primer beads suspended in a lysis buffer. immediately following droplet formation, the cell is lysed and releases its mrnas, which then hybridise with primers on the microparticle surface. the droplets are broken by adding a reagent to destabilise the oil-water interface, and the microparticles collected and washed. the mrnas are then reverse-transcribed in bulk, forming stamps (single-cell transcriptomes attached to microparticles), and template switching is used to introduce a pcr handle downstream of the synthesised cdna. adapted from ref. (macosko et al. ) with permission, copyright© elsevier (b) indrops. cells are encapsulated into droplets with lysis buffer, reverse-transcription mix, and hydrogel microspheres carrying barcoded primers. after encapsulation primers are released. cdna in each droplet is tagged with a barcode during reverse transcription. droplets are then broken and material from all cells is linearly amplified before sequencing. umi unique molecular identifier. adapted from ref. (klein et al. ) with permission, copyright© elsevier page of seen, such systems have allowed experiments inaccessible on the macroscale to be performed in an automated and integrated manner, we have only scratched the surface in terms of their ultimate potential. for example, droplet-based platforms have already been integrated with "machine learning" algorithms to allow the intelligent synthesis of a range of high quality nanomaterials for application in display and photovoltaic technologies (maceiczyk and demello ; reizman and jensen ). such approaches leverage the ability of microfluidic systems to perform the chemistry/biology in an efficient manner and real-time detection to extract information on ms timescales. machining learning methods will almost certainly impact biology in a similar way within the short term. as control architecture is refined, the sophisticated operations, shown for example in fig. a , will no longer be the privilege of a few expert microfluidic laboratories, and dropletbased microfluidics will quickly become a basic tool used by any experimental scientist. even though significant successes in system automation have been made (such as the fluidigm c platform), the automated and large-scale control of droplet networks integrating multiple functional components remains a daunting challenge, requiring the robust understanding and harnessing of nonlinear and multi-phase fluid dynamics. in this respect, valuable progress has already been made in areas such as bubble logic (prakash and gershenfeld ) , control logic (weaver et al. ) and electric circuit analogy (oh et al. ) . moreover, a recent study describing the "random design" of microfluidic systems is of particular interest (wang et al. ) . in this approach, a library of thousands of random microfluidic chip designs was synthesised. the behaviour of each design was then simulated using finite element analysis, with users able to access structures suited to given tasks. we anticipate this type of interaction could form the basis of future microfluidic platform development. indeed, through the collection and assimilation of user-generated data, machine-learning algorithms will allow the creation of entirely new microfluidic tools. unsurprisingly, we feel that the future of droplet-based microfluidics is an exciting one. beating poisson encapsulation statistics using close-packed ordering highthroughput injection with microfluidics using picoinjectors in vitro, long-range sequence information for de novo genome assembly via transposase contiguity parallel synchronization of two trains of droplets using a railroad-like channel network chemically induced coalescence in droplet-based microfluidics haplotype-resolved whole-genome sequencing by contiguity-preserving transposition and combinatorial indexing formation of dispersions using "flow focusing" in microchannels a double droplet trap system for studying mass transport across a droplet-droplet interface 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hard-wired operations on droplets drop-based microfluidic devices for encapsulation of single cells whole-genome haplotyping using long reads and statistical methods high-throughput generation of hydrogel microbeads with varying elasticity for cell encapsulation high-throughput single copy dna amplification and cell analysis in engineered nanoliter droplets droplet barcoding for massively parallel single-molecule deep sequencing perspective on fluorocarbon chemistry agarose droplet microfluidics for highly parallel and efficient single molecule emulsion pcr advancements in next-generation sequencing illumina synthetic long read sequencing allows recovery of missing sequences even in the "finished single-cell and multivariate approaches in genetic perturbation screens kras mutation status is predictive of response to cetuximab therapy in colorectal cancer millisecond-timescale monitoring of pbs nanoparticle nucleation and growth using droplet-based microfluidics synthesis of cesium lead 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species a droplet microchip with substance exchange capability for the developmental study of c. elegans digital pcr provides sensitive and absolute calibration for high throughput sequencing arnold tongues in a microfluidic drop emitter griffiths ad ( ) amplification of complex gene libraries by emulsion pcr functional integration of pcr amplification and capillary electrophoresis in a microfabricated dna analysis device preparation of monodisperse biodegradable polymer microparticles using a microfluidic flow-focusing device for controlled drug delivery single-cell exome sequencing reveals single-nucleotide mutation characteristics of a kidney tumor label-free high-throughput detection and content sensing of individual droplets in microfluidic systems isothermal amplification methods for the detection of nucleic acids in microfluidic devices microvalve-actuated precise control of individual droplets in microfluidic devices high-performance single cell genetic analysis using microfluidic emulsion generator arrays miniaturized pcr chips for nucleic acid amplification and analysis: latest advances and future trends massively parallel single-molecule and single-cell emulsion reverse transcription polymerase chain reaction using agarose droplet microfluidics haplotyping germline and cancer genomes with high-throughput linked-read sequencing massively parallel digital transcriptional profiling of single cells multiplex digital pcr: breaking the one target per color barrier of quantitative pcr the authors thank tobias wolf for the help of collecting droplet pcr reactions in table . key: cord- - g ih zl authors: bax, adriaan; bax, christina e; stadnytskyi, valentyn; anfinrud, philip title: sars-cov- transmission via speech-generated respiratory droplets date: - - journal: lancet infect dis doi: . /s - ( ) -x sha: doc_id: cord_uid: g ih zl nan the relative humidity (rh) of % in which our measurements were conducted is percentage points below the cdc guidelines for healthcare facilities ( %- %) and within the rh reported for common office buildings ( %- %). we assume that the authors were more concerned with the effect of rh on the rate of evaporation from respiratory droplets. again, while the laws of physics dictate that higher rh increases the time needed for evaporation of water, and thereby decreases the time needed for a droplet's fall to ground, to first order this time scales with ( -rh) and has no significant impact for any of the small droplets observed in our work. for example, droplets of micron diameter will fully dry out at % rh in ca ms, many orders of magnitude faster than the time needed to fall to ground if they were to remain fully hydrated. "the duration of recorded speech was s, but the results were artificially extrapolated to min." as clearly described in the results section and figure of our pnas article, light scattering observations resulted from seconds of recorded speech. as explicitly stated in the discussion, these results were used to estimate the number of potential virions emitted in one minute of speaking. there is nothing artificial about normalizing measured results to standard units. for example, we could have stated "an average of virions per second over a period of seconds" but such a number would suggest a precision higher than warranted, considering the wide variation in viral load and the fractional uncertainty in the diameter of the fully hydrated particles. instead, our reported " per minute" provides an order of magnitude estimate. "in the . min preceding the beginning of the speech, we counted at least instances where flying particles were observed" indeed, even when using a high-efficiency particulate air filter, infiltration of particles from outside sources contributed to our low background particle count rate. as indicated in figure a of our pnas article, the decay of observed particles returns to this low background of . particles per frame (for the green curve; smallest particles). this was explicitly stated in the figure legend and was used when fitting the decay curves. "the authors used fluorescent green light to illuminate particles" nowhere did we state or suggest that fluorescent light was involved in any of our measurements. the laser used in our study generated coherent green light with a wavelength of nm. laser light is not fluorescent. our measurements recorded green light scattered from particles passing through the light sheet. "no report of the loudness, measured in decibels, was found in either manuscript, although in the videos it seems that in some cases the study participant was shouting, so the claim of normal speech is dubious." evidently, abbas and pittet failed to read the legend for figure in our pnas paper which reports that the speaker used "a loud (maximum dbb at a distance of cm; average dbb)." notably, the average loudness ( db) is consistent with the cdc's definition of conversational volume ( db). the "shouting" we assume the authors refer to is when the speaker had the mouth covered by a washcloth, which was used to illustrate that even when shouting, the number of detectable speech-generated droplets remains close to background levels when wearing a mouth cover. "the authors were mistaken when stating that high viral loads were found in asymptomatic patients while referring to the study by wolfel and colleagues. only one patient reported being asymptomatic in the severe acute respiratory syndrome coronavirus (sars-cov- ) outbreak in bavaria, germany, and that patient was not included in wolfel and colleagues' study, which included only hospitalised patients." evidently, abbas and pittet misread or misunderstood the results reported by wölfel et al. wölfel et al. report the high viral loads of nine individuals. this patient population was a subset of the covid- cases reported at the end of january in bavaria, germany by boehmer et al. we thank abbas and pittet for referring us to boehmer et al., whose report provides further evidence that presymptomatic spread occurs, with at least one patient, but probably five additional patients, being infected by a presymptomatic carrier. moreover, it is important to note that wölfel's patients were hospitalized not for the severity of symptoms, but preemptively on the basis of a positive covid- test. in fact, / patients ( %) never had a cough (figure a,d,f,i) and wölfel et al. state that "the clinical courses in the patients under study-all of whom were young-to middle-aged professionals without notable underlying disease-were mild". indeed, patient no. did not exhibit symptoms during his hospitalization ( fig. and table ). "the presence of a fan at the bottom of the black box during the speech and for s after the end of speech does not represent real-life conditions" in "real-life" conditions, exhaled air emerges with high humidity at a temperature near ºc and rapidly mixes with room air, as demonstrated by schlieren images. speaking into an enclosure creates thermal and humidity gradients that are nominally eliminated by operating the internal fan for a short period of time during and after speaking. using the fan to achieve a more homogeneous distribution of droplets prior to the actual decay time measurement does not influence the rate at which droplet nuclei subsequently disappear from view. the dispersion of speech droplets achieved by operating the fan for a short period of time is not unlike that produced by air currents generated when a person walks past a speaker. to suggest that use of the fan does not represent real-life conditions is as perplexing as it is irrelevant. we stated that transmission by asymptomatic covid- carriers is plausible. there is now an abundance of evidence for this observation in the scientific literature, as acknowledged by who on july , . while the nuances between presymptomatic and asymptomatic transmission, or even oligosymptomatic transmission, had not yet been extensively discussed within the context of transmission when our work was submitted and published, the key point remains that disease carriers with no symptoms, that is, subjects who are by definition unlikely to be coughing or sneezing, may be transmitting the virus via speaking. the number of speech droplets observed in our studies, and in particular for the fraction that is sufficiently small to remain airborne for many minutes, is far higher than was previously considered by the medical community. multiple studies have shown that the oropharyngeal viral load in asymptomatic or presymptomatic patients is similar to that of symptomatic patients, , with infectivity appearing to peak prior to onset of symptoms. , [ ] [ ] [ ] "second, the authors assumed an average viral load in saliva of × ⁶ copies per ml on the basis of a prospective study wherein viral load was measured in sputum. thus, they assume that viral load in sputum is the same as in saliva." wolfel et al. report throat viral loads as high as × copies per throat swab. considering a throat swab to contain ca - µl of oral fluid, the viral load was as high as ~ × copies per ml. wolfel et al. also explicitly state "there were no discernible differences in viral loads or detection rates when comparing naso-and oropharyngeal swabs (fig. b) ". sputum consists of "lower respiratory tract secretions along with nasopharyngeal and oropharyngeal secretions, cellular debris, and microorganisms". as mentioned above, speech droplets originate from oral fluid, both at the vocal folds (mostly sputum) and at the front of the oral cavity (mostly saliva). oropharyngeal swabs represent an intermediate location. vowel sounds have been associated with high levels of small speech droplets and are minimally modulated by other narrow passages before entering the atmosphere. these droplets therefore are generated at the same physical location as cough droplets. it is important to note that the viral load of a disease carrier, that is, whether it is high or low, equally impacts the probability of disease transmission through the airborne, large-droplet, and fomite pathways. the relative probability of transmission through these pathways is primarily defined by the likelihood that secreted virions reach the respiratory tract of a bystander, not by the viral load of the droplets. only if abbas and pittet wish to argue that the fecal route dominates disease transmission does the absolute viral load of respiratory fluid secretions become relevant. "the group also assume that every rna copy detected is a potentially infectious virion" nowhere did we state or assume that every rna copy detected is a potentially infectious virion. viability of excreted virions will modulate all pathways equally. indeed, as highlighted in figure f and g of wolfel et al., the ability to culture virus from respiratory secretions rapidly decreases after onset of symptoms whereas viral loads decrease substantially slower, indicating that a progressively smaller fraction of virions is viable in culture as the infection progresses. however, the viability of virions modulates all transmission pathways equally. surfing the covid- scientific wave the size and the duration of air-carriage of respiratory droplets and dropletnuclei on air-borne infection -study ii droplets and droplet nuclei guidelines for environmental infection control in health-care facilities indoor air humidity, air quality, and health -an overview mechanisms of airborne infection via evaporating and sedimenting droplets produced by speaking the airborne lifetime of small speech droplets and their potential importance in sars-cov- transmission what noises cause hearing loss visualizing speech-generated oral fluid droplets with laser light scattering virological assessment of hospitalized patients with covid- investigation of a covid- outbreak in germany resulting from a single travel-associated primary case: a case series a schlieren optical study of the human cough with and without wearing masks for aerosol infection control substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (sars-cov- ) who confirms there's 'emerging evidence' of airborne transmission of the role of particle size in aerosolised pathogen transmission: a review sars-cov- viral load in upper respiratory specimens of infected patients viral rna load in mildly symptomatic and asymptomatic children with covid- temporal dynamics in viral shedding and transmissibility of covid- temporal profiles of viral load in posterior oropharyngeal saliva samples and serum antibody responses during infection by sars-cov- : an observational cohort study physiology of airway mucus clearance modality of human expired aerosol size distributions size distribution and sites of origin of droplets expelled from the human respiratory tract during expiratory activities