key: cord-0468490-rvvvxgfp authors: Kant, Pallav; Pairetti, C'esar; Saade, Youssef; Popinet, St'ephane; Zaleski, St'ephane; Lohse, Detlef title: Bags mediated film atomization in a cough machine date: 2022-02-28 journal: nan DOI: nan sha: f93491a2052eba4ef30903bddc4f4eb4faf4ec0e doc_id: 468490 cord_uid: rvvvxgfp We combine experiments and numerical computations to examine underlying fluid mechanical processes associated with bioaerosol generation during violent respiratory manoeuvres, such as coughing or sneezing. Analogous experiments performed in a cough machine -- consisting of a strong shearing airflow over a thin liquid film, allow us to illustrate the changes in film topology as it disintegrates into small droplets. We identify that aerosol generation during the shearing of the liquid film is mediated by the formation of inflated bag-like structures. The breakup of these bags is triggered by the appearance of retracting holes that puncture the bag surface. Consequently, the cascade from inflated bags to droplets is primarily controlled by the dynamics and stability of liquid rims bounding these retracting holes. We also reveal the stabilizing role of fluid viscosity that eventually leads to the generation of smaller droplets. Respiratory droplets (bioaerosols) expelled from oral and nasal cavities during different breathing manoeuvres, such as speaking, singing, coughing and sneezing, are primary vectors of respiratory infections [1] [2] [3] [4] [5] [6] [7] [8] . The size of these droplets, made of muco-salivary fluid lining respiratory tracts, ranges from hundreds of nanometers to a few millimetres [9] [10] [11] [12] . Crucially, the generation of bioaerosols is closely related to interfacial phenomena emerging at the free surface of the airway-lining-fluid [13] [14] [15] [16] . For example, the shearing action of the airflow within the lungs during coughing or sneezing destabilizes the thin layer of mucus accumulated along the airway passages. The ensuing complex fluid mechanical processes, bearing several interfacial instabilities [2] , lead to the disintegration of the mucus layer into droplets with broad size statistics. In addition, a large number of sub micron-sized droplets are also produced due to the capillary breakup of menisci pending the reopening of collapsed terminal bronchioles during normal breathing [17] [18] [19] . Upon exhalation, the fate of these respiratory droplets depends on a number of intrinsic factors such as initial droplet size and composition as well as extrinsic factors like ambient humidity, temperature and ventilation [20] [21] [22] [23] . Therefore, devising an effective infection control strategy, first and foremost, requires an intimate knowledge of the initial size distribution, velocity and ejection angles of bioaerosols generated during the different respiratory manoeuvres. Here, in the context of droplets produced during coughing or sneezing, we study the fragmentation of thin films subject to interfacial stresses induced by a strong airflow. We perform analogous experiments and numerical computations of what we call a cough-machine to illustrate the topological changes experienced by a thin film before disintegrating into minute droplets. The experimental configuration (cough-machine) consists of a 30 cm long model-trachea made of transparent plexiglass, with a 2 cm wide and 1 cm high rectangular crosssection. A thin layer of glycerol-water solution covers the base of this rectangular channel, imitating coating of a muco-salivary fluid. A sharp edged scraper that runs over a rail is used to create a uniform film of the desired thicknesses. The upstream of the channel connects to a pressurized tank via a valve that is actuated to create an airflow mimicking a typical sneeze, and the other end opens to atmosphere. A honeycomb structure is placed at the entrance of the channel to homogenise the inlet turbulence levels. Experiments are carried out for different liquid viscosities, varying over two orders of magnitude, and mean freestream velocities in the range of 10−30 m s. Different freestream velocities are achieved by varying the overhead pressure in the tank. Corresponding numerical simulations were performed using the volume-of-fluid (VOF) method implemented in Basilisk, relevant details of simulations are given in Ref. [16] . Previously, Clark et al. [24] and King et al. [25] have popularised similar experimental configurations to study the flow resistance in airway passages due to the accumulation of mucus along the walls. However, the scope of these investigations was limited to non-atomization conditions where observed interfacial disturbances can be rationalized using modal stability analysis. More recently, Edwards et al. [26] employed a similar apparatus, along with in vivo measurements, to establish a direct link between the interfacial tension of the airway-lining fluid and the flux of exhaled bioaerosols. In contrast, here we use high-speed imaging and Phase-Doppler-Anemometry (PDA) to reveal the mechanics of fragmentation of the thin films and to characterize the resultant droplet size distributions, respectively. The sequence of snapshots in Fig. 1a highlights key events leading to the atomization of a water-glycerol film of thickness H f = 1mm when sheared by an impulsively started airflow, mimicking a cough or sneeze. Since the corresponding Reynolds number Re = ρH f U µ and Weber number W e = ρ g U 2 H f σ are sufficiently large, owing to a shear-induced Kelvin-Helmholtz instability, a localized wave-like interfacial disturbance develops close to the inlet immediately after the airflow initiates [27, 28] ; here, ρ, µ and σ are the density, the dynamic viscosity, and the surface tension of the liquid, ρ g and U are the density and the mean flow velocity of the flowing gas. While this interfacial wave-like disturbance moves downstream at a constant velocity that scales as u wave ∼ U √ ρ g ( √ ρ g + √ ρ)) [28, 29] , the shear stress imposed by the airflow on the thin film modulates its morphology, stretching it into a thin liquid sheet with a thicker (cylindrical) rim at its free edge. At this stage, the liquid sheet disintegrates into small droplets with a wide size distribution primarily through the formation of multiple inflated structures (liquid bags) along the width of the film. Note that these hollow structures are rooted at the crest of the downstream travelling interfacial wave, and are bordered by a thick liquid rim at the top. Since large accelerations are imparted from the gas flow to the liquid sheets during the expansion of the bags, their formation and growth is attributed to a Rayleigh-Taylor type mechanism. Corresponding 2D and 3D numerical simulations (Fig. 1b-c) performed for the exact experimental configuration reveal an intricate interplay between aerodynamics stresses at the film interface and capillarity that controls the formation of the liquid bags. We find that once the amplitude of the initial interfacial perturbation increases significantly, the flow over its windward side develops a stagnation point where the pressure builds up, deforming the liquid into a vertical sheet. Subsequently, local pressure gradients thins the sheet heterogeneously, driving the inflation of several bags across the channel width. Upon the initial inflation, vortex shedding develops on the leeward side producing stagnation points that accelerate the local thinning of the sheets while the bags keep elongating. In our experiments, the bag-mediated fragmentation of iii the sheared thin-films occurs only when the Weber number exceeds the critical value W e c ∼ 8. Remarkably, this threshold value coincides with the limiting value of Weber number above which a droplet subject to impulsive accelerations undergoes similar morphological changes before disintegrating into small droplets [30] [31] [32] [33] . This suggests a strong similarity of the underlying dynamics in the two distinct cases. Accordingly, we recover the same bag-elongation dynamics, L B ∼ t 2 suggested for single droplet case [30] , both in experiments and simulations, see Fig. 2a . Moreover, our numerical computations also capture the exponential thinning of bag thickness during the inflation, h ∼ e −2t [30] . High-speed imaging of the overall fragmentation process reveals that the disintegration of the bag morphologies into small droplets is triggered by the appearance of 'weak-spots', particularly in thinnest parts of the bagsheet [35] . As shown in Fig. 3 , these weak-spots are precursor to retracting holes that puncture the bag. These holes are bounded by thick liquid rims and retract at a constant velocity. The corresponding retraction dynamics thus is controlled by a Taylor-Culick process [36] , and the resulting Taylor-Culick velocity is given by V TC = (2σ ρ h) 1 2 . The exact physical mechanism responsible for the nucleation of such weak spots is a subject of intense debate [35] . Therefore, several nucleation mechanisms relying on chemical and temperature inhomogeneities, presence of foreign particles or microbubbles have been proposed. In addition, weak spots may also result from mechanical forcing, like the application of a pressure gradient, or pressure difference across a film. In such a case, the resulting acceleration may lead to film thickness modulations through a Rayleigh-Taylor mechanism, ultimately causing its puncture. Droplet generation due to the instability of retracting rim Crucially, our experiments reveal that the cascade from liquid sheet to droplets is predominantly controlled by the dynamics and stability of liquid rims formed upon the nucleation of holes. The retracting motion of such liquid rims is susceptible to longitudinal perturbations, resulting in the formation of elongated liquid-filament at the free edge which eventually break into small droplets [37-iv 39] . This transition from a liquid-filament to droplet/s occurs either via end-pinching mode when a filament grows into a bulge that detaches as a single droplet, or via ligament mode when the filament grows progressively to break up into multiple droplets [40] . In the experiments, we observe both modes of droplet generation. Notably, this physical process of droplet generation is controlled by a delicate interplay between Rayleigh-Plateau and Rayleigh-Taylor mechanisms [40, 41] . The size of droplets (less than 50 µm) produced via this mechanism is therefore determined by the size of the liquid rim that continuously evolves in time. Additionally, as shown in the last image of the sequence in Fig. 3 , droplets of larger size (∼ 500 µm) are also produced from the breakup of the corrugated filament at the top-edge of the liquid bag via an aggregation-coalescence process [34] . However, it is important to point out that the majority of the liquid volume that fragments into droplets is located in the bag sheets rather than the corrugated liquid filament. Therefore, the polydispersity and skewness of the resultant droplet size distribution measured in our experiments is primarily attributed to the unsteadiness of the rim dynamics upon hole nucleation in bag sheets. Remarkably, we find that the resultant droplet size distribution, measured at the exit of the cough-machine, is well captured by a log-normal distribution, see Fig. 4a . This behaviour is confirmed for different film viscosities (1-108 cst) and shearing strengths. Note that our measurements include droplets as small as 1 µm that originate from the unsteady rim retraction dynamics. On the one hand, these measurements match very well with previously reported droplet statistics for a real cough [1, 42, 43] but, at the same time, are in contrast with droplet size distribution suggested for bag-mediated liquid fragmentation processes [30] . It has been proposed that in bag-mediated atomization scenarios, the aggregation and coalescence process of corrugations along the liquid filaments bordering inflated structures selects the droplet size distribution. However, our experiments demonstrate that during the bursting of a liquid bag formed from the shearing of a thin-film, drop fragments are predominantly produced via unsteady rim dynamics at the edge of retracting holes. Thus the fragmentation process discussed here is closer to the unsteady sheet fragmentation investigated in Ref. [44] that also yields a log-normal droplet size distribution. In addition, our experiments reveal an important role of fluid viscosity in the overall fragmentation process. We find that an increase in the film viscosity enhances the stability of inflated structures, resulting in the formation of deeper and wider liquid bags; see Fig. S1 . Note that this widening of liquid bags is directly related to the underlying physical mechanism of bag formation, i.e. Rayleigh-Taylor type process, which promotes higher instability wavelengths for an increase in liquid viscosity [45] . Crucially, the enhanced stability of these inflated structures also means that at the time of bursting lower bag-sheet thickness is achieved. In Fig. S1 , we compare the distribution of bag thickness measured for two different film visocity at the same shearing strength. Note that the bag-sheet thickness is estimated from retraction velocities of the holes along the bag interface via the Taylor-Culick relation [36] . A direct consequence of the formation of thin viscous bags is that upon its fragmentation, via the hole retraction mechanism, thinner liquid rims form. Accordingly, as shown in Fig. 4b , for higher film viscosities the mean size of droplet fragments reduces significantly, almost by a factor of two. Interestingly, this transition in mean droplet size occurs at the threshold given by the Ohnesorge number Oh = µ (ρ σ h) 1 2 ∼ 1 local to the bag, indicating the existence of two distinct regimes where different physical processes control the eventual bursting of the inflated structure. In the regime Oh < 1, it is a balance between inertia and capillarity that determine the lifetime of an inflated structure, whereas for Oh > 1 viscous effects stabilize the accelerating bag. We also note that a similar stabilizing effect of fluid viscosity on the stability of thin films, in the context of surface bubbles, has been reported recently in Ref. [46] . However, a detailed investigation is further needed to develop a comprehensive understanding of the stability of inflated structures in these two regimes discussed above, and is out of scope of the current work. In summary, we have analysed physical processes associated with the atomization of a thin film subject to shearing airflow in a closed geometry. Our experiments and numerical simulations offer new insight into that the v overall fragmentation process that is mediated by the formation of inflated liquid-bags. In contrast to previous investigations, we show that the cascade from of the inflated bags to small droplets is controlled by retracting liquid rims bordering the holes that puncture the inflated structures. We also reveal the stabilizing effect of fluid viscosity that eventually leads to the generation of smaller droplets. More importantly, this fundamental study has profound implications for understanding key processes related to the generation of bioaerosols during violent respiratory manoeuvres. Air-borne infection The flow physics of COVID-19 Exhaled droplets due to talking and coughing Aerosol transmission of infectious disease Airborne infectious disease and the suppression of pulmonary bioaerosols A sneeze, New Eng Turbulent gas clouds and respiratory pathogen emissions: potential implications for reducing transmission of COVID-19 Respiratory aerosols and droplets in the transmission of infectious diseases The size and the duration of air-carriage of respiratory droplets and droplet-nuclei Relation between the airborne diameters of respiratory droplets and the diameter of the stains left after recovery Characterization of expiration air jets and droplet size distributions immediately at the mouth opening Viscous airflow through a rigid tube with a compliant lining: a simple model for the air-mucus interaction in pulmonary airways Generation and size distribution of droplet in annular two-phase flow Flow-induced instabilities of a mucus-serous bilayer On shear layer atomization within closed channels: Numerical simulations of a cough-replicating experiment The mechanism of breath aerosol formation Effect of airway opening on production of exhaled particles Propagation and breakup of liquid menisci and aerosol generation in small airways Droplet fate in indoor environments, or can we prevent the spread of infection? Relation between humidity and size of exhaled particles Fine structure of the vapor field in evaporating dense sprays Extended lifetime of respiratory droplets in a turbulent vapor puff and its implications on airborne disease transmission Resistance to twophase gas-liquid flow in airways Clearance of mucus by simulated cough Inhaling to mitigate exhaled bioaerosols Direct numerical simulation of free-surface and interfacial flow Selfsimilar wave produced by local perturbation of the Kelvin-Helmholtz shear-layer instability Two-dimensional shear-layer entrainment Single-drop fragmentation determines size distribution of raindrops Shape and instability of free-falling liquid globules Density contrast matters for drop fragmentation thresholds at low Ohnesorge number On aerodynamic droplet breakup Fragmentation Double threshold behavior for breakup of liquid sheets Viscous sheet retraction Longitudinal instability of a liquid rim Stability of liquid sheet edges On the instability of a free viscous rim Growth and breakup of ligaments in unsteady fragmentation Universal rim thickness in unsteady sheet fragmentation Toward understanding the risk of secondary airborne infection: emission of respirable pathogens Host-to-host airborne transmission as a multiphase flow problem for science-based social distance guidelines Unsteady sheet fragmentation: droplet sizes and speeds Viscous effects in Rayleigh-Taylor instability Lifetime of a single bubble on the surface of a water and ethanol bath The authors thank Gert-Wim Bruggert for the technical support in building the experimental setup, and Pim Wassdorp for the help in PDA measurements. We acknowledge the funding by Max Planck Center Twente, NWO and from the ERC Adv. Grant DDD 740479.