key: cord-0891525-8x0204w5 authors: Lieber, Christian; Melekidis, Stefanos; Koch, Rainer; Bauer, Hans-Jörg title: Insights into the evaporation characteristics of saliva droplets and aerosols: Levitation experiments and numerical modeling date: 2021-01-22 journal: J Aerosol Sci DOI: 10.1016/j.jaerosci.2021.105760 sha: 963cff62cab20ab9cf399adcc9c8e9baaf41a324 doc_id: 891525 cord_uid: 8x0204w5 Understanding the transmission phenomena of SARS-CoV-2 by virus-laden droplets and aerosols is of paramount importance for controlling the current COVID-19 pandemic. Detailed information about the lifetime and kinematics of airborne droplets of different size is relevant in order to evaluate hygiene measures like wearing masks but also social distancing and ventilation concepts for indoor environments. However, the evaporation process of expiratory droplets and aerosols is not fully understood. Consequently, the main objective of this study is to present evaporation characteristics of saliva droplets. An acoustic levitator is utilized in conjunction with microscopic imaging for recording the temporal evolution of the evaporation of saliva droplets under well-defined ambient conditions. Following the evaporation of the water content, a saliva droplet reaches a final size, which remains stable in the timescale of hours. By investigating numerous droplets of different size, it was found that the final droplet diameter correlates well to 20 % of the initial diameter. This correlation is independent of the ambient conditions for a temperature range from 20 °C to 29 °C and a relative humidity from 6 % to up to 65 %. The experimentally obtained evaporation characteristics are implemented into a numerical model, which is based on one-dimensional droplet kinematics and a rapid mixing evaporation model. By taking into account the evaporation-falling curve as presented by Wells, the significance of the experimental results for predicting the lifetime of saliva droplets and aerosols is demonstrated. The numerical predictions may be used to determine the impact of the droplet size and the ambient conditions on the transmission risks of infectious diseases like COVID-19. assumed to be negligible. This assumption is supported by the discussion of numerical results in Section 4.1. 133 Following successful injection of a droplet, the evaporation process of the suspended droplet was recorded 134 using microscopic imaging. A shadowgraphy configuration was chosen for determining the temporal evolution 135 of the droplet diameter (see Figure 2 ). Exemplary microscopic images taken immediately after injecting a 136 saliva droplet into the acoustic levitator are shown in Figure 3 . The contour of the levitated droplet is well 137 recognizable, which is of major importance for determining the evolution of the droplet diameter during the 138 evaporation process. However, two considerably smaller droplets are also observable in all three consecutive 139 images. These droplets are remnants from the injection process, which have not coalesced to the actual 140 droplet under investigation. From some experiments, it has been found that these remnants may hover 141 around the large droplet for extended periods in a manner similar to moons. This phenomenon does not 142 have a considerable impact on the experiment unless the contour of the droplet under investigation and the by the automatic post-processing routine. The working principle of this routine will be elucidated in the last paragraphs of this section. It should be noted that the bias of moon like droplets was only corrected 146 manually for determining the ratio between equilibrium and initial diameter. 147 In addition, a distinct bright spot in the center of the levitated droplet can be observed in Figure 3 . This 148 optical effect is caused by the first order refracted light from the main illumination source. In other words, 149 the droplet is acting as a lens in the optical path of the measurement setup. This is evident as the shape 150 of the rectangular light source can be recognized and is actually imaged more sharply for smaller droplets 151 (cf. Figure 6 ). Even the small droplets shown in Figure 3 are characterized by a rectangular bright spot, 152 which will be referred to as the glare point in the following. This glare point is relevant for the discussion 153 of precipitation phenomena of evaporating saliva droplets, since it relies on the highly transparent nature 154 of saliva. In particular, the glare point will not appear for opaque objects (Blaisot and Yon, 2005; Hovenac, 155 1986). Hence, the glare point can be utilized to distinguish between optically transparent and opaque 156 droplets, which was realized for detecting the crystallization of urea-water droplets by Kontin et al. (2010) . The post-processing of the recorded droplet images is based on a robust threshold algorithm, which has 163 been developed in previous studies (Gepperth et The first results to be presented will focus on a general discussion about the evaporation process of saliva 186 droplets. This includes the comparison to the evaporation of a pure water droplet and the definition of 187 the most important qualitative and quantitative evaporation characteristics. Subsequently, the equilibrium 188 diameter is determined for a total of 75 saliva droplets. The acquired data is used to investigate the impact 189 of the initial droplet diameter as well as the ambient temperature and humidity. Moreover, the measurement The evaporation process of a levitated saliva droplet at an ambient temperature of 23 • C and a 50 % 193 relative humidity is shown in Figure 4 . In the first minutes of the droplet lifetime, an approximately linear 194 evolution of the normalized surface D 2 /D 2 0 is observed. This behavior is known as the classical D 2 -law. Hence, this phase of the evaporation process can be described by a constant reduction rate of the droplet 196 surface. The time axis shown in Figure 4 is normalized by the squared initial diameter of the droplet D 2 0 . The resulting unit corresponds to the reciprocal unit of the reduction rate of the droplet surface. This 198 normalization is suitable for a direct comparison of droplets with different initial diameters. In addition, a pure water droplet is investigated under the same ambient conditions as the saliva droplet. The initial evaporation rate of both droplets is nearly identical (see Figure 4) . Hence, the first stage of the to be stable in the time frame of hours and the final droplet size will be named the equilibrium diameter 227 D eq . However, the glare point is still slightly visible and the spherical shape of the droplet is preserved. Hence, it can be concluded that no complete crystallization did occur in the present levitation experiment. Instead, the equilibrium droplet is found to be partially translucent. This outcome may be caused by 230 a sol-gel transformation of the saliva droplet, which was also speculated by Vejerano and Marr (2018) . In addition, four exemplary levitation experiments are illustrated by means of shadow images of the 261 initial and equilibrium droplets in Figure 6 . Obviously, not all droplets maintain a perfectly spherical shape. Moreover, some images show a blurred droplet contour, which may be caused by small oscillations of the 263 droplet exposed to the acoustic field. These phenomena are of great importance to the discussion of the 264 measurement accuracy. Using the calibration procedure, a maximum deviation of the droplet diameter of 265 2.5 µm was derived. However, non-spherical droplets and small oscillations must also be considered. Hence, 266 the absolute measurement accuracy of the microscopic imaging diagnostics is estimated to be 5 µm. with sufficient accuracy. Therefore, more levitation experiments are performed, which will be elucidated in During all levitation experiments, the temperature and humidity were monitored in the proximity of the 281 droplets in order to assess the impact of the ambient conditions on the evaporation process of saliva droplets. The influence of the humidity is of particular interest, since many studies report a strong dependency levitation experiments were performed at significantly lower humidities of 6 % to 21 % relative humidity. The experimental setup is not very well suited to achieve higher humidity conditions than those of typical 286 indoor environments, as reported in the previous section. Nevertheless, results of three droplets at a relative 287 humidity between 65 % to 70 % could be obtained. The impact of the ambient temperature on the ratio between equilibrium and initial diameter is illustrated 289 in Figure 7a for the complete set of 75 levitation experiments. It was found that no correlation can be derived, The experimentally obtained evaporation characteristics are used in a numerical scheme for predicting 322 the airborne lifetime of saliva droplets and aerosols. First, the modeling approach will be discussed in detail It should be taken into account that these heat and mass transfer equations are mainly coupled by the is considered for the mixture of salts and proteins in saliva droplets in order to prevent any evaporation of 352 these components. This is reflected by the experimental findings of this study (cf. Figure 4) . Additionally, droplet and the gas phase to the heat conduction inside the droplet. As a matter of fact, the assumption is valid over a wide range of thermodynamic conditions for saliva droplets in air. In contrast, the concentra- The second characteristic phase of the evaporation process starts, after the droplet reaches its equilibrium as a multiplier in Equation (1). The precipitated mass fraction is denoted by Y pre . An additional resistance of the permeable shell on heat transfer is not considered. This approach for modeling the precipitation 435 behavior of multi-component droplets is based on the work of Reinhold (2001) and was also used by Kontin In addition, the long-term experiment, which has been presented and discussed in Section 3.1, is compared Figure 11 : Comparison between the experimental and numerical results for two droplets with considerably different evaporation rates (a) and the long-term experiment presented in Figure 4 (b). In summary, it could be demonstrated that precipitation dynamics have to be taken into account for pre-493 dicting the evaporation process and the equilibrium diameter of saliva droplets. The best fit to experimental 494 results was achieved by assuming a formation of a permeable shell around the droplet. Moreover, optical 495 diagnostics suggest a sol-gel transition rather than complete crystallization of the droplet as discussed in 496 Section 3.1. Therefore, the experimental and numerical results provide new insights into the environment 497 the virus is exposed to within the droplet, which may be relevant for predicting the virus lifetime. Nev-498 ertheless, more experimental evidence is needed for further validation of the precipitation dynamics. The 499 most important finding of the present study, however, is that the evolution of the droplet diameter D d can 500 be predicted with sufficient accuracy by the evaporation model. This is relevant to modeling of the droplet 501 kinematics. In the present study, a one-dimensional approach is chosen, which is based on the following 502 equation of motion for a single droplet: It should be noted that the correlation is only valid for perfect spheres, which is justified by the low 506 aerodynamic forces acting on the freely falling droplets. which is defined by the relative velocity between a droplet and the gas phase u g − u d and the kinematic vis-517 cosity of air ν g . According to Equation (11), the evaporation rate increases with increasing droplet diameter 518 if a significant relative velocity between the droplet and the gas phase prevails. However, small droplets re-519 spectively aerosols follow the air flow almost perfectly and are therefore characterized by a negligible relative 520 velocity. Hence, the effect of forced convection is presumably negligible. Furthermore, it is interesting to study if an impact on the precipitation behavior is to be expected for 522 smaller droplets respectively aerosols. For this purpose, the droplet Peclet number dependence on the droplet size is due to forced convection, which was found to be negligible previously. In conclusion, the scaling of the precipitation dynamics to smaller droplets and aerosols is straightforward 533 assuming a negligible relative velocity. For a constant relative velocity, lower concentration gradients inside 534 of the droplet are expected, which leads to less pronounced precipitation dynamics. Following the successful verification of the numerical model, the airborne lifetime of saliva droplets is predicted for ambient and initial conditions identical to those of the water droplets. As indicated in 554 Section 3.1, the evaporation of large saliva droplets is identical to that of pure water (see Figure 12b ). However, complete evaporation of saliva droplets does not occur. Instead, smaller droplets continue to fall 556 even after their water content is consumed by evaporation. Finally, the residual droplets will reach their 557 final velocity, which is mainly dependent on their equilibrium diameter. Consequently, the airborne lifetime 558 increases drastically in comparison to that of pure water droplets, as shown in Figure 12b . • Regime III: For droplets with an initial diameter larger than 150 µm, the airborne lifetime is mainly 565 determined by the initial droplet size. The studied variation of the relative humidity affects the airborne 566 lifetime by less than one second. Hence, droplet evaporation may be neglected with sufficient accuracy. It should be mentioned that during normal respiration, such large droplets are barely generated. • Regime II: For droplets between 50 µm and 150 µm, the droplet lifetime is dominated by the evaporation 569 process. Hence, the impact of the ambient conditions is significant and the airborne lifetime increases 570 with lower relative humidity and higher temperature. In addition, the equilibrium droplet size is 571 becoming increasingly important to smaller initial droplet diameters. The combination of both effects 572 may extend the airborne droplet lifetime of saliva droplets by up to two orders of magnitude compared 573 to water droplets. • Regime I: For droplets with an initial diameter that is smaller than 50 µm, the airborne lifetime is 575 mainly determined by the equilibrium droplet size. The evaporation time of the water content accounts 576 for less than 1 % of the total airborne lifetime. The difference between pure water and saliva can be evaluated in Regimes I and II. For this range of 578 initial droplet sizes, the airborne lifetime may increase from seconds for water to minutes and hours for saliva 579 droplets. Hence, the experimentally determined equilibrium diameter is of great importance to predicting The merits of the numerical model used in the present study are its simplicity and the low computational 605 effort for investigating the airborne lifetime of saliva droplets. In particular, the difference between pure 606 water and actual saliva droplets can be assessed, and the dominating parameters for predicting the airborne 607 transmission risk can be identified. However, the present model includes certain assumptions, which are 608 restricted to the scenario of breathing and talking persons in an indoor environment without ventilation. For a more general investigation of the airborne transmission risk, the interaction of the droplets and the 610 ambient air flow has to be taken into account. In this context, it should be noted that even in an unventilated 611 environment, human respiration can cause small air currents, which may affect the airborne lifetime of small 612 droplets. Furthermore, the initial droplet velocity must be considered for coughing or sneezing events (Xie The droplet evaporation models of these numerical studies can be validated using the experimentally 617 determined evaporation characteristics presented in this study. 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