Aerosol Particles Generated by Coughing and Sneezing of a SARS-CoV-2 (COVID-19) Host Travel over 30 m Distance

A fast-computational 3D model comprising fluid dynamics with heat transfer, mass transfer and diffusion of diluted species has been adapted and employed to evaluate dispersion of aerosol particles in various environments. Effects of convection flow, atmospheric diffusivity and humidity on evolution and travel distances of exhaled aerosol clouds by an infected person are modelled. The modelling clearly demonstrates how aerosol particle dispersion is influenced by weather and geometry of the environment. The results obtained demonstrate that aerosol particles of sizes from 10 μm to 100 μm that potentially can carry SARS-CoV-2 (COVID-19) viruses travel over 30 m in some atmospheric conditions. Modelling of the evolution of aerosol clouds generated by coughing and sneezing enables us to evaluate the deposition dose of aerosol particles in healthy individuals. In realistic weather scenarios viruses can be deposited in the respiratory tract of a healthy individual at up to 200 virus copies in several minutes. A metric based on aerosol particle (volume) size distribution and the ICRP lung deposition model is suggested.

The initial stage of airborne viral disease transmission is caused by virus laden droplets that are 48 generated mainly by coughing, sneezing (Mittal et al., 2020;Jayaweeraa et al., 2020). This 49 creates a population of airborne particles in the vicinity of a host. There is an ambiguity about 50 terminology used for these particles: in some publications they are described as droplets, but in 51 others as aerosol particles (Vuorinen et al., 2020;Yang et al., 2007). Here to avoid an ambiguity, 52 airborne particles (diameter < 100m) generated by infected persons are described as aerosol

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7 concentration of aerosol particles CX,Y,Z,t. An additional mass transfer of water vapor between 126 aerosol particles and the gas phase was simplified and employed as a parameterization of a direct 127 modelling of the mass exchange (Pruppacher and Klett, 1997 In modelling, the dispersion of the aerosol cloud was calculated from a simplified initial 131 aerosol cloud of an elliptical shape with a given aerosol number concentration and cloud 132 boundaries. The subsequent evolution of the aerosol particles concentration was recorded as a 133 concentration CX,Y,Z for a steady-state modelling or as CX,Y,Z,t for time dependent solutions. 134 In this work we developed a simple human head model where we used a cylinder for neck and 135 ellipsoids for the head and nose. This model is a useful simplification. We tested how variations 136 in the size of the model and features of the head affect the aerosol concentration field. It was 137 found that variation in size of parts (by 10%) has less than 1% influence on the aerosol/droplet 138 concentration at distances more than 2m from the source. Therefore, the simplified human model 139 seems to be enabled to obtain sufficiently accurate results. 140 141 Steady-state aerosol source X-Z plane and boundary conditions

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8 First, an open space aerosol dispersion 2D steady-state model was developed and employed to 143 evaluate the influence of the wind velocity on the possibility of transferring aerosol particles from 144 the source to an uninfected person. In the model, aerosol particles of sizes close to those observed 145 in coughing, talking and sneezing experiments were considered. The concentration field of 146 aerosol particles (CX,Z) have been calculated in X-Z space (-3m<X<17m; -2.5m<Z<2.5m). The 147 mouth of the host head was at X=0, Z=0.8m or 1.7m from the ground. 148 The velocity field boundary conditions for the ground and the human surface were u=0, 149 without slip (No slip). The right boundary was at X=17 m was pressure p=1atm. The top 150 boundary condition at Y=2.5 m was u·n=0 with slip. The left boundary at X=-3 m was u=U0·n 151 with U0wind speed. 152 Different boundary conditions for the convection flow inlet were tested, for example a more 153 realistic linear condition U0= 2·(Z+2.5 m)·U0, but the influence on the concentration field was 154 negligible (less than 10% in number concentration) if the total mass flow was constant. It could 155 be explained by the position of the aerosol source quite far above the ground (1.7 m). Therefore, 156 the effect of the ground boundary was small at 1.7 m. A randomization of U0 along the Z co-157 ordinate also gave rather negligible variations in the number concentration field. 158

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The diffusivity of such a patchy turbulence as atmospheric is mainly related to statistical 177 parameters describing the morphology of turbulent events: filling factor, lifetime and height of 178 the patches, etc., (Wilson, 2004). A statistical description of the turbulent characteristics is often 179 employed in order to evaluate the impact of small-scale turbulence on the transport of aerosols. 180 In-situ measurements of atmospheric diffusivity coefficients range from 0.2 to 0.8 m 2 /s (Alisse 181 and Sidi, 2000). There are many uncertainties with the atmospheric turbulence, for example 182 greater values and variations in the atmospheric diffusivity from circa 1 to 100 m 2 /s have been 183 (Kennedy and Shapiro, 1980). In the boundary layer the atmospheric diffusion coefficient is in 184 the range from 0.1 to 160 m 2 /s depending on the stability of the atmosphere, the urban geometry 185 and traffic (Hanna et al., 1982). In street canyons the atmospheric diffusion coefficient is likely to 186 be in the range from 0.1 to 10 m 2 /s, ibid. 187 To investigate aerosol dispersion over long distance simplifications are required (e.g. see 188 aerosol particles (integrated over all sizes) in some papers is from 10 3 cm -3 to 2·10 3 cm -3 (Yang et 210 al., 2007). Average size range of the particles was 1-10 m, and 50% of particles have diameter

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12 the background aerosol. The estimated droplet concentrations for coughing ranged from 2.4 to 5.2 213 cm -3 per cough (Chao et al., 2009). There are many inconsistencies in the literature on particle 214 number and size distribution of aerosol particles generated by speaking, singing, coughing and 215 sneezing. In this paper, the initial concentration of aerosol particles generated by a host 216 considered as an unknown parameter in modelling that does not affect the dispersion of aerosols. 217 If the initial concentration is known, then the modelling results can be readily converted into 218 aerosol particle number concentrations. 219 The majority of data suggests that size range of particles generated by coughing and sneezing 220 by infected humans is from 1 m to 100 m. The particles in the size range from 1 m to 10 m 221 are part of PM10 characteristic and well researched, for example it is known that they stay 222 airborne for some time (minutes to hours) and travel long distances (more than 10s of meters). 223 Dispersion of larger particles 10 m to 100 m is less understood. The larger particles have a 224 greater viral load than the small particles (on average 1000 times greater), therefore, a 225 contribution of larger particles to the COVID-19 aerosol transmission route should be better 226 understood. Here we investigate dispersion of aerosol particles of the size range from 10 m to 227 100 m. 228

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There are many uncertainties with quantification of the viral load. The median viral load in 231 posterior oropharyngeal saliva or other respiratory specimens is 5·2 log copies per ml and 232 maximal virus loading is found circa 10 8 copies/mL (Kai-Wang et al., 2020). The viral loads in 233 throat swab and sputum samples peaked at around 5-6 days after symptom onset, ranging from 234 around 10 3 to 7.11·10 8 copies per mL according to "Evidence summary for SARS-CoV-2 viral 235 load and infectivity over the course of an infection" (2020). The viral loads, as identified by 236 values of RT-PCR assay, have been reported to be highest soon after the onset of symptoms 237 reaching up to 10 8 copies per ml (Zou et al., 2020). There is no direct evidence on the viral load 238 in aerosol particles generated by an infected person. The data obtained from swabs are used here 239 as a proxy to evaluate the number of virus copies in aerosol particles. In the absence of direct 240 measurements, the assumption of equal viral loads in the posterior oropharyngeal saliva and in 241 aerosol particles is accepted here. 242 Here we model atmospheric transfer at various conditions including atmospheric diffusion 243 coefficient (0.1 m 2 /s to 10 m 2 /s), size of aerosol particles/droplets (10m to 100 m) and 244 concentration is modelled in dimensionless units that can be easily adjusted to any starting value. 245 The range of parameters is an essential to limits uncertainties with assumptions on parameters to 246 ensure that using variations in parameters would not change the conclusions dramatically. spread beyond X=12 meters. The concentration field is asymmetric due to influence of the 264 ground boundary conditions. The upwind area is completely clean from aerosol particles emitted 265 from the source. Modelling demonstrates a strong influence of convection on the spread of

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15 aerosol particles along the X-axis, but diffusivity is responsible for dispersion of particles along 267 the Y-axis and Z-axis. 268 On a quiet day, the average air wind speed at the height of 1.5 to 2 meters above the ground 269 is from 0.3 m/s to 1m/s. On a moderate day, with a higher wind speed, for example 3 m/s, red and 270 yellow contour lines are shrunk, but the green line extends beyond the model border, X=17 m, 271 particles. This decreases the area of the plume and therefore, chances that the general public will 275 be exposed to the virus laden aerosol particles. Therefore, in a windy day the viral infection 276 transfer rate should be lower than in a quiet day. 277 The atmospheric diffusivity also influences the aerosol dispersion. An increase in the 278 diffusion coefficient from Dif=0.01 m 2 /s ( Fig. 1A) to Dif=0.1 m 2 /s (Fig. 1C) increases the 279 vertical spread of the contour plots but shortens them in the X-axis. A spectacular manifestation 280 of the effects of diffusion is shown in Fig. 1C with magenta streamlines obtained with Dif=0. 281 This is the case of an unrealistic steady-state laminar flow without turbulent diffusion when an 282 aerosol cloud travels the distance determined by the gravitational force and the wind speed.

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16 The model built enables complicated geometries to be studied. If a car is placed in an open 284 space, for example a parking area near a supermarket then the air flow can be disturbed by the car 285 and change the aerosol concentration field. The flow of aerosol particles is carried over a car near 286 the source and extended zone of high concentration, Fig. 2. 287 In this case a person at X=10 m is in the middle of the green contour line and exposed to 288 aerosol concentration in the range 0.1·C0<CX,,Z < 0.2·C0. Without car a person in the same place 289 would be exposed the aerosol concentration C X,,Z < 0.1·C 0 , Fig. 1C. There is also a large 290 stagnation zone behind the car where several large eddies are formed between X=7 m and 17 m, 291 The influence of heat transfer on the air dynamic and the aerosol particle concentration was 299 investigated in cases when a car shown in Fig. 2 has an elevated boundary temperature as after 300 been driven. In the model runs the surface of the car boundary vas varied from 30 o C to 40 o C. the

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17 influence of the elevated temperature was found to be negligible. Thus, this type of heat transfer 302 was not essential for aerosol cloud dispersion. However, for other geometries and conditions 303 effects of heat transfer can be greater. 304 305 Steady-state aerosol source X-Y plane 306 The aerosol cloud dispersion in the horizontal X-Y plane was calculated at Z=1.7 m in the same 307 way as it was done for modelling aerosol travel in the vertical plane (X-Z). In the model, a 308 concentration field of smaller 10 m diameter particles have been calculated in X-Y space (-309 3m<X<17m; -5m<Y<5m). The aerosol source (the mouth of the host head) was at X=0, Y=0 at 310 1.7m from the ground. 311 The velocity field boundary conditions for boundaries at Y=5 m and at Y=-5 m were allowing 312 slip. The rest of boundary conditions were the same as in the X-Z modelling. 313 It was found that aerosol particles were carried out with the convection flow and spread from 314 the source in all directions. An open space geometry modelled with wind speed 0.3 m/s (0.66 315 mph) shows that small particles travel considerable distances, greater than 15 meters, Fig. 4. 316 An aerosol particle concentration field forms a plume from the source directed downwind. The 317 concentration field is highly asymmetric. The upwind area is completely clean from aerosol

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18 particles emitted from the source. Modelling demonstrates a strong influence of convection on the 319 spread of aerosol particles along the X-axis and diffusivity -along the Y-axis. 320 An increase in the wind speed from 0.3 m/s to 1 m/s leads to decrease of the length of each 321 contour plot. For example, the yellow contour line covers less than 9-meter length, Fig. 5 where 322 in Fig. 4 it is 15 meters. This is explained by a greater dilution of the aerosol at higher speed of 323 wind. This supports findings in the modelling in X-Z plane that an increase in the wind speed 324 reduces exposure to aerosol particles. considerably (Vuorinen et al., 2020). The convection is also influenced by buoyancy, movement 333 of people, machines and animals. In this modelling, all the driving forces of convection except for 334 the wind velocity were integrated into an atmospheric diffusion coefficient.

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19 The initial size of the aerosol cloud generated by a single cough was assumed to be 0.5m x 1m 336 ellipse with concentration of particles C0 =5 cm -3 . After the first 6 seconds the cloud has grown 337 up to 6 meters, see aerosol particles concentration contour line CXY =0.1 ·C0 (green line) in Fig. 6. 338 Then the cloud moved with the wind further along the X-axis and become wider in the X-Y plane, 339 see a supplementary video. At the same time the particle concentration in the cloud is decreasing 340 due to dispersion by atmospheric diffusion. The black contour line disappeared first and then the 341 red line disappeared also. Therefore, non-steady-state modelling confirms that aerosol particles 342 generated by a cough can travel considerable distances from the source in excess of 10 meters. 343 344 3D modelling in confined spaces 345 The modelling in open spaces was adapted to confined spaces. For this the wind speed was 346 replaced by convection driven by buoyancy (e.g., caused by heating radiators and electronic 347 devices) and ventilation. These create a complex non-uniform 3D velocity field. In modelling, 348 integrated diffusion coefficients were employed as in the modelling of the open spaces. 349 The rectangular geometry with a 4 m x 6 m footprint and 3 m height with an inlet and an 350 outlet ventilation and with 3 beds was modelled, Fig. 7. The ventilation flow rate was Q=0.1m 3 /s 351 and the volume exchange is 5 times per hour (V=72m 3 ). Boundary conditions were as described

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20 It was found that from the inlet the ventilation flow was directed to the floor where it 354 changed direction and moved almost horizontally, see the Y-Z plane at X=0.5 m in Fig. 8. The 355 effects of buoyancy (driven by differences in temperature) on the convection flow were found to 356 be greater in the confined space than in open spaces. If a radiator in a confined space (not shown 357 in Fig. 7) was at T=50 o C or 30 o C higher than the wall temperature, the heat induced convection 358 velocity flow was the same order of magnitude than the ventilation flow velocity. Therefore, in 359 confined spaces heat transfer has to be taken into account. 360 A possible scenario of contaminated ventilation with the initial aerosol concentration C0=1 cm -3 361 was modelled. Modelling shows that in the confined space, aerosol particles occupy a 362 considerable part of the room volume. If a person is in the bed at Y=1 m he/she is exposed to C,XY 363 > 0.2·C0 that is greater than the exposure level for a person in the bed at Y=5 m where C,XY < 364 0.1·C0., Fig. 9. (1) First, to calculate the viral load, one has to find the total volume of aerosol particles in 1 cm 3 396 of air that deposited in the respiratory tract (Vpd). 397

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(2) 398 The accumulated dose of the viral load (ADpd) is the total number of virus copies deposited in 399 the respiratory tract after number of breathing cycles n and the volume of a single breath (V1). 400 The viral load of the posterior oropharyngeal saliva is  Evaporation of water from aerosol 401 particles/droplets results in increasing the viral load (Baron and Willeke, 2001). This effect is 402 accounted for by the humidity factor Hf that ranges from 1 for a humid air to 300 for the dry air

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23 It should be noted that n may or may not be constant. It is influenced by the physical activity, 405 fitness level, age and gender. The average breath rate is ~5 cycles per minute. 406

ADpd=Vpd·V1·n··Hf
(3) 407 The number of breath cycles and the concentration of the aerosol particles define the 408 deposition dose of a person that is exposed to an aerosol. The humidity in modelling was 409 RH=50% (low humidity) and RH=90% that is close to humidity of the exhaled air Rh=87%. 410 Let us consider a healthy person standing at point {12m,0,1.7,t} as in Fig.4 where he/she is 411 exposed to aerosol particles Dp=20 mm with CX,Y,Z,t,Dp =1 cm -3 , n=10 and  = 10 5 virus copies per 412 cm -3 . The viral dose received by the person was found to be 20 copies of viruses in a humid air 413 and considerably more in dryer air (circa 100 copies depending on the RH). 414 The critical viral load dose for COVID-19 is not well studied and further research is required. 415 However, there is a demand to quantify the risk of the infection transfer via the aerosol route. 416 The expressions (2) and (3) can be used to quantify the dose and potentially to be employed as a 417 measure of the risk associated with exposure to airborne viruses like SARS-CoV-2. 418 The modelling developed here is a simplified approach where all statistical variabilities of 419 the aerosol evolution in real environments are accounted for by the integrated turbulent diffusion 420 coefficient superimposed on the laminar flow solution. There is a question of uncertainties

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24 associated with this approach. However, it is unlikely that these uncertainties affect It is assumed here that the aerosol particleair boundary can be treated according to 435 Cunningham by introducing a slip correction factor (Baron and Willeke, 2001). This limitation is 436 common in the aerosol science and very well validated. In addition, the density of aerosol 437 particles/droplets was assumed to be 1.0 g/cc. It is a limitation, but it is unlikely that a small 438 density change may noticeably affect the length of particle dispersion in the air.

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Another assumption is the isotropic diffusion of the atmosphere along the model vertical 440 dimension (from the ground level up to 5m). The main reason for this is lack of reliable data on 441 anisotropic diffusivity near the ground in complex environments and large uncertainties with 442 experimental results. To minimize effects of these uncertainties modelling were carried out with a 443 range of diffusion coefficients. Magenta streamlines in Fig. 1C show an unrealistic case of aerosol particle trajectories without 632 the atmospheric diffusion (Dif=0). 633  particles in the cloud is C0 =5 cm -3 . An extended version of the geometry is shown in Fig. 4. 652