The effects of ventilation strategies on mitigating airborne virus transmission in a generic indoor space representative of a lobby area or information desk found in a hotel, company, or cruise ship are presented. Multiphase computational fluid dynamics simulations are employed in conjunction with evaporation modeling. Four different ventilation flow rates are examined based on the most updated post-COVID-19 pandemic standards from health organizations and recent findings from research studies. Three air changes per hour provide the best option for minimizing droplet spreading at reasonable energy efficiency. Thus, a higher ventilation rate is not the best solution to avoid spreading airborne diseases. Simultaneous coughing of all occupants revealed that contagious droplets could be trapped in regions of low airflow and on furniture, significantly prolonging their evaporation time. Multiphase flow simulations can help define ventilation standards to reduce droplet spreading and mitigate virus transmission while maintaining adequate ventilation with lower energy consumption. The present work significantly impacts how heat, air-conditioning, and ventilation systems are designed and implemented.

The COVID-19 pandemic prompted the investigation of virus transmission in closed spaces.1–5 Past research discussed the air filtration, air purification, and efficiency of high-efficiency particulate air (HEPA) filters, which are supposed to capture more than 99% of particles, provide high ventilation rates with 50% fresh air and 50% filtered while providing more than 20 changes of air in a low ceiling room.6 However, previous studies also showcased the inevitability of virus transmission when two persons are close.7 

The most recent standards and regulations on room safety regarding airborne transmission of viruses focus on high rates of air exchanges.8–11 This can be inefficient as large energy consumption is needed to maintain high air flow rates while comfort can be reduced due to the creation of strong air drafts.

Assuming three occupants on average in an indoor space, the current 2023 ASHRAE standards10 for the ventilation flow rate will give more than 200 m3/h, i.e., around 3.9 times higher than the pre-COVID, 2019 ASHRAE, values.12 For more people, 30 occupants per 100 m2 per the default ASHRAE Standard 62.1-2019,12 the 2019 ASHRAE flow rate will still be significantly lower, as the ventilation flow rates recommendations considerably increased after the latest pandemic.

The World Health Organization (WHO),8 the European Federation of HVAC Associations,9 and research studies13 recommend 36 m3/h per person leading to a ventilation rate of 108 m3/h in our example. The Federal Public Service (FPS) Health, Food Chain Safety, and Environment of Belgium defined the minimum flow rate for their Standard A Level at a slightly higher value of 40 m3/h per person.14 Furthermore, the most recent guidelines from the Centers for Disease Control and Prevention (CDC)11 suggest a minimum of 5 air changes per hour (ACH) and aiming for higher values if possible. For 6 ACH, a flow rate of 342 m3/h would be required for the typical room considered in this paper.

Adequate ventilation, which leads to quick desiccation, harms the viability of Gram-negative bacteria, such as Escherichia coli.15 The study of the number and viability of viruses surviving on a surface after leaving the host is a subject of ongoing investigation. Recent studies, Guo et al.16 and references therein, on droplet evaporation, including experiments on the decay of viral concentration and infectious activity of Covid-19 and other viruses, had shown that the decrease in water in the evaporated droplets deteriorates the living environment of the virus rapidly and virus concentration plummets within minutes and the risk of transmission is negligible compared to when it first left the host. However, complete evaporation of the saliva droplets may not necessarily mean that all viruses17 or bacteria15 become instantly inactive. Therefore, we should aim for a minimum droplet spread inside the ventilated rooms and different ventilation strategies depending on the occupancy of the room. Saliva droplets evaporate faster than the room's air renewal, regardless of the ventilation strategy.18 This highlights the importance of considering evaporation when modeling the spread of saliva droplets.

This study examines a generic low-ceiling lobby room and shows how applying the most recent ventilation standards can affect the transmission of airborne viruses. Droplet evaporation is implemented,19,20 an effect which researchers often omit.21 Here, we show results ranging from 1.9 to 6 ACH to capture all recent ventilation and virus-spreading restriction recommendations.

In Sec. II, the simulation methods and models are outlined. Section III presents the geometry and a mesh independence study. The results are discussed in Sec. IV. The conclusions drawn from this study are summarized in Sec. V.

We have selected to simulate four cases with different flow rates at the ventilation system based on the latest recommendations from international standards and organizations.8–11 At the same time, we also include a case where the flow rate is calculated based on a recent publication by our team18 suggesting that 3 ACH are the optimum balance between droplet spreading, people's comfort, and energy efficiency. Details about the ambient-air conditions and other simulation parameters are given in Table I. In these four cases, one of the walking persons is coughing, which is considered the source of infectious saliva droplets. In addition, we present results from an extreme case where all three occupants of the room are coughing simultaneously (case 5). At the same time, the ventilation system operates at its lowest flow rate settings, as in case 1.

TABLE I.

Simulation conditions. The air changes per hour (ACH) vary depending on the flow rate of the ventilation system. The total flow rate of the ventilation system is also presented for each case.

T (°C) P (atm) RH (%) ACH
20  55  1.9–6 
Case 1 (m3/h)  Case 2 (m3/h)  Case 3 (m3/h)  Case 4 (m3/h) 
108.00  170.91  270.00  341.82 
T (°C) P (atm) RH (%) ACH
20  55  1.9–6 
Case 1 (m3/h)  Case 2 (m3/h)  Case 3 (m3/h)  Case 4 (m3/h) 
108.00  170.91  270.00  341.82 

Each person's mouth has been considered a circular inlet with a diameter equal to 14.62 mm, corresponding to the hydraulic diameter of a realistic mouth opening.4 Saliva has been considered a Newtonian fluid with water properties, although it is complex and varies from person to person. Taking its viscosity close to that of water is a valid approximation.22 We also consider that human bodies would have an average temperature of 34 °C at their surface. In Table II, we provide further details regarding the mouth's inlet conditions. We have assigned different breathing velocities to standing and sitting persons based on the data provided in Ref. 23, where they have combined expired flow rates of men and women of all ages from birth to 81 years or older during various activity levels. For the sitting person behind the desk, we have assigned a lower breathing rate ( V breath l), around the average value for sedentary persons. A higher breathing rate ( V breath h) has been assigned to the standing persons, indicating light activity.

TABLE II.

Breathing and coughing conditions. The person's mouth is always considered an inlet with the same relative humidity (RH) as the environment and the specified temperature.

Tmouth (°C) Vcough (m/s) V breath l (m/s) V breath h (m/s)
34  8.5  0.45  0.97 
Tmouth (°C) Vcough (m/s) V breath l (m/s) V breath h (m/s)
34  8.5  0.45  0.97 

The results presented in Secs. III–V have been produced through multiphase simulations, where the air has been modeled as a fluid mixture with a multi-component gas (dry air and water vapor) while saliva droplets as Lagrangian particles. To achieve the values given in Table I, the gas mass fractions at the air inlets have been specified as 0.99207-dry air and 0.00793-water vapor, while liquid water is only inserted during the coughing event from the person's mouth.

We initially perform a simulation without any droplets in the domain for 180 s until the flow is fully developed. Then, we imitated a human cough for 0.12 s, where saliva droplets are ejected from the mouth of the infected person. The size of the droplets is determined based on the Rosin–Rammler distribution law,24 also known as Weibull distribution,25 given by the following equation:
f = n d ¯ p ( d p d ¯ p ) n 1 e ( d p / d ¯ p ) n ,
(1)
where dp is the saliva droplet diameter, n = 8 and d ¯ p = 80 μm. This is an appropriate distribution for dispensing water and water-like cloud droplets.26 This is a well-known and justified practice regarding the droplet's size distribution near the origin of ejection.4,27

The total mass of the injected saliva into the domain is 7.7 mg per coughing person, which agrees well with existing experimental measurements reported in the literature.27,28 The number of expelled saliva droplets varied in each case between 2400 and 4000 droplets, in agreement with the literature.28–31 The velocity applied at the mouth during the cough is u x = 8.5 m/s, as measured by Scharfman et al.32 During the coughing event, the saliva droplets and the air expelled from the person's mouth have the same high velocity of 8.5 m/s, independent of whether the person is sitting or standing. The simulation continues for another 20 s, where all saliva droplets have evaporated except for case 5. In this latter case, with all three persons coughing and producing saliva droplets, we observe trapped droplets slowly evaporating after more than 40 s of simulation. In all cases, during the initial 180 s and after the coughing event, the air is expelled from the mouth with V breath l = 0.45 or V breath h = 0.97 m/s, depending on the position and activity of the person.

This study focuses on the latest recommendations on ventilation standards, which consider the recent COVID-19 pandemic and their effect in a lobby/office area with a low ceiling and at least three persons at any time. Droplets' evaporation plays a crucial role, while in all cases, the overall flow velocity is less than 1 m/s, except for the coughing event when the velocity increases for a small period to 8.5 m/s. Taking into account the above, we perform all simulations with the established software Star-CCM+ 2210,33 employing a compressible, unsteady multiphase solver with the Ranz–Marshall model applied for the Nusselt and Sherwood numbers.34,35 Within Star-CCM+, we have used numerical algorithms and models that have been extensively tested and validated in the broader computational fluid dynamics (CFD) literature for different fluid dynamics problems. A description of these models is provided below. Furthermore, we have assessed the accuracy of the present simulations regarding the droplets spreading distance (without air conditioning) against other CFD simulations,4 confirming that the results are comparable. Following the first multiphase studies4,19 on the airborne transmission of saliva droplets, several studies have confirmed the droplets' spread distance for given environmental conditions. Therefore, the present results can safely be considered as accurate as possible within the boundaries of computational uncertainty.

A laminar multi-component gas model allows us to add the different substances of the Eulerian fluid, i.e., air and water vapor (humidity), leading to a more accurate representation of the gas in the simulated room, similar to our recent publication.18 The flow is laminar and may transition to turbulence. The transition will only be captured if the grid is significantly refined to capture the details of the emanated jet from the mouth. Past research36,37 using large eddy simulation (LES) has found similar distances for the droplets spreading with the ones predicted by Dbouk and Drikakis4,19 using RANS models. We have further found that our predictions without turbulence models indicate similar distances for the droplets spreading with the above-mentioned studies. The above-mentioned numerical behavior is because of the dynamic of the droplets spreading and the overall low slip velocities. Moreover, the Reynolds number, as defined here and by all the authors in the literature, though an indicative measure of the nature of the flow, is not the most representative measure to characterize the droplet dynamic. We plan to investigate the above in a future work where we will identify the correct measure for characterizing droplet behavior vs the initially calculated Reynolds number. Nonetheless, the results regarding droplet distances and scattering are not affected by not using a turbulence model, as per the above-mentioned discussion.

The survival of droplets also depends on the relative humidity and temperature. We have investigated these effects in a previous study,19 showing that high temperature and low relative humidity lead to high evaporation rates of saliva-contaminated droplets, thus significantly reducing the virus viability. Moreover, the droplet cloud's traveled distance and concentration continue to be significant, even at high temperatures if the relative humidity is high too. In our calculations, we utilize the ideal gas law to express the density as a function of temperature and pressure. The dynamic viscosity of air and water vapor is calculated based on Sutherland's law. In all simulations, we use a second-order implicit temporal solver and a segregated flow solver with activated secondary gradients and flow-boundary diffusion fluxes.

The linkage between the momentum and continuity equations is achieved with a predictor–corrector approach. Essentially, the solver uses a collocated variable arrangement and a Rhie-and-Chow-type pressure-velocity coupling combined with a SIMPLE-type algorithm. This solver can handle mildly compressible flows and low Rayleigh number natural convection, as in the cases studied here. Convection is solved with a second-order upwind scheme, which introduces linear interpolation of cell values on either side of the upstream or downstream face. A positivity rate limit of 0.2, necessary for compressible segregated solvers, controls the maximum allowable pressure correction update. Similarly, a second-order segregated fluid temperature model solves the total energy equation, with temperature as the solved variable. Enthalpy is calculated from temperature according to the equation of state. Two transport equations are solved sequentially with a second-order segregated species solver and, along with the global mass continuity, leading to updating the two mass fractions defining the mixture composition of the air in the simulated room.

We have used the Venkatakrishnan limiter with second-order accuracy to reconstruct the gradients at the cell faces. The scale factor a = min ( a f ) for a cell that expresses the ratio of the limited and unlimited values is calculated based on the following equation:
a f = ( 2 r f + 1 ) / [ r f ( 2 r f + 1 ) + 1 ] ,
(2)
where r f = ( ϕ f ϕ 0 ) / ( max ( ϕ 0 , ϕ neighbors ) ϕ 0 ) and ϕ f is the face value while ϕ 0 is the cell centroid value.

We apply no-slip and adiabatic boundary conditions at all solid surfaces for the Eulerian model. The maximum time step used in the implicit temporal solver was 0.01 s, which was reduced to 0.5 ms during the coughing event.

The droplet's Lagrangian phase equations were discretized employing implicit numerical schemes at second order with two-way coupling and a quasi-steady evaporation model. Second-order temporal and spatial discretization of the governing equations was used in all production runs. In the Lagrangian framework, the equation of conservation of momentum for a liquid droplet of mass md is given by
m d d v d d t = F d + F p + F v m + F g .
(3)
In this study, we calculate the drag ( F d), pressure gradient ( F p), and gravity ( F g = m d g) forces, while the virtual mass force ( F v m) can be safely ignored for the particle sizes studied here.38,39 The drag force calculates the force on a material particle due to its velocity relative to the continuous phase based on
F d = 1 2 C d ρ A d | v s | v s ,
(4)
where Cd is the drag coefficient, v s = v v d is the droplet slip velocity, and Ad is the projected area of the droplet. The drag coefficient in the above-mentioned equation is a function of the small-scale flow features around individual particles. Resolving those features for thousands of particles is intractable from a computational efficiency perspective. It is common practice to obtain the drag coefficient from correlations, typically derived from experimental or theoretical studies. For the small liquid droplets in a viscous continuous phase, we consider the most appropriate correlation to be the Schiller–Naumann,40 which is formulated as
C d = { 24 R e d ( 1 + 0.15 R e d 0.687 ) , if    R e d 10 3 , 0.44 , if    R e d > 10 3 ,
(5)
where Red is the droplet Reynolds number. For the pressure gradient force, we do not need any correlation as it is based on the droplet's volume (Vd) and the static pressure of the continuous phase (pstatic),
F p = V d p static .
(6)

Droplet collision, atomization, and secondary breakup are not considered due to the low concentration of particles in the room.29 A stick boundary condition is applied when droplets reach a solid surface, a common practice in the literature for this range of particle sizes.29,30,38 The authors recognize that, in reality, some of the particles could be reflected on solid surfaces or re-enter the air after deposition. However, their effect on our observations would be infinitesimal.

Droplets have a constant density equal to 997.561 kg/m3, while the effect of the nonvolatile compounds, such as salt and lipids, on the size change during the evaporation of the droplets was ignored. The latent heat of vaporization is calculated directly as a difference in the enthalpy of the gas and liquid states as follows:
L ( T d ) = h vap ( T d ) h liq ( T d ) ,
(7)
where Td is the droplet temperature, h vap ( T d ) is the static enthalpy of the vapor component corresponding to the droplet material, evaluated at the droplet temperature, and h liq ( T d ) is the static enthalpy of the droplet material, evaluated at the droplet temperature. The saturation pressure psat is the pressure of each vapor component when in equilibrium with the corresponding liquid component and is a key material property. In this implementation, we use the Antoine equation, which is based on the logarithm of the ratio p sat / p atm as we show in the following equation:41 
ln ( p sat / p atm ) = 11.949 3978.205 / ( T d 39.801 ) .
(8)

The total computation time of a single case (200 s of simulation) was about 5 days, run in parallel over 2 Intel-Xeon Gold 6138 CPUs with 20 cores each at a frequency of 2 GHz. The incoming air is considered clean, i.e., free from contaminants, without specifying whether it is outdoor air or treated with filtered recirculated air.

A generic low-ceiling room representing various functions, e.g., an office, an information desk, or a cruise ship lobby area, is selected. The floor dimensions are given in Fig. 1, where the room height of 2.11 m is based on the usual available height in cruise ships. A standard air conditioning unit is placed at the room's center with a square outlet (482 cm2) and four rectangular inlets (55 × 5 cm2 each) that expel air at an angle of 45°. There are also four additional circular openings ( 25 cm), with two acting as fresh air inlets and the other two as additional outlets. We also include a desk with computer monitors and a chair.

FIG. 1.

Schematic representation of the simulation domain with key dimensions. Ventilation inlets and outlets are highlighted.

FIG. 1.

Schematic representation of the simulation domain with key dimensions. Ventilation inlets and outlets are highlighted.

Close modal

In reality, rooms contain several pieces of furniture, electronic devices, and other decoration items, depending on the use of space. We have considered the minimal amount of items in the room because the air velocities are very small. Thus, the droplets scattering on surrounding items are considered negligible when the flow reaches the objects in the room. Based on this, adding further or different furniture and other objects will only increase the complexity of the meshing process without offering additional information or altering our conclusions about air circulation effects due to ventilation. Any object in the immediate area of the coughing person will be covered by saliva droplets, which will evaporate, as it happens in case 5, with the sitting person covering a portion of the desk. However, complex spaces, such as libraries, auditoriums, and open indoor spaces, would require bespoke study as the air circulation will be constrained by bigger obstacles, such as partitions and bookshelves. This will also affect the virus scattering. Moreover, the equilibrium contact angle of a sessile droplet on various surfaces is essential in connection with surface-borne transmission. There are pertinent studies investigating this critical issue.42–46 We do not examine the transmission from contact surfaces in this paper, but the reader can find information in the above papers. Finally, although it is not clear how viruses behave when they come in contact with different materials, treatment of surfaces with environmental probiotics offers antiviral protection for walls and fabrics.47 

The geometry was meshed with polyhedral non-uniform cells ( 540 × 10 5), with significant refinement in all inlet and outlet regions, where a conical refinement area is defined in each case. For example, at the mouth and up to a distance of 0.5 m in the streamwise direction, the cells have a maximum isotropic size of 2 mm compared to the overall targeted cell size of 10 cm. Enhanced quality triangles were used for the surface meshing method and five core mesh optimization cycles with a quality threshold of 0.6 for the entire mesh. A characteristic snapshot of the mesh is given in Fig. 2, where the refinement regions in front of the coughing person and the ventilation inlets and outlets are visible. The greatest volume change was 0.01 in less than 0.1% of the cells, while the mesh had 100% face validity.

FIG. 2.

Snapshot of the polyhedral mesh utilized in the simulations (case B) highlighting the areas of refinement.

FIG. 2.

Snapshot of the polyhedral mesh utilized in the simulations (case B) highlighting the areas of refinement.

Close modal

Moreover, we conducted a mesh convergence study on main local (random points) and global flow parameters (averaged values over the whole room), like the temperature (T), relative humidity (RH), and the axial velocity (Ux). In Fig. 3, we show the results from four different meshes, including the selected one for producing the results in the following sections. The number of cells varied from 74 400 to more than 1.3 × 10 6 cells, while the results are from 180 s of simulation and averaging over the last 40 s.

FIG. 3.

Comparison of various meshes on the calculated values of T, RH, and Ux at two random locations in the room and their averaged value over the whole volume. The error bars show one standard deviation of the sample.

FIG. 3.

Comparison of various meshes on the calculated values of T, RH, and Ux at two random locations in the room and their averaged value over the whole volume. The error bars show one standard deviation of the sample.

Close modal

In all cases, we have employed the same meshing approach and refinement techniques, which led to very good convergence at the two finest meshes, as shown in Fig. 3. In addition, the error of the chosen mesh to the maximum and minimum pressure in the domain was also less than 1.5%. The coarsest mesh tested exhibited errors over 29% in pressure.

No-slip boundary conditions have been applied on all walls, the ceiling, the floor, and the person's body. Outlet boundary conditions with a specified mass flow rate have been applied in the air outlets, as shown in Fig. 1, with 1/2 of the flow directed to the A/C outlet and the rest shared between the circular outlets leading to a pressure balance in the room. The Air inlets provide the overall targeted mass flow rate with the air blowing downward from the circular inlets and at an angle of 45° from the A/C unit.

Initially, we studied the effect of different ventilation standards when the person standing near the center of the room coughs. The persons have a minimum physical distance of 1.95 m between them, exceeding the recommended social distancing rule of 1.5 m for most European Countries.48 In any case, we should have in mind that these rooms have dynamic occupancy and persons are free to approach each other without any restrictions, so we will examine the penetration and scattering of the droplet cloud, highlighting the areas of increased contamination risk due to droplet concentration.

In case 1, we apply a flow rate equal to 36 m3/h per person (or 108 m3/h for our room with three persons) as recommended by the World Health Organization (WHO),8 the European Federation of HVAC Associations,9 and also a recent research study.13 This is the lowest flow rate we will examine here. However, it is double what the pre-COVID-19 standards suggested.12 It strongly indicates how much our understanding of virus spreading has changed and the significance we pay to good ventilation after the recent pandemic.

In case 2, the flow rate of the ventilation system increases to 171 m3/h based on our recent findings from the study of the virus spreading in a cruiser cabin,18 where the optimum balance between the minimization of droplet spreading, good ventilation levels, comfort, and energy consumption were achieved with 3 ACH. In case 3, we have selected to conform to the latest ASHRAE standard 241-2023,10 which suggests a minimum clean airflow rate based on the following equation:
Q ̇ ASHRAE 23 = ECA × P ,
(9)
where ECA is the equivalent clean airflow rate required per person from Table V-I of the Standard, and P is the number of people in the room. We have selected ECA = 25 l/s, which corresponds to the recommended values for lobbies, common residential spaces, places of religious worship, auditoriums, etc., while P = 3. Based on the above, the total flow rate for case 3 equals 270 m3/h, which is significantly higher than the previous two cases and leads to an ACH of 4.8. In case 4, we apply the highest ventilation rate based on the recommendations we find from ventilation standards and health organizations. The Centers for Disease Control and Prevention (CDC) propose a minimum of 5 ACH or more,11 so here we have selected 6 ACH, which, based on the volume of the room, will give a total flow rate of 341.8 m3/h. In Figs. 4–7, we can observe a side view of the coughing person with the saliva droplets at various instances after the coughing event for the four different cases.
FIG. 4.

Visualization of the saliva droplet cloud at various instances after the coughing event in case 1. The size of each sphere indicates the relative diameter of the saliva droplets, although they have been enlarged for visualization purposes. The distance below the arrow indicates the maximum penetration of the saliva droplets at the current time, while the percentage of evaporated saliva mass is also given.

FIG. 4.

Visualization of the saliva droplet cloud at various instances after the coughing event in case 1. The size of each sphere indicates the relative diameter of the saliva droplets, although they have been enlarged for visualization purposes. The distance below the arrow indicates the maximum penetration of the saliva droplets at the current time, while the percentage of evaporated saliva mass is also given.

Close modal
FIG. 5.

Visualization of the saliva droplet cloud at various instances after the coughing event in case 2. The size of each sphere indicates the relative diameter of the saliva droplets, although they have been enlarged for visualization purposes. The distance below the arrow indicates the maximum penetration of the saliva droplets at the current time, while the percentage of evaporated saliva mass is also given.

FIG. 5.

Visualization of the saliva droplet cloud at various instances after the coughing event in case 2. The size of each sphere indicates the relative diameter of the saliva droplets, although they have been enlarged for visualization purposes. The distance below the arrow indicates the maximum penetration of the saliva droplets at the current time, while the percentage of evaporated saliva mass is also given.

Close modal
FIG. 6.

Visualization of the saliva droplet cloud at various instances after the coughing event in case 3. The size of each sphere indicates the relative diameter of the saliva droplets, although they have been enlarged for visualization purposes. The distance below the arrow indicates the maximum penetration of the saliva droplets at the current time, while the percentage of evaporated saliva mass is also given.

FIG. 6.

Visualization of the saliva droplet cloud at various instances after the coughing event in case 3. The size of each sphere indicates the relative diameter of the saliva droplets, although they have been enlarged for visualization purposes. The distance below the arrow indicates the maximum penetration of the saliva droplets at the current time, while the percentage of evaporated saliva mass is also given.

Close modal
FIG. 7.

Visualization of the saliva droplet cloud at various instances after the coughing event in case 4. The size of each sphere indicates the relative diameter of the saliva droplets, although they have been enlarged for visualization purposes. The distance below the arrow indicates the maximum penetration of the saliva droplets at the current time, while the percentage of evaporated saliva mass is also given.

FIG. 7.

Visualization of the saliva droplet cloud at various instances after the coughing event in case 4. The size of each sphere indicates the relative diameter of the saliva droplets, although they have been enlarged for visualization purposes. The distance below the arrow indicates the maximum penetration of the saliva droplets at the current time, while the percentage of evaporated saliva mass is also given.

Close modal

The contour plot in the background of the image shows the velocity magnitude of the air. As we have mentioned earlier, the bodies have a constant temperature of 34 °C, which is higher than the ambient room temperature, creating an upward flow stream close to the person. The air expelled from the mouth during the coughing event is also of high velocity (8.5 m/s), which is then decreased to the breathing value of 0.97 m/s, as justified in Sec. II.

By the end of the coughing event at t = 0.12 s, only a small percentage of the total saliva mass had been evaporated. In all cases, the droplets have traveled a maximum distance of 26 cm, maintaining the shape of a coherent cloud. A second after the coughing event, we can still observe a coherent saliva cloud; however, many droplets travel independently further away from the cloud. Droplets have reached a distance between 72 and 75 cm, depending on the case, while most have started falling toward the floor. A closer observation can reveal a stratification of the saliva cloud based on the size of the droplets, with the larger ones being at the bottom, closer to the floor. In contrast, smaller droplets maintain a higher elevation.

At 4 s, we observe the highest penetration in the time instances we visualize here. Droplets have traveled almost a meter away from the coughing person in case 1, while the maximum penetration is around 8%–5% less in the other cases, reaching a maximum distance between 90 and 92 cm. In all cases, more than 60% of the initial saliva mass has been evaporated by this time. The droplets have a wider elevation, and most are below the waist height of the person.

At the latest time instance of 10 s, most of the initial mass of the droplets have evaporated with only 2% of the initial mass being active, although there are still more than 1000 droplets in the room from the originally expelled 2400 in case 1, for example. In all cases, less than half of the droplets injected in the room remain active. The largest droplets have settled on the floor in all cases, and the majority has a low elevation below the knee of the person. However, in cases 2–4, they maintain a higher distance from the person, up to 71 cm compared to 47 cm in case 1. Because the droplet size and overall mass of the saliva cloud are considerably reduced, the higher penetration distance at the latest time instance is not of high concern.

Overall, the differences we observe after this first analysis of the results for the different cases are concentrated to the maximum penetration distance at t = 4 and 10 s. Cases 2 and 4 at this point show the same efficiency in minimizing droplet spreading, with case 2 having the advantage of a lower flow rate and, as a result, reduced energy consumption and better comfort levels for the occupants.

At this point, it is important to examine the total time needed for the evaporation of all the ejected saliva droplets. In Fig. 8, we can see that the four cases we have introduced above behave the same, with all droplets evaporating after 18 s.

FIG. 8.

(a) Total mass reduction of the droplets and (b) evolution of the maximum droplet diameter.

FIG. 8.

(a) Total mass reduction of the droplets and (b) evolution of the maximum droplet diameter.

Close modal

We also introduce at this point a fifth case, which is an extreme possibility of all three persons in the room coughing at the same time. The ventilation flow rate and all other parameters have been maintained as in case 1. In Fig. 8, we can see that some saliva still exists in case 5 even at t = 20 s. This can be more clearly shown when we plot the evolution of the maximum droplet diameter in the room in Fig. 8(b). There, we can observe that in cases 1–4, the maximum droplet diameter falls very quickly after t = 16 s, in contrast with case 5, where one or more large droplets evaporate much slower and are still present in the room even after 40 s.

After examining the simulation results, we found that all the remaining droplets in case 5 are trapped in a region with almost no ventilation, on the desk and next to the arm of the sitting person. In Fig. 9, we can see the different saliva clouds formed by the three coughing persons at t = 1 and 4 s after the coughing event. Droplets with an index of 2 (orange color) are those injected by the same person as in cases 1–4, droplets with an index of 4 (blue color) are injected by the other standing person in the room, while droplets with index 3 (green color) are those from the sitting person.

FIG. 9.

Two different time instances, top view of the room with all occupants coughing. The upper figure is at t = 1 s, and the lower is at t = 4 s. Red areas are outlets, and blue areas are fresh air inlets. Insets show the droplets from a side view.

FIG. 9.

Two different time instances, top view of the room with all occupants coughing. The upper figure is at t = 1 s, and the lower is at t = 4 s. Red areas are outlets, and blue areas are fresh air inlets. Insets show the droplets from a side view.

Close modal

Focusing on the behavior of the saliva clouds in these initial seconds, we can observe the room's different areas. As a result, the different local airstreams can affect the spreading of saliva droplets. Looking from a top view, we can deduce that the cloud of orange droplets is quickly losing its initial symmetry, and there is also a tendency for the droplets to move downwards as we look at this top-view image and away from them (penetration). In contrast, the blue cloud maintains a much more symmetrical structure even at t = 4 s and the whole cloud has moved slightly to the left of the coughing person. The more interesting behavior is observed near the sitting person with the green cloud of saliva droplets. The cloud quickly deforms, with many particles trapped close to the person and his right arm. In this case, many droplets maintain their original elevation and gain height at the initial 4 s (insets in Fig. 9).

To further quantify this and any other differences or similarities between the different sources of saliva droplets, we have gathered all the droplets' penetration distances and elevations in one graph (see Fig. 10). As expected at the initial stage and just after the end of the coughing event (t = 0.12 s), the saliva cloud in all cases has almost the same shape, with the droplets from the sitting persons (green color) having the lower penetration and those from one of the standing persons (blue color) having the higher values. At t = 1 s, the saliva clouds from the standing persons are still very similar, while the droplets from the sitting person concentrate at a higher elevation, with much smaller penetration lengths. We can also clearly observe orange droplets breaking from the main cloud and traveling at higher penetration and elevation distances.

FIG. 10.

Elevation vs penetration graph of the saliva droplet clouds of case 5 at various time instances after the coughing event. The circle's size indicates the droplet size, while the color indicates the person that injected the particles. (a) t = 0.12, (b) t = 1, (c) t = 4, and (d) t = 10 s.

FIG. 10.

Elevation vs penetration graph of the saliva droplet clouds of case 5 at various time instances after the coughing event. The circle's size indicates the droplet size, while the color indicates the person that injected the particles. (a) t = 0.12, (b) t = 1, (c) t = 4, and (d) t = 10 s.

Close modal

At a later time (t = 4 s), the shapes of the saliva clouds from the standing persons maintain their similarities, with all droplets below the ejection level. In contrast, individual orange droplets have traveled further away, reaching distances close to 1 m. In contrast, the green droplets from the sitting person have gained significant elevation, with some already settling on the desk's surface. The overall penetration distance of the green cloud is significantly smaller compared to the other two saliva clouds, with the majority of them being below 30 cm and only a few reaching a maximum of 60 cm. One of the reasons that the droplets originating from the sitting person are achieving much lower penetration values could be that the breathing velocity is around half that of the standing persons (0.45 vs 0.97 m/s). Thus, during the coughing event, the saliva droplets and the air expelled from the person's mouth have the same high velocity of 8.5 m/s, independent of whether the person is sitting or standing. Still, when the person resumes normal breathing velocities, there are differences between standing and sitting.

At t = 10 s, most of the droplets from the standing persons have reached the ground, while all are in a distance less than 60 cm. Blue individual droplets penetrate the air further, while the previously observed orange droplets at high penetration lengths have evaporated. Returning to the sitting person, most droplets have settled on the desk at a distance less than 30 cm away, with only a couple still floating around them (Fig. 8).

The results indicate differences in the behavior of the saliva cloud, depending on the location of the coughing person. Major differences can be observed when the saliva droplets can be trapped in areas of low ventilation and with high upstream velocities, usually close to humans or other heated objects. At least 98% of the originally ejected saliva mass has evaporated in less than 20 s. At the same time, droplets from different coughing persons do not reach others, at least for the conditions considered here.

Going back to the original four cases and the effect of the ventilation flow rate, we examine further how the droplets spread after the coughing event and until their complete evaporation. In Fig. 11, we present the droplets' maximum penetration, scattering, and vertical distance for each case.

FIG. 11.

Case A: (a) maximum distance of droplets away from the mouth in the x direction (penetration). (b) Maximum distance of droplets away from the mouth in the y direction (spanwise scattering). (c) Maximum distance of droplets away from the mouth in the normal to the floor direction (elevation).

FIG. 11.

Case A: (a) maximum distance of droplets away from the mouth in the x direction (penetration). (b) Maximum distance of droplets away from the mouth in the y direction (spanwise scattering). (c) Maximum distance of droplets away from the mouth in the normal to the floor direction (elevation).

Close modal

The maximum liquid penetration distance of 1 m is achieved under the conditions of case 1, while all the other cases have around 10% smaller penetration values. Big differences that have not been revealed until now become apparent when we study the scattering behavior of the droplets [Fig. 11(b)]. The cases with lower flow rates have similar behavior and a maximum scattering around 25 cm. For higher ventilation rates, the scattering of the droplets dramatically increases and reaches distances close to 40 cm for case 4. Finally, the elevation of the droplets, or how quickly they fall toward the floor, seems to be almost unaffected, with the first droplets reaching the floor around 8 s after the coughing event.

From the above, the flow rate of case 2 is recommended because it provides both low penetration and scattering values. Any value between case 1 and case 2 could be acceptable, and the selection could be based on other factors, such as comfort and energy consumption. Recently, we have made similar observations and recommendations for a range of flow rates, from 1.5 to 15 ACH, for a cabin.18 The present results strengthen our belief that higher ventilation rates do not always lead to reduced virus-spreading risk; on the contrary, they can increase it occasionally. Our findings suggest an optimum value close to 3 ACH, at least for our examined cases and conditions. Moreover, the present work further highlights how computational fluid dynamics can be used in complement with ventilation standards and toward the reduction in airborne infection transmission, a necessity also underlined in the ASHRAE 241-2023.10 

Moreover, we investigated possible similarities or differences in droplet dynamics between the two cases with the biggest scattering difference and small penetration difference, i.e., cases 2 and 4. We compared the droplets' dynamics and their evolution (Fig. 12). Just after the coughing event (t = 0.12 s), the differences are marginal with droplets at a penetration distance between 12 and 16 cm, maintaining higher velocities in case 4 [see Figs. 12(a) and 12(e)].

FIG. 12.

Particle penetration and velocity for two different cases, left column [(a)–(d)] case 2 and right column [(e)–(h)] case 4 at four different time instances, 0.12 s [(a) and (e)], 1 s [(b) and (f)], 4 s [(c) and (g)], and 10 s [(d) and (h)]. The circle's color indicates the droplet's slip velocity and its diameter.

FIG. 12.

Particle penetration and velocity for two different cases, left column [(a)–(d)] case 2 and right column [(e)–(h)] case 4 at four different time instances, 0.12 s [(a) and (e)], 1 s [(b) and (f)], 4 s [(c) and (g)], and 10 s [(d) and (h)]. The circle's color indicates the droplet's slip velocity and its diameter.

Close modal

At t = 1 s [Figs. 12(b) and 12(f)], the saliva clouds have similar shapes, and the stray droplets have similar sizes, numbers, and penetration distance. Larger droplets retain higher slip velocities than smaller ones that quickly adhere to the flow velocity. The individual (stray) droplets with higher penetrations also have the highest velocity, following local streams of high velocity. These droplets are of medium to small size and have low slip velocities. The saliva cloud in case 4 is shifted to the left of the penetration axis compared to case 2. Specifically, the saliva cloud of case 2 has penetrated 5 cm further compared to case 4.

At t = 4 s, the droplets maintain higher overall velocities in the high flow rate case (case 4). There is also a tendency of higher mass and high-velocity droplets to penetrate further away compared to case 2. The few stray droplets are of medium to small size and have low velocities.

At later times [Figs. 12(d) and 12(h)], high-mass large droplets maintain some velocity, even in regions of almost no air stream velocity, namely, close to the room's floor. All droplets have slowed down and settled in low-elevation areas by this time. The main difference between the two cases is the behavior of the small, slow-moving droplets. In case 2, they are almost equally spread at all distances at a narrow velocity band, with those at higher penetrations having lower velocities. In case 4, the spreading of the small droplets is still quite even, but the velocity spreading is larger, and in this case, those at low penetrations are the ones with low velocities. Overall, the two cases have no big differences, although the ventilation flow rate doubles in case 4 compared to case 2.

Furthermore, we touch on another important issue of ventilation systems affecting virus spreading: the mean age of air or how quickly it is refreshed in a specific room. We compare the lowest flow rate case (case 1) with the one that minimizes droplet spreading (case 2) (Fig. 13). The orange-colored regions are those where the air has not been refreshed after 3 min. As expected, the regions below the circular ventilation inlets are those where air is quickly refreshed compared to the areas below the outlets. Case 2 exhibits a smaller volume of non-refreshed air in the room due to the higher ventilation rate than case 1. In both cases, the effect of the desk, the sitting person, and the rest of the equipment restricts the circulation and refreshment of air in that region. This can also explain the trapped, slowly evaporating droplets observed in case 5. Based on the ventilation flow rates, in case 1, at least 32 min for a complete room refreshment are required. This value is reduced to 20 min for case 2. These time scales are two orders of magnitude greater than the saliva droplets evaporation time (20 s). Therefore, the infection could be attributed to fomite rather than airborne transmission in all studied cases.

FIG. 13.

Comparison of air refreshment after 3 min of ventilation for two cases. At the visualized flow rates, the room's air is refreshed 1.9 and 3 times per hour. Colored regions show air that has not been refreshed.

FIG. 13.

Comparison of air refreshment after 3 min of ventilation for two cases. At the visualized flow rates, the room's air is refreshed 1.9 and 3 times per hour. Colored regions show air that has not been refreshed.

Close modal

The ventilation effects on virus spreading in a generic low-ceiling room representative of a lobby area or information desk found in a hotel, company, or cruise ship were studied. Four different ventilation flow rates are considered based on health organizations' most recent standards and recommendations and a flow rate suggested in our previous study.18 We confirm here that 3 ACH provide the necessary balance between droplet spreading minimization and energy efficiency. The results reveal that a higher ventilation rate is not always the best strategy to avoid spreading airborne diseases. The above-mentioned conclusion is reinforced when comparing the scattering droplet dynamics for all the cases considered here. Higher ventilation rates lead to longer distances of droplet spreading. Case 2 (3 ACH) is recommended due to the low penetration and scattering values.

We also tested the effect of multiple persons coughing simultaneously, the differences in droplet spreading in the same room, and conditions from different source points. This brought to the surface the effect of furniture and regions of low ventilation and relatively high upstream flow, such as near-sitting persons or other heated objects. Droplets can be trapped and evaporate much slower than those exposed to the ventilation air streams.

Given the results presented in this study, excessively high flow rates, over 5 ACH, can have the opposite effect, leading to higher droplet spreading and high energy costs and adding probable discomfort to the occupants. Ventilation strategies like those proposed by WHO8 and REHVA9 lead to results close to those observed with the best flow rate of 171 m3/h or 3 ACH tested here. Higher flow rate strategies, like those proposed by the recent ASHRAE Standard10 and CDC,11 do not offer any advantage in this case and also create higher droplet scattering. There could be cases where a higher than 3 ACH is needed, such as in large rooms with multiple occupants, i.e., restaurants or ballrooms.

The recommendation of 3 ACH provides the best balance between droplets' spreading reduction, comfort, and energy consumption and can be extrapolated to different spaces and the number of occupants. However, we recommend performing CFD simulations to examine the air circulation within the space for more complex spaces, e.g., open, flexible, activity-based indoor spaces. Understanding air circulation is important as it will determine the droplet transmission penetration and scattering. This applies to all respiratory viruses and airborne pathogens, which require a substrate, i.e., the saliva droplet, for transmission and survival.

Computational fluid dynamics can provide significant insight into improving ventilation standards, creating optimized and per-case ventilation suggestions that would be able to reduce airborne infection transmission while maintaining good ventilation levels, comfort, and energy consumption. Despite several simulation studies published in the literature, it is noteworthy that several studies incorrectly omit evaporation. In the present study, we used a well-established evaporation model. Other heat and mass transfer models could be considered in the future,19 though we expect that the key conclusions of this study will remain the same. Uncertainties arising from the numerics, e.g., comparing second-order and higher-order accurate methods, would be worth investigating. Still, again, the high-level conclusion about the optimal ventilation rate (lower vs higher rate) is expected to stay the same. The quantitative details of the results will always depend on the numerical uncertainties.

Finally, implementing an air conditioning system will depend on the space details. In a previous study concerning air purifiers,49 the authors proposed a new indoor air circulation system that more efficiently absorbs airborne virus particles than conventional approaches. The proposed concept used in-ceiling multi-fans instead of placing small purifier equipment on the floor. The overall design of air conditioning systems should consider similar ideas.

This paper was supported by the European Union's Horizon Europe Research and Innovation Actions programme under Grant Agreement No. 101069937, project name: HS4U (HEALTHY SHIP 4U). Views and opinions expressed are those of the author(s) only and do not necessarily reflect those of the European Union or the European Climate, Infrastructure, and Environment Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.

The authors have no conflicts to disclose.

Konstantinos Ritos: Data curation (lead); Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal); Software (lead); Validation (lead); Writing – original draft (lead); Writing – review & editing (equal). Dimitris Drikakis: Conceptualization (lead); Formal analysis (equal); Funding acquisition (lead); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (lead); Writing – original draft (equal); Writing – review & editing (equal). Ioannis William Kokkinakis: Formal analysis (supporting); Investigation (supporting); Methodology (equal); Visualization (supporting); Writing – review & editing (supporting).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
Y.
Yan
,
X.
Li
,
X.
Fang
,
P.
Yan
, and
J.
Tu
, “
Transmission of COVID-19 virus by cough-induced particles in an airliner cabin section
,”
Eng. Appl. Comput. Fluid Mech.
15
,
934
950
(
2021
).
2.
W.
Wang
,
F.
Wang
,
D.
Lai
, and
Q.
Chen
, “
Evaluation of SARS-COV-2 transmission and infection in airliner cabins
,”
Indoor Air
32
,
e12979
(
2022
).
3.
F.
Wang
,
T.
Zhang
,
R.
You
, and
Q.
Chen
, “
Evaluation of infection probability of Covid-19 in different types of airliner cabins
,”
Build Environ.
234
,
110159
(
2023
).
4.
T.
Dbouk
and
D.
Drikakis
, “
On coughing and airborne droplet transmission to humans
,”
Phys. Fluids
32
,
053310
(
2020
).
5.
T.
Dbouk
and
D.
Drikakis
, “
On airborne virus transmission in elevators and confined spaces
,”
Phys. Fluids
33
,
011905
(
2021
).
6.
S.
Bushwick
,
T.
Lewis
, and
A.
Montañez
,
Evaluating COVID Risk on Planes, Trains and Automobiles
(
Scientific American
,
2020
).
7.
T.
Dbouk
and
D.
Drikakis
, “
On respiratory droplets and face masks
,”
Phys. Fluids
32
,
063303
(
2020
).
8.
WHO
(
2021
). “
Roadmap to improve and ensure good indoor ventilation in the context of COVID-19
,”
World Health Organization
. https://www.who.int/publications/i/item/9789240021280.
9.
REHVA
(
2021
). “
COVID-19 guidance 4.1, how to operate HVAC and other building service systems to prevent the spread of the coronavirus (SARS-CoV-2) disease (COVID-19) in workplaces
,”
Federation of European Heating, Ventilation and Air Conditioning Associations
. https://www.rehva.eu/activities/covid-19-guidance/rehva-covid-19-guidance.
10.
ASHRAE
(
2023
). “
ANSI/ASHRAE standard 241–2023, control of infectious aerosols
”, see https://www.ashrae.org/technical-resources/bookstore/ashrae-standard-241-control-of-infectious-aerosols.
11.
CDC
(
2023
). “
COVID-19 ventilation in buildings 2023
,”
The Centers for Disease Control and Prevention
. https://www.cdc.gov/coronavirus/2019-ncov/community/ventilation.html.
12.
ASHRAE
(
2019
). “
ANSI/ASHRAE standard 62.1–2019, ventilation and acceptable indoor air quality
”, see https://ashrae.iwrapper.com/ASHRAE_PREVIEW_ONLY_STANDARDS/STD_62.1_2019
13.
Y.
Li
,
P.
Cheng
, and
W.
Jia
, “
Poor ventilation worsens short-range airborne transmission of respiratory infection
,”
Indoor Air
32
,
e12946
(
2022
).
14.
FPS
(
2022
). “
Legal framework regarding indoor air quality
,”
Federal public service - Public Health
. https://www.health.belgium.be/en/closer-legal-framework-indoor-air-quality.
15.
X.
Xie
,
Y.
Li
,
T.
Zhang
, and
H.
Fang
, “
Bacterial survival in evaporating deposited droplets on a teflon-coated surface
,”
Appl. Microbiol. Biotechnol.
73
,
703
712
(
2006
).
16.
L.
Guo
,
M.
Wang
,
L.
Zhang
,
N.
Mao
,
C.
An
,
L.
Xu
, and
E.
Long
, “
Transmission risk of viruses in large mucosalivary droplets on the surface of objects: A time-based analysis
,”
Infect. Dis. Now
51
,
219
227
(
2021
).
17.
N.
van Doremalen
,
T.
Bushmaker
,
D. H.
Morris
,
M. G.
Holbrook
,
A.
Gamble
,
B. N.
Williamson
,
A.
Tamin
,
J. L.
Harcourt
,
N. J.
Thornburg
,
S. I.
Gerber
,
J. O.
Lloyd-Smith
,
E.
de Wit
, and
V. J.
Munster
, “
Aerosol and surface stability of HCoV-19 (SARS-CoV-2) compared to SARS-CoV-1
,”
N Engl. J. Med.
382
,
1564
1567
(
2020
).
18.
K.
Ritos
,
D.
Drikakis
, and
I.
Kokkinakis
, “
Virus spreading in cruiser cabin
,”
Phys. Fluids
35
,
103329
(
2023
).
19.
T.
Dbouk
and
D.
Drikakis
, “
Weather impact on airborne coronavirus survival
,”
Phys. Fluids
32
,
093312
(
2020
).
20.
R.
Dhand
and
J.
Li
, “
Coughs and sneezes: Their role in transmission of respiratory viral infections, including SARS-COV-2
,”
AJRCCM
202
,
651
659
(
2020
).
21.
X.
Zhao
,
S.
Liu
,
Y.
Yin
,
T. T.
Zhang
, and
Q.
Chen
, “
Airborne transmission of covid-19 virus in enclosed spaces: An overview of research methods
,”
Indoor Air
32
,
e13056
(
2022
).
22.
W.
van der Reijden
,
E.
Veerman
, and
A.
Nieuw Amerongen
, “
Shear rate dependent viscoelastic behavior of human glandular salivas
,”
Biorheology
30
,
141
152
(
1993
).
23.
U. S. EPA
(
2011
). “
EPA exposure factors handbook
,” Exposure factors handbook—Chapter 6: Inhalation rates. https://www.epa.gov/expobox/exposure-factors-handbook-chapter-6.
24.
P.
Rosin
and
E.
Rammler
, “
The laws governing the fineness of powdered coal
,”
J. Inst. Fuel
7
,
29
36
(
1933
).
25.
W.
Weibull
, “
A statistical distribution function of wide applicability
,”
J. Appl. Mech.
18
,
293
297
(
1951
).
26.
Y.
Liu
,
Y.
Laiguang
,
Y.
Weinong
, and
L.
Feng
, “
On the size distribution of cloud droplets
,”
Atmos. Res.
35
,
201
216
(
1995
).
27.
X.
Xie
,
Y.
Li
,
H.
Sun
, and
L.
Liu
, “
Exhaled droplets due to talking and coughing
,”
J. R. Soc., Interface
6
,
703
714
(
2009
).
28.
S.
Zhu
,
S.
Kato
, and
J. H.
Yang
, “
Study on transport characteristics of saliva droplets produced by coughing in a calm indoor environment
,”
Build. Environ.
41
,
1691
1702
(
2006
).
29.
L. K.
Norvihoho
,
H.
Li
,
Z.-F.
Zhou
,
J.
Yin
,
S.-Y.
Chen
,
D.-Q.
Zhu
, and
B.
Chen
, “
Dispersion of expectorated cough droplets with seasonal influenza in an office
,”
Phys. Fluids
35
,
083302
(
2023
).
30.
M.
Zhao
,
C.
Zhou
,
T.
Chan
,
C.
Tu
,
Y.
Liu
, and
M.
Yu
, “
Assessment of COVID-19 aerosol transmission in a university campus food environment using a numerical method
,”
Geosci. Front.
13
,
101353
(
2022
).
31.
H.
Li
,
F. Y.
Leong
,
G.
Xu
,
Z.
Ge
,
C. W.
Kang
, and
K. H.
Lim
, “
Dispersion of evaporating cough droplets in tropical outdoor environment
,”
Phys. Fluids
32
,
113301
(
2020
).
32.
B. E.
Scharfman
,
A. H.
Techet
,
J. W. M.
Bush
, and
L.
Bourouiba
, “
Visualization of sneeze ejecta: Steps of fluid fragmentation leading to respiratory droplets
,”
Exp. Fluids
57
,
1
9
(
2016
).
33.
Siemens Digital Industries Software
, “
Simcenter STAR-CCM+, version 2210
” (
2022
).
34.
W. E.
Ranz
and
W. R.
Marshall
, “
Evaporation from drops, Part I
,”
Chem. Eng. Prog.
48
,
141
146
(
1952
).
35.
W. E.
Ranz
and
W. R.
Marshall
, “
Evaporation from drops, Part II
,”
Chem. Eng. Prog.
48
,
173
180
(
1952
).
36.
M.
Auvinen
,
J.
Kuula
,
T.
Grönholm
,
M.
Sühring
, and
A.
Hellsten
, “
High-resolution large-eddy simulation of indoor turbulence and its effect on airborne transmission of respiratory pathogens-model validation and infection probability analysis
,”
Phys. Fluids
34
,
015124
(
2022
).
37.
H.
Calmet
,
K.
Inthavong
,
A.
Both
,
A.
Surapaneni
,
D.
Mira
,
B.
Egukitza
, and
G.
Houzeaux
, “
Large eddy simulation of cough jet dynamics, droplet transport, and inhalability over a ten minute exposure
,”
Phys. Fluids
33
,
125122
(
2021
).
38.
M.
Abuhegazy
,
K.
Talaat
,
O.
Anderoglu
, and
S. V.
Poroseva
, “
Numerical investigation of aerosol transport in a classroom with relevance to COVID-19
,”
Phys. Fluids
32
,
103311
(
2020
).
39.
M.-R.
Pendar
and
J. C.
Páscoa
, “
Numerical modeling of the distribution of virus carrying saliva droplets during sneeze and cough
,”
Phys. Fluids
32
,
083305
(
2020
).
40.
L.
Schiller
and
A.
Naumann
, “
Ueber die grundlegenden Berechnungen bei der Schwerkraftaufbereitung
,”
VDI Z.
77
,
318
320
(
1933
).
41.
R.
Reid
,
J.
Prausnitz
, and
B.
Poling
,
The Properties of Gases and Liquids
, 4th ed. (
McGraw-Hil
,
1987
).
42.
P.
Katre
,
S.
Banerjee
,
S.
Balusamy
, and
K. C.
Sahu
, “
Fluid dynamics of respiratory droplets in the context of COVID-19: Airborne and surface borne transmissions
,”
Phys. Fluids
33
,
081302
(
2021
).
43.
S.-J.
Jang
,
S.-S.
Baek
,
J.-Y.
Kim
, and
S.-H.
Hwang
, “
Preparation and adhesion performance of transparent acrylic pressure sensitive adhesives for touch screen panel
,”
J. Adhes. Sci. Technol.
28
,
1990
2000
(
2014
).
44.
Y.-L.
Hsieh
,
J.
Thompson
, and
A.
Miller
, “
Water wetting and retention of cotton assemblies as affected by alkaline and bleaching treatments
,”
Text. Res. J.
66
,
456
464
(
1996
).
45.
S.
Chandra
and
C.
Avedisian
, “
On the collision of a droplet with a solid surface
,”
Proc. R. Soc. London, Ser. A
432
,
13
41
(
1991
).
46.
R.
Bhardwaj
and
A.
Agrawal
, “
Likelihood of survival of coronavirus in a respiratory droplet deposited on a solid surface
,”
Phys. Fluids
32
,
061704
(
2020
).
47.
M.
Koilybayeva
,
Z.
Shynykul
,
G.
Ustenova
,
K.
Waleron
,
J.
Jońca
,
K.
Mustafina
,
A.
Amirkhanova
,
Y.
Koloskova
,
R.
Bayaliyeva
,
T.
Akhayeva
,
M.
Alimzhanova
,
A.
Turgumbayeva
,
G.
Kurmangaliyeva
,
A.
Kantureyeva
,
D.
Batyrbayeva
, and
Z.
Alibayeva
, “
Gas chromatography–mass spectrometry profiling of volatile metabolites produced by some bacillus spp. and evaluation of their antibacterial and antibiotic activities
,”
Molecules
28
,
7556
(
2023
).
48.
SAGE
(
2020
). “
Transmission of SARS-CoV-2 and mitigating measures EMG-SAGE 4th June
,”
Scientific Advisory Group for Emergencies
.
49.
T.
Dbouk
,
F.
Roger
, and
D.
Drikakis
, “
Reducing indoor virus transmission using air purifiers
,”
Phys. Fluids
33
,
103301
(
2021
).