Boundary conditions for exhaled airflow from a cough with a surgical or N95 mask.

Wearing surgical or N95 masks is effective in reducing the infection risks of airborne infectious diseases. However, in the literature there are no detailed boundary conditions for airflow from a cough when a surgical or N95 mask is worn. These boundary conditions are essential for accurate prediction of exhaled particle dispersion by computational fluid dynamics (CFD). This study first constructed a coughing manikin with an exhalation system to simulate a cough from a person. The smoke visualization method was used to measure the airflow profile from a cough. To validate the setup of the coughing manikin, the results were compared with measured data from subject tests reported in the literature. The validated coughing manikin was then used to measure the airflow boundary conditions for a cough when a surgical mask was worn and when an N95 mask was worn, respectively. Finally, this study applied the developed airflow boundary conditions to calculate person-to-person particle transport from a cough when masks are worn. The calculated exhaled particle patterns agreed well with the smoke pattern in the visualization experiments. Furthermore, the calculated results indicated that, when the index person wore a surgical and a N95 mask, the total exposure of the receptor was reduced by 93.0% and 98.8%, respectively.

INTRODUCTION

Airborne infectious disease transmission is receiving more attention from the public due to the spread of COVID‐19, which has caused millions of deaths and huge economic losses around the world. , , , , Airborne infectious diseases can be transported by exhaled droplets and droplet nuclei containing pathogens, which can spread in the environment when an infected person breaths, sneezes, or coughs. , , , , , Such airborne transmission frequently occurs in crowded public places, such as hospitals and schools. , , , A cough is one of major airborne infectious disease symptoms, and thus coughing is one of the most common infection routes. , If a coughing patient is in close proximity to a heathly person, the healthy person has a high probability of being infected by the droplets generated by the infected person's coughing. Many studies have numerically investigated the dispersion of exhaled particles from a cough in an indoor environment using computational fluid dynamics (CFD). For example, Gupta et al. investigated the transmission of exhaled droplets from an index patient's cough in a commercial airplane using the CFD method. Chen et al. applied the smoke visualization method to develop simplified models for the CFD boundary conditions of a cough with mouth covered. It was found that covering the mouth when coughing can reduce the exposure of the receptor and the risk of infection. These studies have provided great insight into the dispersion of exhaled particles from a cough in an indoor environment.

Wearing face masks is an effective way to reduce airborne infectious disease transmission when coughing, and masks have been widely used around the world. , , Various types of face masks are available on the market, including cotton masks, surgical masks, and N95 masks. , Cotton masks provide limited protection from infection although they are reusable and comfortable. Surgical masks and N95 masks are most often recommended and welcomed in public for prevention of infection by airborne diseases. Numerous scientific studies have assessed the performance of surgical masks and N95 masks. , , , , , , , For example, Mark et al. compared the performance of a surgical mask and an N95 mask in preventing influenza for health care workers and found that the N95 mask was superior. Huo and Zhang measured the actual efficiency of face masks, taking the leakage that occurs during wearing into consideration. The measured average actual efficiency levels of surgical masks and N95 masks were 65% and 85%, respectively. Fischer et al. developed a simple and low‐cost optical measurement method to assess the efficacy of various homemade masks and mask alternatives in efficacy of masks to reduce the transmission of respiratory droplets. For a better understanding of the protection effectiveness of masks, airflow leakages from masks should be studied. Some studies have focused on the dispersion of exhaled air from a person's cough when a surgical or N95 mask is worn. Various visualization methods, such as schlieren imaging, , light scattering, infrared thermograph, and laser‐based visualization, , , have been reported. For example, Tang et al. used schlieren imaging to investigate the airflow generated by a cough. It was found that a cough without mask wearing generated a turbulent jet, while the jet from a cough with a mask was redirected in a harmless direction. However, the literature provided scant data on the CFD airflow boundary conditions for a cough when a surgical or N95 mask is worn. Without the airflow boundary conditions, it is challenging to predict the exhaled particle transport from a cough when a face mask is worn.

To overcome this challenge, this study aimed to develop boundary conditions for exhaled airflow from a cough when either a surgical or an N95 mask is worn. This investigation first constructed a coughing manikin with an exhalation system to simulate a cough from a person. The smoke visualization method was used to measure the airflow profile from a cough. The results were compared with those measured in subject tests in the literature to validate the setup of the coughing manikin. The validated coughing manikin was then used to measure the airflow boundary conditions for a cough when a surgical mask is worn and when an N95 mask is worn, respectively. Next, the boundary conditions were implemented in the CFD program. Finally, this study applied the Eulerian method to calculate the particle dispersion from a cough with mask worn and compared the results with those of the smoke tests.

COUGHING MANIKIN

Coughing manikin setup

Figure 1 shows the coughing manikin, which was equipped with an exhalation system to simulate a cough from a person. The head of the manikin was 3D‐printed according to a digital model of the manikin geometry. The mouth opening was set as a square with an area of 4.0 cm2, because the subject tests by Gupta et al. showed that the mean mouth opening area for the male subjects was 4.0 cm2. Furthermore, they found that the mouth opening area was almost a constant when there was cough flow from the mouth. Thus, the impact of moving lips on the cough airflow was neglected. Several light‐emitting diode (LED) bulbs were installed inside the manikin to mimic the heat generation by the human body. The surface temperature distribution captured by an infrared camera showed that the average manikin surface temperature was around 32 °C, indicating that the manikin emitted heat like a real person. The exhalation system consisted of an air compressor, a flow controller (CN‐500‐A2‐12, Shanghai CIXI Instrument Co., Ltd., China), and a 3‐way electronic valve (VT307, HAORIDUO, China) to supply the exhalation airflow. The devices were connected by polyurethane tubes, and the airflow was delivered to the mouth of the manikin. The 3‐way electronic valve was controlled to be open for a short period of time to mimic the coughing period. The exhalation system was set according to the measured airflow rate as a function of time from coughs in subject tests by Gupta et al.

FIGURE 1

Coughing manikin: (A) photographic image and (B) schematic of the exhalation system

Visualization of airflow from a cough

A smoke visualization method was used to obtain the cough airflow profile. First, tobacco smoke was released inside the head of the manikin. Since the temperature of burning tobacco smoke is close to that of exhaled air, the exhaled smoke flow was expected to closely follow the cough airflow. The pressure of the air compressor was set at 0.5 MPa, and the duration for opening of the electronic valve was set at 0.2 s. A camera with a frame rate of 67 Hz was used to capture the smoke trajectory when the manikin coughed. To ensure high‐quality flow visualization, a light source and a dark background were used.

For each time step in a cough, the airflow velocity () can be calculated as the travel distance of the smoke () divided by the time step size (): The time step size () was 0.015 s in this study. The smoke travel distance and direction were determined from monochrome frames as shown in Figure 2 using the method proposed in our previous study based on the digital color Y'UV model. The RGB values for each frame were converted to the Y'UV values by MATLAB. The smoke jet can then be quantitatively distinguished from the background color based on the luma component (Y′), and the distance traveled by the smoke jet () can determined accordingly. The direction of the smoke jet's central line was visually approximated as a line that equally divided the smoke in the two‐dimensional plane. The 3D direction was determined by the frames taken from both the side and bird views. Based on this method, the airflow velocity profile for a cough could then be determined. To ensure repeatability, the smoke visualization experiments were repeated three times.

FIGURE 2

Monochrome photographs of the travel trajectory of smoke from a cough by the manikin. The corresponding video is provided in Figure S4

Validation of coughing manikin

Figure 3 compares the measured cough velocity profile obtained in this study with that from human subject tests in the literature. The experimental data in this study are presented as the averaged results from the three repeated tests with error bars representing the maximum and minimum values. The peak velocity from the coughing manikin was 9.32 m/s, which was close to that from the subject tests (10.01 m/s). The cough velocity angle was 36.1°, which was consistent with the angle measured in previous human subject tests. In the smoke visualization, after 0.23 s, the smoke became too thin to be distinguished from the background by the digital color Y'UV model. Therefore, the corresponding low airflow velocity could not be obtained. However, since the cough airflow volume after 0.23 s was only 8.6% of the total cough airflow volume in the human subject test results, this limitation did not have a major impact on the general cough profile. The total cough airflow volume from the coughing manikin was 0.00055 m3, which was again similar to that from the human subject tests (0.00056 m3). In general, the comparison confirmed that the coughing manikin constructed in this study could cough like a real person. Therefore, the validated coughing manikin was used to measure the airflow boundary conditions for a cough when a surgical mask was worn and when an N95 mask was worn, as described in the following section.

FIGURE 3

Comparison of the measured cough velocity profiles from this study and from human subject tests in the literature

BOUNDARY CONDITIONS OF AIRFLOW FROM A COUGH WITH A MASK

Cough with a surgical mask

Airflow visualization

Smoke visualization experiments were conducted to determine the airflow boundary conditions for a cough when a surgical mask is worn. The experimental setup was the same as that in Section 2.2. Figure 4 shows monochrome photographs of the travel trajectories of smoke from the coughing manikin wearing the surgical mask. Air jets were produced by upper, side, and lower leakages. Furthermore, some air penetrated the surgical mask. Based on the method described in Section 2.2, the smoke travel distances and directions from the five leakages for each time step can be obtained from the monochrome photographs. The airflow velocity magnitudes in the determined smoke direction for each time step can then be calculated by Equation (1) as the travel distance of the smoke divided by the time step size.

FIGURE 4

Monochrome photographs of the travel trajectories of smoke from a cough by the manikin wearing a surgical mask. The corresponding video is provided in Figure S2

Boundary conditions

In the monochrome photographs of the smoke travel trajectories in Figure 5, it can be observed that there were five air leakages. As illustrated in Figure 5B, the air leakages from the surgical mask were denoted as S1 (upper leakage), S2 (air penetrating the mask), S3 (side leakages), and S4 (lower leakage). Note that S3 represents two air leakages, one on each side, that had the same shape. The shapes and areas of all the leakages are shown in Figure 5. Note that leakage S2 represents the air penetrating the surgical mask. From the smoke visualization, the boundaries of S2 can be determined. A hot‐wire anemometer (HT9829, XINSITE Corporation, China) with the resolution of 0.01 m/s was used to test the air velocity near the mask to confirm the boundaries of S2. Furthermore, the porosity of the surgical mask was measured using a mercury intrusion porosimeter to obtain the effective area of S2. The measured 3D porosity (P 3) was 80.6%. If the pores inside the surgical mask are assumed to be isotropic, the 2D porosity (P 2) can be calculated by: According to Equation (2), P 2 was 65.8%. Therefore, the effective area of S2 was 10.13 cm2. Note that the tightness of masks is a statistical problem depending on how people wear masks. However, it is challenging to directly measure the areas of all the leakages by human subject tests. Only were the areas of the side leakages of surgical masks, i.e., S3 in Figure 5, large enough to be directly measured. Therefore, this study recruited 20 human subjects to wear surgical masks and directly measured the side leakage areas. There were 10 males and 10 females with the age from 20 to 40 years old. The average measured side leakage area of the human subjects was 0.74 cm2, which was close to that of the manikin (0.71 cm2). This comparison partially confirmed that the leakages of the surgical mask worn by the manikin were representative. To develop the CFD airflow boundary conditions for a cough when a surgical mask is worn, this study created a geometric model based on the actual shapes and dimensions of the coughing manikin wearing a surgical mask. To consider the porosity in the geometry of S2, the random cell method proposed by Zhang et al. was used to randomly open the cells with a probability of 65.8%. As shown in Figure 5A, the geometric models of the surgical mask created in this study accurately represent an actual surgical mask.

FIGURE 5

(A) Geometric model for the coughing manikin with a surgical mask and (B) the shapes and areas of the air leakages

The airflow velocity angles and profiles of S1, S2, S3, and S4 are shown in Figure 6. Again, to ensure repeatability, the smoke visualization experiments were repeated for three times. The error bars represent the maximum and minimum values of the three tests. When the surgical mask was worn, the peak velocity was significantly reduced to 2.18 m/s for leakage S1, 2.34 m/s for leakage S2, 3.07 m/s for leakage S3, and 2.40 m/s for leakage S4. The total airflow volume from the air leakages was 0.00051 m3, which was slightly lower than that from an uncovered cough. The airflow velocity profiles and angles obtained from the smoke visualization experiments were then implemented into the ANSYS Fluent simulation software by user‐defined functions (UDFs) to serve as the boundary conditions of a cough when a surgical mask is worn.

FIGURE 6

Airflow velocity profiles and angles of air leakages S1, S2, S3, and S4 for a cough when a surgical mask is worn

Cough with a N95 mask

The airflow from a cough from the manikin wearing a N95 mask was visualized using the same smoke tests, as shown in Figure 7. The air jets were from the upper and side leakage locations. Note that the smoke penetrating the N95 mask cannot be observed clearly from the side view; thus, the bird's‐eye view is also included in the figure. In the bird's‐eye view, the air penetrating the N95 mask can be seen. Based on the method described in Section 2.2, the travel distances and directions of the smoke were then determined from the monochrome photographs for a cough from the manikin wearing the N95 mask.

FIGURE 7

Monochrome photographs of the travel trajectories of smoke from a cough by the manikin wearing a N95 mask: (A) side view and (B) bird's‐eye view. The corresponding video is provided in Figure S6

According to the visualization, there were four air leakages from the N95 mask, which were denoted as N1, N2, and N3, as illustrated in Figure 8. Note that N2 includes two air leakages, one on each side. The shapes and areas of N1, N2, and N3 are shown in Figure 8B. The measured 3D porosity of the N95 mask was 77.8%. Assuming that the pores in the N95 mask were isotropic, the 2D porosity of the N95 mask was calculated by Equation (2), and was equal to 63.3%. Therefore, the effective area of N3 was 14.6 cm2. Based on the leakages, a geometric model for the coughing manikin wearing a N95 mask was then built. To consider the porosity in the geometry of N3, the random cell method proposed by Zhang et al. was used to randomly open the cells with a probability of 63.3%. and it accurately represents the actual N95 masks as shown in Figure 8A.

FIGURE 8

(A) Geometric model of the coughing manikin wearing a N95 mask and (B) the shapes and areas of the air leakages from the N95 mask

The airflow velocity profiles and angles are shown in Figure 9. Again, to ensure repeatability, the smoke visualization experiments were repeated for three times. The error bars represent the maximum and minimum values of the three tests. When the N95 mask was worn, the peak velocity was reduced significantly to 2.26 m/s for leakage N1, 2.51 m/s for leakage N2, and 2.13 m/s for leakage N3. The total cough airflow volume from the air leakages was 0.00049 m3, which was lower than that when the surgical mask was worn. The airflow velocity profiles and angles were then implemented into ANSYS Fluent via UDFs and used as the CFD boundary conditions for a cough when a N95 mask is worn.

FIGURE 9

Airflow velocity profiles and angles of air leakages N1, N2, and N3 for a cough from the manikin wearing a N95 mask

Boundary conditions for particles

Previous studies have measured the size distribution of exhaled particles from a cough by human subject tests [e.g., Ref. 8, 9, 16, 42, 43, 44, 45, 46]. For example, Chao et al. reported that the coughed droplets in close proximity to the mouths are in the supermicrometer size. However, Morawska et al. indicated that the majority of coughed droplets are within the sub‐micrometer size range. The discrepancy on the size distribution was mainly due to the instrument and measurement methodology. In general, face masks can effectively capture coarse particles (>2 μm) exhaled from a cough because of the strong inertial impaction. Therefore, it would be reasonable to assume that most of the cough particles escaped from the mask and leakages are fine particles (<2 μm). For the particle boundary conditions, the measured size‐dependent fine particle concentrations from a cough in the literature, , can be directly used as the particle concentration at the inlet boundaries of the open leakages, i.e., S1, S3, and S4 for surgical mask and N1 and N2 for N95 mask. However, for the leakages in the masks, the particle filtration by the mask materials should be considered. Previous studies have measured the size‐dependent particle filtration efficiency for surgical mask and N95 mask [e.g., Ref. 47, 48, 49, 50], . Since the inlet boundary was set as the outer surface of the mask, the particle concentration can be defined as at the inlet boundary of the mask material leakages, i.e., S2 for surgical mask and N3 for N95 mask. The boundary conditions for an uncovered cough and a cough with a surgical or N95 mask developed in this study are summarized in Table S1 in the supplementary material.

VERIFICATION AND CASE STUDY

This investigation conducted CFD simulations of particle dispersion from a cough when a surgical mask is worn and when an N95 mask is worn, respectively, using the boundary conditions developed in this study. Namely, the leakage geometry models developed in Figures 5 and 8 were implemented into the manikin geometry model of CFD simulations. The airflow velocity profiles and angles at the air leakages developed in Figures 6 and 9 were used as the boundary conditions of airflow. The calculated results were compared with the smoke patterns in the monochrome photographs for verification of the developed boundary conditions. The receptor's exposure to exhaled particles from the cough of the infected person with and without the wearing of a surgical or N95 mask were compared with assess the effectiveness of wearing face masks.

Case setup

A scenario with two manikins in a ventilated room was used for exhaled particle dispersion simulations. As shown in Figure 10, the room had dimensions of 3 m in length, 3 m in width, and 2.3 m in height. The inlet and outlet were located on the right wall with the width of 3 m and height of 0.2 m. Two manikins were seated face to face with a distance between their mouths of 1.2 m. The left‐hand person wearing a mask was assumed to be the index person who coughed once. The air change rate of this room was set at 3 ACH, and the supply air velocity and temperature were set at 0.0278 m/s and 21 °C, respectively. The manikins generated heat and the surface temperature was set at 32 °C, and all the walls were assumed to be adiabatic. The geometric models for surgical and N95 masks developed in this study were used in the simulations. The measured airflow velocity profiles and angles were implemented by UDFs to serve as the inlet boundary conditions.

FIGURE 10

Configuration of the ventilated room with two manikins for the case study

The renormalization group (RNG) k–ε model was employed to calculate the turbulent flow. , The Eulerian drift‐flux model, which treats the particle phase as a continuum, was used to calculate the exhaled particle dispersion in the room. The drift‐flux model solves the scalar transport equation: where is the particle concentration, is the time, is the averaged air velocity, is the coordinate, is the Brownian diffusivity which can be calculated by the equation in Hinds, is the turbulent viscosity, is the turbulent Schimdt number which was set at 1.0, , and is the particle source term. The particle gravitational settling velocity, , can be calculated by: where is the particle relaxation time, is the gravitational acceleration which was −9.8 m/s2 in the y direction, is the Cunningham coefficient caused by slippage which can be calculated by the equation in Hinds, is the particle density which was set at 1000 kg/m3, is the particle diameter, and is the dynamic viscosity of air which was set at 1.79 × 10−5 kg/(m·s). The Eulerian model has been validated using experimental data in our previous studies, , the details of which can be found in the Figure S1.

As a demonstration of the use of the developed cough airflow boundary conditions, this case study assumed the particle diameter to be 0.5 μm as the representative diameter of fine particles exhaled from a cough based on the results by Morawska et al. The measured filtration efficiency of 0.5 μm particles for surgical mask ranged from 40% to 78% and that for N95 mask ranged from 80% to 95% in the literature [e.g., Ref. 47, 48, 49, 50]. This study also conducted laboratory experiments to measure the size‐dependent particle filtration efficiency for surgical mask and N95 mask in a small duct using NaCl particles with two particle counters (9306, TSI Inc., USA). Our results show that, after eliminating the charges, which represents the condition after long time use, the filtration efficiency of 0.4–0.5 μm particles for surgical mask and N95 mask was 61.5% and 83.1%, respectively. Since our measurements fell into the filtration efficiency range in the literature, the following case studies assumed the filtration efficiency of 0.5 μm particles to be 61.5% and 83.1%, respectively, for surgical mask and N95 mask. The calculated particle concentrations, , were normalized by the cough concentration, , set at the mask leakage boundaries.

A total of 1.43 million unstructured tetrahedron grid cells were generated for the case in which the manikins coughed without mask worn, 1.75 million cells for the case with surgical mask, and 2.12 million cells for the case with N95 mask; these cell numbers passed the grid‐independence tests. The detailed information about the grid‐independence tests can be found in the Figure S2. The average y+ was 31.5, and the standard wall function was applied to connect the solution variables on the walls and in the near‐wall cells. The pressure and velocity were coupled by the SIMPLE algorithm. The discretization method was set as the second order upwind. The calculations of airflow and particle dispersion were performed simultaneously with a time step size of 0.1 s.

Verification of the boundary conditions

The contours of the particle concentration distribution from a cough with a surgical mask on the two planes, i.e., the middle plane of the manikins (z = 1.5 m) and the bounded plane perpendicular to S3, are shown in Figure 11A. The calculated particle patterns were compared with the smoke patterns from the tests. The comparison results at 0.15 s are shown in the figure as an example. Note that, for fine particles <2 μm, both measurements and simulations confirmed that they would well follow the airflow and disperse in a similar manner to gas. , Since the smoke particle sizes are <2 μm and the case studies in this paper assumed the particle diameter to be 0.5 μm, the fine particles should well follow the airflow in both the experiments and simulations. The comparison showed that the particle dispersion pattern from the CFD calculations using the developed boundary conditions closely matched the smoke patterns from the smoke tests. For the case of a cough when a N95 mask is worn, the side‐view contours of the particle concentration distribution on the two planes, i.e., the middle plane of the manikins (z = 1.5 m) and the bounded plane perpendicular to N2, are shown in Figure 11B. Furthermore, the bird's‐eye‐view contours of the particle concentration distribution on the plane perpendicular to axis y (y = 1.02 m) reveal the particle dispersion from leakage N3. In general, the particle concentration patterns from the CFD simulations agreed well with the smoke patterns for a cough when a N95 mask is worn. The patterns were also compared with the visualization reported in the literature and show good agreement, the details of which can be found in the Figure S7. The good agreement serves as a partial demonstration that the airflow boundary conditions of a cough when a surgical or N95 mask is worn accurately represent the actual airflow pattern.

FIGURE 11

Comparison between the calculated particle dispersion and smoke test pattern from a cough when (A) a surgical or (B) a N95 mask is worn. The corresponding videos are provided in Figure S7

Influence of mask wearing on receptor's exposure

To investigate the influence of mask wearing by the index person on the receptor's exposure, the cases with uncovered cough, cough with a surgical mask, and cough with an N95 mask were compared. Figure 12 shows the contours of the particle concentration distribution after a cough for the three cases. When a mask was not worn, the receptor was directly exposed to the exhaled particles from the cough of the index person. Meanwhile, when the index person wore a surgical or N95 mask, the direct exposure of the receptor was successfully prevented. However, whether the index person wore a mask or not, the receptor experienced indirect exposure to the exhaled particles, which spread throughout the whole space at around 120 s. The particle concentrations as a function of time in the breathing zone of the receptor for all the cases are compared in Figure 13. The calculated particle concentrations in all cases were normalized by the maximum concentration that occurred in the uncovered cough case. As shown in Figure 13A, a peak particle concentration in the breathing zone of receptor was observed immediately after the uncovered cough, which was the direct exposure. However, when the index person wore a surgical or N95 mask, no peak particle concentration was observed in the first 60 seconds; the peaks were observed at around 120 s, which was the indirect exposure. Since the surgical and N95 masks reduced the concentration of exhaled particles by 61.5% and 83.1%, respectively, the particle concentrations during the indirect exposure were much lower than the concentration when the index person did not wear a mask.

FIGURE 12

Contours of particle concentration distribution after a cough for (A) case with uncovered cough, (B) case with surgical mask worn, and (C) case with N95 mask worn. The corresponding videos are provided in Figure S8

FIGURE 13

Comparison of (A) the particle concentration as a function of time in the breathing zone of the receptor and (B) the direct exposure and indirect exposure, when the index person coughed with and without the wearing of a mask. “Non‐momentum” represents the case with non‐momentum particles released near the uncovered mouth with the same emission rate

To simplify the complicated boundary conditions for coughing when a mask is worn, two more cases with non‐momentum particles released near the uncovered mouth, with the same emission rates as for the surgical and N95 mask cases, are included here for comparison. These non‐momentum cases for coughing with mask wearing are denoted as non‐momentum (surgical mask) and non‐momentum (N95 mask), respectively, in Figure 13A. It can be observed that the cases with release of non‐momentum particles exhibited similar particle concentration profiles as the cases with detailed complex mask geometry and boundary conditions. This study further calculated the normalized inhaled dose for all the cases by: where is the normalized inhaled dose, is the normalized particle concentration in the breathing zone, and is the breathing flow rate. According to the International Organization for Standardization (ISO/TS 16976‐1), the breathing flow rate of a person with a body surface area of 1.84 m2 and moderate activity was 0.00047 m3/s. The normalized inhaled dose was divided into two parts: direct exposure from 0 to 60 s and indirect exposure from 60 to 360 s. As shown in Figure 13B, for the uncovered cough case, the direct and indirect exposure levels were 0.0031 and 0.0055, respectively. However, there was almost no direct exposure for the cases with mask wearing, while the indirect exposure levels for the cases with surgical and N95 masks were 0.0006 and 0.0001, respectively. Therefore, for the studied cases, when the index person wore a mask, the direct exposure of the receptor could be prevented, and the indirect exposure could be reduced significantly. Consequently, the total exposure of the receptor was reduced by 93.0% and 98.8% when the index person wore a surgical mask and a N95 mask, respectively. Moreover, the indirect exposure levels for the non‐momentum cases for surgical and N95 masks were 0.0005 and 0.0001, respectively, which were close to the cases with detailed boundary conditions. Although the emission rate of the non‐momentum case was same as that of the case with detailed mask boundary conditions, the differences in airflow and particle boundary conditions still caused the errors in the particle dispersion predictions. Therefore, if such errors can be tolerated, simplified non‐momentum boundary conditions can be used to represent the complex boundary conditions of airflow from a cough when a mask is worn.

DISCUSSION

This study conducted smoke visualization experiments to determine the airflow boundary conditions of a cough when a mask is worn. There were some limitations in the experiments. First, in addition to smoke visualization, methods such as schlieren imaging and light scattering , , , , , can be used. It would be worthwhile to cross check the results from different visualization approaches to confirm the results. Furthermore, when the effective areas of S2 and N2 were calculated, the 2D porosity of the masks was determined from the measured 3D porosity and the isotropic hypothesis. However, the microstructures of actual masks are complex and anisotropic , , ; these challenges should be considered. In future research, it would be worthwhile to develop a novel approach to measure the 2D porosity of masks. As for the numerical simulations, the use of the Eulerian model may lead to a certain degree of numerical diffusion. To avoid this issue, the Lagrangian model which tracks the trajectory for each particle on the basis of Newton's law can be used. Furthermore, as a demonstration of the use of the developed cough airflow boundary conditions, the case study assumed the particle diameter to be 0.5 μm as the representative diameter of fine particles exhaled from a cough. To obtain more realistic results, it is worthwhile to consider the size‐dependent particle exhalation and filtration using the method described in Section 3.3. In addition, the reduction in the total exposure of the receptor attributed to wearing a mask by the index person depends on various factors such as person‐to‐person distance, ventilation rate, airflow distribution, etc. Therefore, the total exposure reduction results in this case study cannot be extended to other scenarios, but the proposed method can be used for a wide range of applications. Finally, the vitality of virus attached on the particles was not considered in this study, which is crucial for more accurate infection risk assessments.

Although the labeled particle removal efficiency of commercially available face masks is usually higher than 99%, the actual removal efficiency for exhaled particles ranged from 40% to 78% for surgical masks and 80% to 95% for N95 masks. , , , For surgical masks, the protection effectiveness may not be sufficiently high in environments with high infection risk. Meanwhile, the protection effectiveness of N95 masks is excellent, but the air permeability is poor, which usually results in breathing difficulty and other discomfort. Furthermore, the particle removal efficiency of surgical masks would significantly decrease with wearing time due to the dissipation of electrostatic effects. To overcome these challenges, it is crucial to develop novel face masks from materials with high particle removal efficiency and low air resistance such as electrospun nanofibers, , , , , , , , for better personal protection and comfort.

CONCLUSIONS

This study developed boundary conditions for exhaled airflow from a cough when a surgical mask or an N95 mask is worn, using a coughing manikin and smoke visualization. The boundary conditions were then implemented in a CFD program and applied in a person‐to‐person particle transport case. Within the scope of this study, the following conclusions can be drawn:

The coughing manikin constructed in this study can produce a cough profile similar to that from human subject tests in the literature, and it can be used for smoke tests while wearing a mask.

The developed boundary conditions, including the leakage shapes, areas, and porosity, and the air velocity profiles and angles, can be used in CFD calculations for airflow from a cough when a surgical mask or an N95 mask is worn.

In the studied cases, when the index person wore a surgical or N95 mask, direct exposure of the receptor was prevented, and indirect exposure was reduced significantly. Consequently, the total exposure of the receptor was reduced by 93.0% and 98.8% when the index person wore a surgical mask and a N95 mask, respectively.

Simplified non‐momentum boundary conditions can be used to represent the complex boundary conditions of airflow from a cough when a mask is worn, if the associated error due to the differences in boundary conditions can be tolerated.

AUTHOR CONTRIBUTIONS

Yue Pan: investigation (lead), methodology (supporting), data curation (lead), and writing—original draft (lead). Haiqiang Zhang, Zhuolun Niu, and Yuting An: data curation (supporting). Chun Chen: conceptualization (lead), methodology (lead), supervision (lead), and writing—review and editing (lead).

CONFLICT OF INTEREST

None.

Appendix S1

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Figure S1

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Figure S2

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Figure S3

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Figure S5

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Figure S6

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Figure S7

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Figure S12

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Figure S13

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Figure S16

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