Transport and Fate of Virus-Laden Particles in a Supermarket: Recommendations for Risk Reduction of COVID-19 Spreading Downloaded from ascelibrary.org by 186.80.54.213 on 05/17/21. Copyright ASCE. For personal use only; all rights reserved. Fangda Cui, Ph.D. 1; Xiaolong Geng, Ph.D. 2; Orthodoxia Zervaki 3; Dionysios D. Dionysiou, Ph.D., M.ASCE 4; Joseph Katz, Ph.D. 5; Sarah-Jane Haig, Ph.D. 6; and Michel Boufadel, Ph.D., P.E., F.ASCE 7 Abstract: The transport of virus-laden particles was investigated numerically in an archetypical supermarket configuration of area 1,200 m2 and ceiling height of 4.5 m. The particles were tracked using a Lagrangian particle tracking code coupled with the computational fluid dynamics (CFD) model Ansys Fluent. Air transport was assumed to occur due to indoor ventilation. Flow dynamics were simulated using the Reynolds-averaged Navier Stokes (RANS) approach. The movement and spreading of 5- and 20-μm particles were studied with 0%, 25%, and 100% attachment efficiencies on surfaces in the supermarket. We found that the indoor airflows can significantly enhance the transport of particles (e.g., >15 m for 5 μm, and >5 m for 20 μm); therefore, the 6-ft (2.0 m) social distance recommended by health experts would not be sufficient to prevent the transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). We found that the attachment on surfaces reduces the transport of particles significantly within the supermarket, and that an attachment efficiency of 25% results in transport similar to that resulting from 100% efficiency. This suggests that the type of surfaces is not crucial in terms of air transport of particles. We support the existing approaches for reducing exposure between people through the adoption of one-way movement within an aisle. However, we also propose placing display shelves within the aisles in a staggered way to form baffles that would both increase the surface area and block the transport of airborne particles. We found that virusladen particles could be sucked into the ventilation system through return vents, and could pose potential infection risks for the buildings connected to the same ventilation system. Hence, high-efficiency particulate air (HEPA) filters and pleated filters with a minimum efficiency reporting value (MERV) greater than 12 are recommended. DOI: 10.1061/(ASCE)EE.1943-7870.0001870. © 2021 American Society of Civil Engineers. Author keywords: Fate and transport of particles; Computational fluid dynamics; Lagrangian particle tracking; Random walk; COVID-19; Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2); Virus. Introduction A novel coronavirus named severe acute respiratory syndrome corovirus 2 (SARS-CoV-2) has become a serious global health crisis due to its rapid spread. Since March 2020, the coronavirus has 1 Research Associate, Center for Natural Resources, John A. Reif Jr. Dept. of Civil and Environmental Engineering, New Jersey Institute of Technology, Newark, NJ 07103. ORCID: https://orcid.org/0000-0002 -7346-0310. Email: [email protected] 2 Research Assistant Professor, Center for Natural Resources, John A. Reif Jr. Dept. of Civil and Environmental Engineering, New Jersey Institute of Technology, Newark, NJ 07103. Email: [email protected] 3 Ph.D. Student, Dept. of Chemical and Environmental Engineering, Univ. of Cincinnati, Cincinnati, OH 45221. Email: [email protected] 4 Professor, Dept. of Chemical and Environmental Engineering, Univ. of Cincinnati, Cincinnati, OH 45221. ORCID: https://orcid.org/0000-0002 -6974-9197. Email: [email protected] 5 Professor, Dept. of Mechanical Engineering, Johns Hopkins Univ., Baltimore, MD 21218. Email: [email protected] 6 Assistant Professor, Dept. of Civil and Environmental Engineering, Univ. of Pittsburgh, Pittsburgh, PA 15260. ORCID: https://orcid.org/0000 -0002-0004-8894. Email: [email protected] 7 Director and Professor, Center for Natural Resources, John A. Reif Jr. Dept. of Civil and Environmental Engineering, New Jersey Institute of Technology, Newark, NJ 07103 (corresponding author). Email: boufadel@ gmail.com Note. This manuscript was submitted on November 16, 2020; approved on December 15, 2020; published online on January 21, 2021. Discussion period open until June 21, 2021; separate discussions must be submitted for individual papers. This paper is part of the Journal of Environmental Engineering, © ASCE, ISSN 0733-9372. © ASCE caused globally more than 1.19 million deaths and nearly 45.8 million infected cases. The SARS-CoV-2 virus is transmitted through two main routes: (1) touching a surface that has the virus deposited on it and subsequently touching the eyes, nose, or mouth, or (2) the inhalation of airborne virus-laden particles exhaled by an asymptomatic or actively infected individual (Cevik et al. 2020; Meyerowitz et al. 2020; Prather et al. 2020). At the beginning of the pandemic, SARS-CoV-2 was assumed to spread mainly through person-to-person contact or via fomites (i.e., touching shipping boxes with virus particles attached to them). Hence, the original protective measures recommended by the Centers for Disease Control and Prevention (CDC) were just hand washing and daily disinfection. Lewis (2020) discussed the disagreement among scientists and experts regarding the airborne transmission of SARS-CoV-2. Based on a preprint regarding the aerodynamic analysis of SARS-CoV-2 within two Wuhan hospitals (Liu et al. 2020), Lewis argued that it is likely that SARSCoV-2 can be transmitted via the airborne route. Soon after Lewis’s letter, Stadnytskyi et al. (2020) studied the airborne lifetime of small speech droplets (ranging from 1 to 50 μm), and found that 1 min of loud speaking generated at least 1,000 virus-containing droplet nuclei that remain airborne for more than 8 min in a quiescent enclosure, which provided indirect evidence of the airborne transmission of SARS-CoV-2. Allen and Marr (2020) reviewed numerous studies that demonstrated a potential risk for airborne transmission of SARS-CoV-2 in indoor environments; however, there is limited information about what built environment factors impact the fate and transport of virus-laden particles. Therefore, a better understanding of the physical dynamics of airborne 04021007-1 J. Environ. Eng., 2021, 147(4): 04021007 J. Environ. Eng. Downloaded from ascelibrary.org by 186.80.54.213 on 05/17/21. Copyright ASCE. For personal use only; all rights reserved. transmission in an indoor environment becomes essential for assessing and mitigating the COVID-19 contagion processes. Many of the reported studies regarding the transmission of COVID-19 focus on experimental investigations of the spreading of virus-laden particles. Although experimental studies are important, these approaches are often time-consuming, and due to the brevity of the pandemic, computational approaches are integral to put mitigation strategies into place. The computational fluid dynamics (CFD) and Lagrangian particle tracking techniques have been widely used to study the transport of aerosol particles. For example, Gupta et al. (2011) studied the transport of expiratory particles within a section of an aircraft cabin by coupling CFD with the Lagrangian method. They found the bulk airflow pattern in the cabin played the most important role in particle transport. Zhang et al. (2020) studied the transport of exhaled droplets within an enclosed environment by assuming a bimodal droplet distribution using Ansys Fluent. Their study revealed that the aerosol source location and ambient air movement could be crucial factors of aerosol trajectory in terms of direct and indirect influence. Recently, Wang et al. (2020) studied the transport and fate of human expiratory particles using Lagrangian particle tracking, quantified the fate of particles, and discussed the potential influences by ambient conditions. Mittal et al. (2020) studied the airborne transmission of exhaled particles using large-eddy simulation and assessed the transmission risk from perspectives of wearing masks and keeping a social distance. The objective of this paper is to numerically investigate the transport and fate of virus-laden particles in a large indoor ventilation environment (e.g., an assumed supermarket). The fluid dynamics in a large-scale indoor environment (42 × 30 × 4.5 m) were simulated using steady-state Reynolds-averaged Navier Stokes (RANS) simulation. The obtained fluid dynamics were then used as inputs of our in-house Lagrangian particle tracking code NEMO3D (Cui et al. 2018, 2020) to study the fate and transport of particles. The attachment of particles on surfaces was modeled using three different attachment efficiencies (the possibility of a particle attached to a surface when it hits the surface) of 0%, 25%, and 100%. The layout of the paper is as follows: In the “Methodology” section, we explain the methodology used to perform the investigation; in the “Results” section, we present our simulation results; and in the “Discussion” and “Summary and Conclusion” sections, we discuss the implications of the results and conclude the paper, respectively. ∇ · ðρkuÞ ¼ ∇ · ∇ · ðρεuÞ ¼ ∇ · μt ε2 pffiffiffiffiffi ð4Þ ∇ε þ ρC1 Sε − ρC2 μþ σε k þ νε The values of the model parameters were obtained from Shih et al (1995). Inherent in the current formulation is the assumption that temperature does not play a role in the movement of air masses. This assumption is likely violated near the mouth of a person exhaling (temperature 37°C) and at locations where the air speed is very small (e.g., corners). However, the uncertainty in the indoor flow is much larger than the temperature gradients (Dbouk and Drikakis 2020a; Mittal et al. 2020). Hence, the assumption of neglecting temperature-induced air currents seems warranted herein. Lagrangian Particle Tracking The movement of particles, treated as rigid spheres, was simulated herein according to the equation dxp ¼ up þ ∇D þ up0 dt The fluid dynamics of the indoor environment were modeled using three-dimensional (3D) steady-state RANS equations, given by ∇ · ðρuÞ ¼ 0 ð1Þ ∇ · ðρu ⊗ uÞ ¼ −∇p þ ∇ 2 · ðμ þ μt Þ ∇u þ ∇T u − ∇ · uI þ ρg ð2Þ 3 where ρ = fluid density; p = mean pressure; μ = dynamic viscosity; μt = dynamic eddy viscosity; g = vector of acceleration of gravity; and u ¼ ðu; wÞ is the mean velocity vector. Eqs. (1) and (2) represent the conservation of mass and the conservation of momentum, respectively. The realizable k-ε turbulence model (Shih et al. 1995) was used to simulate the turbulence and achieve turbulence closure of Eqs. (1) and (2). The model is given by ð6Þ where xp ¼ ðxp ; yp ; zp Þ is particle location; up ¼ ðup ; vp ; wp Þ is the particle velocity; ∇D ¼ ð∂Dx =∂x; ∂Dy =∂y; ∂Dz =∂zÞ is the gradient of eddy diffusivity D; and up0 ¼ ðup0 ; vp0 ; wp0 Þ is the turbulence velocity fluctuation, as discussed in the “Turbulent Diffusion” section. If the particle is assumed to be massless, then the particle velocity up would be equal to the fluid velocity u, as adopted herein. The settling velocity of the particles is calculated based on Stokes law, given by wb ¼ Cs Computational Fluid Dynamics ð3Þ where Eqs. (3) and (4) represent the transport equation of turbulent kinetic energy (TKE) k and the turbulent energy dissipation rate ε; and the constants σk and σε = turbulent Prandtl numbers for k and ε, respectively. The modulus of the mean strain rate tensor S ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Sij Sij (where the Einstein summation notation is used) is given as follows: 1 ∂ui ∂uj Sij ¼ þ ð5Þ 2 ∂xj ∂xi Methodology © ASCE μ μ þ t ∇k þ Pk − ρε σk ðρp − ρÞ 2 gd 18μ ð7Þ where d = particle diameter; and ρp = particle density. In Eq. (7), the Cunningham slippage correction factor Cs adjusts the slip between the particles and the continuous gas phase, given by γ ð8Þ Cs ¼ 1 þ K m α þ β exp − Km where α ¼ 1.257; β ¼ 0.4; and γ ¼ 1.1. The Knudsen number K m can be calculated by Km ¼ 2λ d ð9Þ The mean free path between fluid particles λ in Eq. (9) is given by 04021007-2 J. Environ. Eng., 2021, 147(4): 04021007 1 λ ¼ pffiffiffi 2πN d̄ ð10Þ J. Environ. Eng. Downloaded from ascelibrary.org by 186.80.54.213 on 05/17/21. Copyright ASCE. For personal use only; all rights reserved. where d̄ and N = average diameter of air molecules and number of air molecules in a cubic meter, respectively. Evaporation could be important at the initial stage of transport after exhaled particles leave the mouth (Xie et al. 2007; Dbouk and Drikakis 2020a). However, for airborne particles (much less than 50 μm), the evaporation process could complete within 2–3 s in a typical indoor environment (i.e., 20°C with a relative humidity of 50%). After evaporation, saliva droplets become droplet nuclei and continue transport as constant-sized particles following the indoor airflow. Our focus is to investigate large-scale bulk transport of virus-laden particles within an indoor ventilation environment (e.g., a predesigned supermarket), and hence we needed to use individual sizes that do not change with time. In addition, we are not considering that there is only one person standing in a giving direction. The temperature and humidity are usually kept constant within an indoor commercial building like a supermarket. Therefore, the impact of the weather (e.g., change in temperature and humidity) on the transport of particles (Dbouk and Drikakis 2020c) is not essential under such scenarios. Based on all the aforementioned reasons, the evaporation will not be modeled in the present study. (Mittal et al. 2020). We build on the knowledge acquired in these studies by adding an intermediate efficiency of 25% and by considering the presence of surfaces in the space. Spatial Moments of the Particles We used the method of moments to compute the displacement of the plume centroid and the value of the variance (i.e., spreading) of the particle plume. These quantities could be considered as upscaled quantities for the particle plume, and we have used this approach in prior works (Boufadel et al. 2006, 2007). The moments can be estimated numerically by the equation M c;q ðtÞ ¼ vp0 ¼ Ry qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Dy =Δt ð11bÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Dz =Δt ð11cÞ wp0 ¼ Rz where the random noises Rx , Ry , and Rz follow a Gaussian [0,1] distribution; and Δt = time step. In the present study, we assume isotropic turbulence (Dx ¼ Dy ¼ Dz ¼ D), and the eddy diffusivity D can be evaluated by D¼ νt Sct ð12Þ where ν t = kinematic eddy viscosity that can be solved from Eqs. (3) and (4). The turbulent Schmidt number Sct ranges from 0.3 to 1.2 for indoor airflow environments, and the value of 0.7 was adopted in the present study. Attachment of Particles on Surfaces The interaction mechanism of a fluid particle with a solid surface is very complex because it depends on surface roughness and wettability, particle size, fluid components, impact speed and angle, and degree of hydrophilicity (Cassie and Baxter 1944; Yiantsios and Karabelas 2003; Yarin 2006; Crick and Parkin 2013). The particle could splash, spread, bounce, and attach onto surfaces. Therefore, it is not feasible to account for all these perspectives in the study along with the CFD and Lagrangian particle tracking. In the published numerical studies, researchers usually assumed a 100% attachment efficiency on surfaces (Wan et al. 2007; Zhang et al. 2020), or they would consider a system consisting of only the emitter (infected person) and the receptor (exposed person) © ASCE mi ðsc;i ðtÞÞq ; and q ¼ 0; 1; 2 ð13Þ i¼1 where N = number of particles; mi = mass of the ith particle; and sc;i = coordinate in the c direction of the ith particle at time t. The centroid of the plume in any direction c is given as Pc ¼ Turbulent Diffusion Because the instantaneous velocity due to turbulence is not resolved in the present simulation, the transport of particles due to turbulence is accounted for herein using the eddy diffusivity and a random walk approach (Boufadel et al. 2006, 2007; Geng et al. 2016). The fluctuation velocities up0 ¼ ðup0 ; vp0 ; wp0 Þ were estimated by pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð11aÞ up0 ¼ Rx 2Dx =Δt N X Mc;1 ðtÞ Mc;0 ðtÞ ð14Þ The variance in direction c is given as M ðtÞ M c;1 ðtÞ 2 σ2c ðtÞ ¼ c;2 − M c;0 ðtÞ M c;0 ðtÞ ð15Þ Computational Domain and Simulation Setup The computational domain of the CFD simulation is shown in Fig. 1. The size of the domain is 42 × 30 × 4.5 m. There are 20 supply vents and 14 return vents located in the ceiling. The dimensions of the supply vents are 0.5 × 0.5 m, and the dimensions of the return vents are 1.0 × 0.5 m. The downward inlet velocity of the supply vents had a magnitude of 1.6 m=s. The entrance doors were assumed closed and treated as no-slip walls in simulations. Display shelves with different heights (1, 2, and 1.2 m) were placed in the domain to simulate the space of a supermarket. More detailed dimensions can be found in the Appendix. More than 22 million tetrahedron cells were used for the simulation to capture the general behavior of indoor airflow. The cell size was refined up to 1 cm near the supply and return vents. A boundary layer of 10 cells’ thickness was set up around all the walls (i.e., sidewalls and middle display shelves) with a first cell thickness of 1 mm. Second-order numerical schemes were adopted for iterations to ensure the absence of oscillation. The simulation was iterated sufficiently long because no apparent changes for residues were observed. The residuals for both momentums and turbulent quantities were below 5 × 10−4 . A large number of articles have been published regarding the size distribution of exhaled particles, such as Holmgren et al. (2010), Han et al. (2013), and Bake et al. (2019). However, no consensus has been made among these studies. For example, Zhang et al. (2017) argued that the size distribution of exhaled particles should be bimodal, whereas a trimodal size distribution of exhaled particles was reported by Johnson et al. (2011). The goal of the present study was not to assume a size distribution but to track individual particle sizes selected to capture behaviors of the observed range of airborne particles; hence, two particle sizes, 5 and 20 μm, were considered herein for Lagrangian particle tracking simulations. No published studies provide the information on surface attachment efficiency of airborne particles; hence, for both sizes of particles, three different attachment efficiencies—no attachment (0%), 25%, and 100%—were selected to study the impact of 04021007-3 J. Environ. Eng., 2021, 147(4): 04021007 J. Environ. Eng. Downloaded from ascelibrary.org by 186.80.54.213 on 05/17/21. Copyright ASCE. For personal use only; all rights reserved. Fig. 1. (Color) 3D view of the computational domain. The supply vents are indicated by the dark red arrows, and the return vents are on the sides, indicated by light blue arrows. The entrance doors are indicated by purple rectangles. There are display shelves of different sizes inside the domain. The domain was stretched in the z-direction to show the geometry clearly. attachment of particles on surfaces on the transport and fate of particles. Water density and viscosity at 25°C were used for simulations. The transport equation [Eq. (6)] was discretized using a fourth-order Runge-Kutta scheme to guarantee a sufficient solution accuracy. In each simulation, 500 particles were initially released within a small spherical region (centered at x ¼ 15 m, y ¼ 19.8 m, and z ¼ 1.7 m) at t ¼ 0 s. After the initial release, 500 new particles were released from the same region every 10s until t ¼ 200 s; hence, 10,000 particles were released in each simulation in total. The total simulation time was 1,200 s with a relatively small time step (Courantnumber < 0.25). The large number of particles and the small time step were adopted to ensure the simulation results can statistically represent the dispersion pattern of particles. Results Fig. 2 shows the airflow velocity magnitude contours at the slice of x ¼ 2.2, 7.6, 11.6, 18, and 24 m. It is observed that the airflow retained relatively large velocity magnitudes under the supply vents (red colors under the supply vents in contours at x ¼ 18 and 24 m). However, the magnitude of airflow velocity gradually decreased away from the supply vents (contours at x ¼ 7.6 and 11.6 m). In particular, at x ¼ 7.6 m (1.6 m away from the supply vents), the velocity magnitude dropped to 5 × 10−2 m=s, which is almost two orders of magnitude lower than the velocity at the supply vent (1.6 m=s); nevertheless, the flow velocity was still at least one order of magnitude higher than the settling velocity of considered particles. Around the return vents, airflow exhibits comparable velocities to those of airflow under the supply vents (contours at x ¼ 2.2 m). In contrast, the airflow decreased in velocity and © ASCE was obstructed and became diffuse after hitting the floor or display shelves (contours at x ¼ 18 and 24 m in Fig. 2). Fig. 3 shows the eddy diffusivity contours at the slice of x ¼ 2.2, 7.6, 11.6, 18, and 24 m. The eddy diffusivities under the supply vents were relatively small (less than 5.0 × 10−3 m2 =s, see contours of eddy diffusivities at x ¼ 18 and 24 m), which indicates the mean airflow dominated the transport of particles under the supply vents. Recall that the velocities under the supply vents were large (Fig. 2). In contrast to the velocity magnitude, the eddy diffusivities became large away from the supply vents and were mainly around 1.5 × 10−2 m2 =s in most of the locations (contours at x ¼ 7.6, 11.6, and 18 m). At x ¼ 2.2 m, the eddy diffusivities were relatively small under all the return vents. The large variation of the eddy diffusivities was obviously observed in the contours, which reflects the significance of considering the gradient of eddy diffusivities in the transport of particles [Eq. (6)]. Fig. 4 shows the spatial distribution of the 5-μm particles at different times for the situation of 0% attachment efficiency. The particles started to spread after the release and reached distances about 5 m from the source at t ¼ 100 s [Fig. 4(a)]. Although the velocities were small (less than 0.05 m=s) away from the supply vents (Fig. 2 at x ¼ 7.6 and 11.6 m), the eddy diffusivities were relatively high and reached up to 0.035 m2 =s in certain regions (Fig. 3). Therefore, turbulent diffusion significantly contributed to the spreading of particles. Particles kept spreading and reached distances of tens of meters from the released location at t ¼ 400 s [Fig. 4(b)], especially in the direction toward the back of the supermarket. At t ¼ 700 s, several particles already reached the sidewalls of the domain, but the particle number concentration was much higher close to the source. At t ¼ 1,000 s, the particles were distributed more or less uniformly through the whole domain [Fig. 4(d)]. The airflow came into the domain from the supply vents 04021007-4 J. Environ. Eng., 2021, 147(4): 04021007 J. Environ. Eng. Downloaded from ascelibrary.org by 186.80.54.213 on 05/17/21. Copyright ASCE. For personal use only; all rights reserved. Fig. 2. (Color) Velocity magnitude contours at the slice of x ¼ 2.2, 7.6, 11.6, 18, and 24 m. Note the large velocity magnitude under the supply vents and around the return vents. The supply vents and return vents right above the slice contours are indicated by the dark red arrows and light blue arrows, respectively. The entrance doors are indicated by purple rectangles. The domain was stretched in the x-direction to show contours clearly. Fig. 3. (Color) Eddy diffusivity contours at the slice of x ¼ 2.2, 7.6, 11.6, 18, and 24 m. Note the eddy diffusivity was relatively small under the supply vents. The supply vents and return vents right above the slice contours are indicated by the dark red arrows and light blue arrows, respectively. The entrance doors are indicated by purple rectangles. The domain was stretched in the x-direction to show contours clearly. and left through the return vents (Fig. 2). The particles circulated within the domain due to the generated air velocities and turbulent diffusion, and the particles were diluted after stopping the release. Many particles were sucked into the return vents [x ¼ 2 and 28 m at the ceiling in Figs. 4(c and d)]. Recall that under the return vents, the velocities were larger than 1.0 m=s (Fig. 3 at x ¼ 2.2 m), but the eddy diffusivities were less than 5.0 × 10−3 m2 =s (Fig. 4 at x ¼ 4.4 m); whenever a particle was transported into the return vents, it was not able to escape. © ASCE Fig. 5 shows the spatial distribution of the 5-μm particles at different times with a 25% attachment efficiency. At t ¼ 100 s, the distribution of particles was quite similar in comparison with the situation of 0% attachment efficiency [comparing Fig. 5(a) with Fig. 4(a)] because the particles had not reached the surfaces and no attachment occurred. The particles kept spreading due to the air velocity and turbulence. At t ¼ 400 s, with a 25% attachment efficiency, hundreds of particles were attached to the ceilings and display shelves [orange and light blue dots in Fig. 5(b)], but most 04021007-5 J. Environ. Eng., 2021, 147(4): 04021007 J. Environ. Eng. Downloaded from ascelibrary.org by 186.80.54.213 on 05/17/21. Copyright ASCE. For personal use only; all rights reserved. Fig. 4. (Color) Spatial distribution of 5-μm particles at t ¼ 100, 400, 700, and 1,000 s with a nonattachment condition. The domain was stretched in the z-direction to show the results clearly. The deep blue spheres indicate particles suspended in the air. The 5-μm particles spread thoroughly through the whole domain without any attachment, and some particles were sucked into the return vents. of the particles were still free to move around [deep blue dots in Fig. 5(b)]. The number of nonattached particles in the air significantly decreased when time increased from t ¼ 400 to 700 s [Fig. 5(c)], and tens of particles also settled to the ground [yellow dots in Fig. 5(c)], which was due to gravity and downward airflow under the supply vents (Fig. 2 at x ¼ 18 and 24 m). At t ¼ 1,000 s, more than 95% of the total number of particles were attached to different surfaces, and several hundreds of particles still moved around due to airflow [Fig. 5(d)]. Only a few particles were sucked into the return vents due to the attachment of particles on surfaces [Fig. 5(d) around x ¼ 2 or 28 m at the ceiling]. Fig. 6 shows the spatial distribution of the 5-μm particles at different times with a 100% attachment efficiency. Several particles were attached to the ceiling and display shelves at t ¼ 100 s with a 100% attachment efficiency [the orange and light blue dots Fig. 6(a)]. Comparing Figs. 6(b and c) with Figs. 5(b and c) shows that the behavior of the spread particles was similar between the two cases with different attachment efficiencies, but more particles © ASCE were attached to surfaces under the high attachment efficiency at the same time. This is probably because, in a near-wall region, the velocities and eddy diffusivities were small (e.g., boundary layer theory); whenever particles were transported to a near-wall region, they moved around the region and finally were attached to the wall. At t ¼ 1,000 s, the particles spread slightly less (about 1–2 m) than those of lower attachment efficiency [comparing Fig. 6(d) with Fig. 5(d)]. Fig. 7 shows the zoomed-in views of the spreading of the 5-μm particles at different times with a 100% attachment efficiency. The particles started to move and spread after the release [Fig. 7(a)]. Instead of falling on the ground, most particles transport upward and spread in all directions from the source [Fig. 7(b)]. This is because the effect of mean flow and turbulent diffusion on the movement of particles is much more dominant than the effect of gravity (Figs. 2 and 3). At t ¼ 200 s, it is observed that a number of particles have attached to the display shelves (light blue dots), ceilings (orange dots), and ground (yellow dots). However, most of the 04021007-6 J. Environ. Eng., 2021, 147(4): 04021007 J. Environ. Eng. Downloaded from ascelibrary.org by 186.80.54.213 on 05/17/21. Copyright ASCE. For personal use only; all rights reserved. Fig. 5. (Color) Spatial distribution of 5-μm particles at t ¼ 100, 400, 700, and 1,000 s with a 25% attachment efficiency. The domain was stretched in the z-direction to show the results clearly. The deep blue spheres indicate particles suspended in the air, and the orange, light blue, and yellow spheres indicate the particles attached to the ceiling, display shelves, and ground and sidewalls, respectively. A large number of particles attached to different surfaces and stopped spreading. particles (larger than 80%) were still suspended in the air and kept spreading [Fig. 7(c)]. The number of active particles significantly decreased at t ¼ 300 s as a result of the attachment of particles on various surfaces [Fig. 7(d)]. Fig. 7(d) also shows that a number of particles settled on the ground. This is because the strong airflow under the supply vents transports particles down to the ground [note the supply vents in the ceiling in Figs. 7(c and d)]. Fig. 8 shows the spatial distribution of the 20-μm particles at different times in the case of 100% attachment efficiency. The 20-μm particles spread much slower in all directions than the 5-μm particles with the same attachment efficiency [comparing Figs. 8(a and b) with Figs. 6(a and b)]. Also, the number of particles attached to the ceiling was much less than for the 5-μm particles. This is because the 20-μm particles have a higher settling velocity; the particles settle down rapidly in places with low flow velocities and eddy diffusivities (Figs. 2 and 3). At t ¼ 300 s, most of the 20-μm particles reached distances around 5 m from the source, whereas 5-μm particles were transported more than 10 m [comparing Fig. 8(b) with Fig. 6(b)]. The 20-μm particles gradually spread © ASCE due to the airflow and turbulent diffusion [Figs. 8(b and c)]. At t ¼ 700 s, more than 99% of the 20-μm particles were attached to different surfaces, and only tens of particles remained unattached [Figs. 8(c)]. At t ¼ 1,000 s, the 20-μm particles were mainly located within a region from x ¼ 7.5–22.5 m and y ¼ 10–20 m and thus spread much less than 5-μm particles [Fig. 8(d)]. Fig. 9 shows the temporal evolution of the fraction of the attached particles in all the cases. For 5-μm particles with 25% attachment efficiency, the fraction of attached particles increased slowly, while it increased most rapidly for 20-μm particles with 100% attachment efficiency. At t ¼ 1,000 s, almost no particles remained in the air for the 20-μm particles with 100% attachment efficiency, whereas there were more than 5% of the total particles suspended in the air for 5 μm with 25% attachment efficiency. For the same surface attachment efficiency, the attachment rate (e.g., the increasing rate of the fraction of the attached particles) of the 5-μm particles was less than that of the 20-μm particles. In other words, more 5-μm particles remained in the air in comparison with 20-μm particles at the same time point. This is 04021007-7 J. Environ. Eng., 2021, 147(4): 04021007 J. Environ. Eng. Downloaded from ascelibrary.org by 186.80.54.213 on 05/17/21. Copyright ASCE. For personal use only; all rights reserved. Fig. 6. (Color) Spatial distribution of 5-μm particles at t ¼ 100, 400, 700, and 1,000 s with a 100% attachment efficiency. The domain was stretched in the z-direction to show the results clearly. The deep blue spheres indicate particles in the air, and the orange, light blue, and yellow spheres indicate the particles attached to the ceiling, display shelves, and ground and sidewalls, respectively. The particles spread less in comparison with the case of 25% attachment efficiency. probably because the 5-μm particles have smaller settling velocity and thus tended to be transported upward more and spread horizontally instead of falling to the ground. For the same particle size, decreasing the attachment efficiency slowed down the trapping of particles by the surrounding surfaces. Changing the attachment efficiency did have a noticeable impact on the attachment between particles and surfaces. However, with four times less attachment efficiency, the attachment rate did not decrease four times for both sizes of particles. This suggests that the surface area available for the attachment of the particles (i.e, the area of display shelves, ceiling, and floors) was large. Alternatively, the airflow was sufficient to spread the particles rapidly to contact a large surface area (Figs. 5–8). Fig. 10 shows the centroids (relative to the initially released location Pxo , Pyo , and Pzo ) and variances of the particles in all the directions for different cases. The x-direction is along the aisles, while the y-direction is perpendicular to them. Figs. 10(a and b) show that the temporal evolution of the centroids of the 5-μm particles horizontally is similar for cases with different attachment © ASCE efficiencies. These could also be visually observed from Figs. 4–6. Fig. 10(a) shows only a slight change in the x-direction (along the aisle), which is probably due to the evenly distributed vents along the aisle. The centroids of the 20-μm particles were negative and smaller than those of the 5-μm particles [Figs. 10(a and b)], which indicates that 20-μm particles moved more backward than forward. Also, for 20-μm particles, the horizontal centroids with no surface attachment decreased more rapidly than those with 25% and 100% attachment efficiencies. This is due to the pattern of airflow and does not have a particular significance in and of itself (i.e., a different air pattern could make the centroid of the 20-μm particles move more in the positive x-direction). Without considering surface attachment, many 20-μm particles gradually spread out horizontally due to the airflow and eddy diffusivity instead of settling down to the ground and attaching to surfaces, leading to a rapid change in the horizontal centroids. Fig. 10(c) shows that the vertical centroids of the 5-μm particles in different cases are higher than those of 20-μm particles. It is understandable because the 20-μm particles having large settling velocity tended to fall to the ground. 04021007-8 J. Environ. Eng., 2021, 147(4): 04021007 J. Environ. Eng. Downloaded from ascelibrary.org by 186.80.54.213 on 05/17/21. Copyright ASCE. For personal use only; all rights reserved. Fig. 7. (Color) Spatial distribution of 5-μm particles at t = 10, 100, 200, and 300 s with a 100% attachment efficiency observed from x ¼ 0 m and about 3 m downstream the releasing source (x ¼ 0 m, y ¼ 20 m, and z ¼ 1.8 m). The deep blue spheres indicate free transport particles, and the orange, light blue, and yellow spheres indicate the particles attached to the ceiling, display shelves, and ground and sidewalls, respectively. The variation trend of the vertical centroid in different cases is similar, excluding the case of 5-μm particles with no surface attachment. The vertical centroid increased rapidly before t ¼ 300 s and decreased slowly until t ¼ 1,000 s. This is because, at the © ASCE beginning of the simulation, the particles moved upward due to the airflow and turbulence; and later on, many particles were pushed down to the ground by strong downward airflows under the supply vents [Figs. 7(b–d)], or attached to the surfaces of 04021007-9 J. Environ. Eng., 2021, 147(4): 04021007 J. Environ. Eng. Downloaded from ascelibrary.org by 186.80.54.213 on 05/17/21. Copyright ASCE. For personal use only; all rights reserved. Fig. 8. (Color) Spatial distribution of 20-μm particles at t ¼ 100, 400, 700, and 1,000 s with a 100% attachment efficiency. The domain was stretched in the z-direction to show the results clearly. The deep blue spheres indicate free transport particles, and the orange, light blue, and yellow spheres indicate the particles attached to the ceiling, display shelves, and ground and sidewalls, respectively. The 20-μm particles spread much less widely than the 5-μm particles in each direction. Fig. 9. (Color) Temporal evolution of the number fraction of attached particles for the 25% and 100% attachment efficiency cases (no particles attach for the 0% attachment efficiency case). © ASCE display shelves at low heights. For 5-μm particles with no surface attachment, the particles kept spreading vertically, and the vertical centroid remained high because the gravity of the particles was small. The variances of the particle cloud reflect how the particles spread in each direction [Figs. 10(d–f)]. The change of variances in the x- and y-directions was similar for each case [comparing Fig. 10(d) with Fig. 10(e)]. Figs. 10(d and e) show that small particles spread more than large particles in the horizontal directions with the same attachment efficiency. In addition, for the same particle size, decreasing the attachment efficiency enhanced the spread of particles horizontally. For the cases with 25% and 100% attachment efficiencies, the horizontal variances of particles tend to level off after a certain period. This is because more and more particles attached to surfaces after the release (Fig. 9), and finally, particles stopped spreading [Figs. 5(d), 6(d), and 8(d)]. Without considering the surface attachment, the particles kept spreading horizontally within 1,000 s. Fig. 10(f) shows the vertical variance of particles for all the cases. While considering the surface attachment, the temporal evolution of the particles tended to level off after a certain 04021007-10 J. Environ. Eng., 2021, 147(4): 04021007 J. Environ. Eng. Downloaded from ascelibrary.org by 186.80.54.213 on 05/17/21. Copyright ASCE. For personal use only; all rights reserved. (a) (d) (b) (e) (c) (f) Fig. 10. (Color) Temporal evolution of the centroid (relative to the initially released location Pxo , Pyo , and Pzo ) and variance in each direction under various scenarios. period due to the trapping of particles by surfaces. With different attachment efficiencies, the extent of spreading in the vertical direction was similar for each particle size. However, the spread of particles without attachment in the vertical direction increased for 20-μm particles, but declined for the 5-μm particles. This is because the 5-μm particles tended to be uniformly distributed throughout the height, whereas the distribution of 20-μm particles was biased to the ground floor due to gravity. Fig. 11 shows the temporal evolution of normalized mean concentration of nonattached particles within a vertical slice of volume (2 × 3 × 1.5 m) 5 m downstream of the released location. For the 5-μm particles, the concentration of suspended particles started © ASCE to increase after t ¼ 150 s and reached its peak value around t ¼ 400 s. The airspeed away from vents was approximately 0.1 m=s (Fig. 2), and thus it is tempting to consider that the peak would reach the 5-m distance in a time of ð5=0.1Þ ≈ 50 s. This is probably true for an individual particle, but due to the presence of turbulent diffusion (Fig. 3), the released particles spread, more or less, in 3D, and it took time for their peak to reach the selected location 5 m from the source. After t ¼ 400 s, the particle concentration gradually decreased until the end of the simulation (t ¼ 1,200 s) because the release stopped at t ¼ 200 s. For the 5-μm particles, the maximum concentration was around 20% of the source for the nonattachment (or 0% attachment) situation. 04021007-11 J. Environ. Eng., 2021, 147(4): 04021007 J. Environ. Eng. virus will increase the possibility of getting COVID-19. Therefore, for indoor businesses, such as supermarkets and shopping malls, disinfection should be performed frequently to inactivate and reduce the number of virions present in the built environment, and customers and employees should be encouraged to wear personal protective equipment (e.g., gloves). Downloaded from ascelibrary.org by 186.80.54.213 on 05/17/21. Copyright ASCE. For personal use only; all rights reserved. Social Distance and Wearing Masks Fig. 11. (Color) Normalized mean concentration of nonattached particles within a volume of 6 m3 (2 × 3 × 1.5 m) 5 m downstream of the released location (centered at x ¼ 15 m, y ¼ 19.8 m, and z ¼ 1.7 m). The mean concentration was calculated over a sliding window of 60 s, and the normalization was performed with 500=m3 , which is the concentration of particles of each release. The peak was around half that value (i.e., 0.1 of the source) for the 25% attachment efficiency, and the 100% attachment efficiency case had a slightly smaller peak. The peaks also occurred at earlier times as the attachment efficiency increases. This is probably because particles near surfaces are subjected to small velocities (law of the wall), and when they attach, they no longer reach the 5-m-downstream location, and thus only the fast ones reach the 5-m location. The difference in the time to peak is small, though, a few tens of seconds. For the 20-μm particles, the increasing rate and the peak value of the particle number concentration were much smaller than those of 5-μm particles. With the same attachment efficiency, the peak concentration of 20-μm particles was less than 30% of that of the 5-μm particles. This is because a large number of 20-μm particles settled to the ground due to the effect of gravity. The peak concentration also dramatically decreased with a 25% efficiency in comparison to the case without considering the attachment. However, increasing the attachment efficiency from 25% to 100% did not provide a considerable impact on the evolution of number concentrations of 20-μm particles, which is thus similar to the 5-μm particles. The results in Fig. 11 revealed that the attachment efficiency has a major impact on the transport of small particles (5 μm) in comparison with the 20-μm particles. Discussion Viability of Virus on the Surfaces van Doremalen et al. (2020) conducted experiments on SARSCoV-2 stability on various surfaces (plastic, stainless steel, copper, cardboard). They found that viable SARS-CoV-2 could still be detected up to 72 h after application to plastic and stainless steel. On the cardboard and copper, SARS-CoV-2 remained viable up to 24 and 4 h, respectively. Because most exhaled particles are very small (i.e., less than 10 μm), they are very likely to spread widely and attach to different surfaces (see results in Figs. 4–6). Although the infectious dose (the amount of virus needed to be inhaled to cause infection) of SARS-CoV-2 is still unknown, touching viable © ASCE The CDC recommends that people stay a social distance of 2 m (about 6 ft) from others to reduce the risk of inhaling virus-laden particles. However, the results from this study indicate that this distance should be increased because the indoor airflow significantly enhanced the spread of particles to more than 15 m from the source for small-sized particles (<micrometers). Furthermore, such spreading was especially pronounced for small particles (<5 μm), which can reach deep into the respiratory system. Even large-sized particles (e.g., 20 μm) can migrate more than 5 m from the source before fully settling down. Hence, keeping a social distance is probably not sufficient to prevent people from being infected by the virus in an indoor ventilation environment. But an increase in the distance between the source and potential targets undoubtedly reduces the viral load (Fig. 10); however, the practice of achieving this is questionable. The numerical study presented by Dbouk and Drikakis (2020b) shows that wearing a mask can significantly decrease the number of particles exhaled into the air and shorten the spreading distance of exhaled particles. In addition, wearing a mask can prevent shoppers from inhaling virusladen particles (Ayenigbara et al. 2020). Hence, wearing a mask is highly suggested for any indoor ventilation environment like supermarkets. Attachment of Particles on Surfaces It is shown in Figs. 4, 5, 6, 10, and 11 that enhancement of the attachment of particles on surfaces can reduce the spreading of particles horizontally, which subsequently decreases the potential risk of being infected through inhaling virus-laden particles. The attachment of particles on surfaces can be enhanced using two complementary approaches: increasing the contacting area or using materials with a high attachment efficiency. The former method is much easier to implement. One practice in supermarkets is to make aisles one way to reduce exposure, and we believe that the exposure of shoppers to virus-laden particles could be further enhanced by placing baffles in the aisles to cause the air to zigzag through the aisle [Fig. 12(a)]. The air would invariably hit the baffles, and the virus-laden particles would attach. One could also place barrier shields on the top of the shelves to prevent the transport of particles between aisles [Fig. 12(b)]. Baffles and shields can increase the surface area for deposition, but they could also create dead zones where the particles get suspended, especially if the attachment efficiency is small. Therefore, the proposed solutions herein would need to be closely investigated in future studies. As we discussed in the “Viability of Virus on the Surfaces” section, the viability of the virus on different surfaces is distinct. Hence, the material with a high attachment efficiency but low viability of virus particles should be selected to produce the barrier shields and baffles. Filter in the HVAC System In the indoor built environment, air-conditioning filters are used to remove airborne contaminants in a room. The ability of filters to trap particles is commonly reflected by the minimum efficiency reporting value (MERV) defined in the American Society of 04021007-12 J. Environ. Eng., 2021, 147(4): 04021007 J. Environ. Eng. Downloaded from ascelibrary.org by 186.80.54.213 on 05/17/21. Copyright ASCE. For personal use only; all rights reserved. Fig. 12. (Color) Proposed solution to control the spreading of exhaled virus-laden particles: (a) conceptual schematic illustration; and (b) a 3D example. Heating, Refrigerating, and Air-Conditioning Engineers Standard 52.2 (ASHRAE 2017), with higher values being associated with a better capability to trap small particles. For example, a MERV rating of 16 requires the filters to be able to trap at least 75% of all 0.3- to 1.0-μm particles; a MERV rating of 12 is capable of trapping particles from 1 to 3 μm with an efficiency higher than 90%. Typically, filters for residential and commercial applications range from MERV 1 to 12. Based on our simulation results, it is likely that the small-sized particles (<5 μm) were sucked into return vents with the air currents, which may cause the transmission of SARS-CoV-2. Hence, filters with high MERV levels are required to prevent virus-laden particles from getting into ventilation systems. Summary and Conclusions In the present study, the transport of virus-laden particles in an indoor ventilation environment (e.g., a supermarket) was studied by © ASCE coupling CFD with Lagrangian particle tracking. The fluid dynamics of the indoor airflow were simulated by using the commercial CFD package Ansys Fluent. The fluid dynamics was then imported into our in-house Lagrangian particle tracking code NEMO3D to simulate the transport of particles. The transport and fate of 5- and 20-μm particles were studied, and three different attachment efficiencies were considered: • With a 100% attachment efficiency, the 5-μm particles spread by more than 15 m horizontally, while the 20-μm particles transported much less, around 5.0 m horizontally from the source. In both cases, the transport distance of particles is much larger than 2 m, indicating that the 2-m (6-ft) social distance strategy is probably not sufficient to prevent infection within an indoor ventilation environment, and wearing a mask is necessary. • The impact of the attachment efficiency on the transport and fate of particles is not negligible. Decreasing the attachment efficiency enhanced the spread of particles in the horizontal direction. Therefore, it is a good strategy to prevent the spreading of 04021007-13 J. Environ. Eng., 2021, 147(4): 04021007 J. Environ. Eng. Downloaded from ascelibrary.org by 186.80.54.213 on 05/17/21. Copyright ASCE. For personal use only; all rights reserved. Fig. 13. (Color) Detailed dimensions of the computational domain: (a) top view (supply and return vents); and (b) bottom view (display shelves). particles by increasing the attachment between the particles and surfaces, either by increasing the contacting areas (i.e., using baffles or shields) or strengthening the attachment between the particles and surfaces (i.e., using materials with a high attachment efficiency). • There are a large number of particles attached to display shelves, which are likely to be touched by the customers. Wearing gloves might also be necessary to protect people from getting infected or at least ensure that people disinfect their hands when leaving the store (most stores provide disinfectants to customers entering the store). • The particles in this study were sucked into the return vents, and the low MERV filters are not able to prevent the virus-laden saliva particles from flowing into the ventilation channels, which caused potential dangers of infection for the buildings connected to the same ventilation system. Understanding how the particles transport within the indoor environment will be critical for the pandemic-response department, such as the CDC, to adjust the guidelines for infection control. It is also helpful for the government and people to take effective measures to contain the virus. The present study can also be used as a reference for further refined studies. Appendix. Dimensions of Designed Supermarket The detailed dimensions of the designed supermarket are given in Fig. 13. Data Availability Statement Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request (numerical results). © ASCE Acknowledgments This work was funded by a National Science Foundation (NSF) RAPID Grant (CBET 2028271). However, it does not necessarily reflect the views of the funding agency, and no official endorsement should be inferred. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by NSF Grant No. TG-BCS190002. Specifically, we used the Comet computer cluster, which is an NSF-funded system at the San Diego Supercomputer Center (PSC). Input from Dr. Seema Lakdawala of the University of Pittsburgh is appreciated. References Allen, J. G., and L. C. 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