key: cord-291836-dlsas702
authors: Yang, Xia; Ou, Cuiyun; Yang, Hongyu; Liu, Li; Song, Tie; Kang, Min; Lin, Hualiang; Hang, Jian
title: Transmission of pathogen-laden expiratory droplets in a coach bus
date: 2020-04-12
journal: J Hazard Mater
DOI: 10.1016/j.jhazmat.2020.122609
sha: 
doc_id: 291836
cord_uid: dlsas702

Abstract Droplet dispersion carrying viruses/bacteria in enclosed/crowded buses may induce transmissions of respiratory infectious diseases, but the influencing mechanisms have been rarely investigated. By conducting high-resolution CFD simulations, this paper investigates the evaporation and transport of solid-liquid mixed droplets (initial diameter 10 μm and 50 μm, solid to liquid ratio is 1:9) exhaled in a coach bus with 14 thermal manikins. Five air-conditioning supply directions and ambient relative humidity (RH = 35% and 95%) are considered. Results show that ventilation effectiveness, RH and initial droplet size significantly influence droplet transmissions in coach bus. 50 μm droplets tend to evaporate completely within 1.8 s and 7 s as RH = 35% and 95% respectively, while 0.2 s or less for 10 μm droplets. Thus 10 μm droplets diffuse farther with wider range than 50 μm droplets which tend to deposit more on surfaces. Droplet dispersion pattern differs due to various interactions of gravity, ventilation flows and the upward thermal body plume. The fractions of droplets suspended in air, deposited on wall surfaces are quantified. This study implies high RH, backward supply direction and passengers sitting at nonadjacent seats can effectively reduce infection risk of droplet transmission in buses. Besides taking masks, regular cleaning is also recommended since 85%-100% of droplets deposit on object surfaces.

Highlights  Droplet evaporation and transport(initial size 10μm/50μm) in bus are studied by CFD. [3, 7, 8] , hospital isolation rooms [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] or operating rooms [19] , general indoor environments [20, 21] . Besides for vehicle indoor environments, a number of studies emphasized indoor transmission in airplane cabins [22] [23] [24] [25] and high-speed train [26] . For instance, Zhang and Li [26] used CFD (Computational Fluid Dynamics) simulations to study the respiratory particle dispersion process (without droplet evaporation) in four different boundary conditions of air supply and exhausts in a highspeed rail cabin. However, there is a lack of study on ventilation and droplet dispersion in the coach bus.

Respiratory infectious diseases can be transmitted via three routes, namely contact, airborne and fomite [27] . Similarly, a higher risk of infection is associated with close proximity to the source patient and decrease rapidly with the distance [28] [29] [30] [31] [32] [33] . With the same initial concentration, a larger quantity of mass released may be expected to experience a slower dilution [34, 35] . Due to the initial velocity, the exhaled gas and particles can travel in the air over a distance which is determined by the ventilation airflow, gravity force related to particle diameters and buoyancy forces of thermal J o u r n a l P r e -p r o o f bodies [16, 17, 26, 31, 33, [36] [37] [38] . Larger particles (>50μm) may settle on wall surfaces or floors quickly because the significance of gravity is greater than ventilation. Smaller particles (0.5-10μm) may remain suspended for a sufficient time and lead to disease transmission over larger range [16, 23, 26, 39] .

Apart from the initial droplet size, the droplet evaporation and dispersion may be influenced by the relative humidity (RH) in ambient environment as well [40] . Wei and

Li [41] discovered that droplet dispersion with the diameter of 50μm was very sensitive to RH in the jet-like cough airflow. By calculating the droplet lifetimes and droplet size variation with different RH, Xie et al. [42] indicated that the droplet size was dictated by its evaporation and droplets smaller than 100μm would evaporate before falling to the ground 2m away. The shrinking aerosols would ultimately form droplet nuclei small enough to suspend in the air for substantial time. Accordingly, instead of using pure water droplets for model testing [42] , test droplets containing nonvolatile content were investigated by Liu et al. [43] and employed in our study too, which would ultimately form droplet nuclei after evaporation. Due to the great impact of initial droplet size on disease transmission, many studies were carried out to reveal the size profile information of droplets during different expiratory activities [38, 44, 45] . It is difficult to identify the actual droplet size exhaled from different patients with various human activities. Therefore, we first emphasize and adopt the initial droplet diameters of 10μm and 50μm as involved in most previous studies.

In summary, there are many studies on the diffusion of tracer gases and particulate matter for indoor transmission in hospital ward, airplane cabin and general indoor environment etc. However, it is still a lack of studies on droplet evaporation and dispersion in enclosed bus environments.

This paper aims to investigate the effect of RH and indoor airflow pattern with body J o u r n a l P r e -p r o o f thermal plume on the evaporation and dispersion of exhaled droplets with different initial diameters in enclosed bus environment. The enclosed bus model followed the realistic coach bus that went from Guangzhou to Huizhou in Guangdong province P.R.

China and carried a Korean patient infected by MERS (Middle East Respiratory Syndrome) in May 2015, who did not wear a mask and did not give a cough/sneeze or talk with others either. The other thirteen people were isolated for three weeks after this trip and fortunately no one was infected by this source patient. Similarly but unfortunately, infectious cases have been found on public transport [6] , which was identified as airborne transmission. Therefore, it is necessary to study the droplet dispersion in this enclosed bus environment. By cooperating with CDC of Guangdong province, we adopted the same passenger locations and average ventilation flow rates in the enclosed bus taken by MERS patient in CFD model settings. Then the impacts of RH, initial droplet diameters and air-conditioning supply directions can be investigated as case studies by CFD simulations. Through statistics of the number of droplets trapped, suspended and escaped to predict the chance of infection, this study attempts to provide some recommendations for reducing the risk of droplet transmissions in enclosed bus environments.

In this study, Ansys FLUENT [46] was applied in the validation and following numerical cases study. As displayed in Fig. 1a , based on the experimental data of Yin et al. [47] in an inpatient ward furnished with one patient, one visitor, one bed, a TV set and a piece of medical equipment, CFD validation study was first conducted to verify the ability of CFD in predicting indoor airflow and temperature distribution. According J o u r n a l P r e -p r o o f to the experiment [47] , air was supplied from a near-floor diffuser with the temperature of 19.5℃ and ventilation rate of 4 ACH (114CFM), and air was exhausted through the bathroom exhaust and main exhaust with the ventilation rate of 36CFM and 78CFM

respectively. The heat generated by patient, visitor, equipment and TV was 106Watt,

110Watt, 36Watt and 24Watt. More details can be found in Yin et al. [47] . In our CFD simulations, the mesh was generated with the maximum grid size of 5cm (fine grid, total tetrahedral cells of 1.8 million) and 10cm (coarse grid, total tetrahedral cells of 0.38 million) near wall surfaces and finer grids near heating surfaces.

As shown in Fig. 1b source and the exhaust where the airflow was unstable, both the particle concentration measured in experiment and CFD display a large fluctuation. The particle concentration on TG1, TG3, TG4 is relatively small and has similar profile shape. The results show not very good simulation of concentration values but sufficiently well in predicting the changing shape and magnitude of particle concentration. On the whole, the above results prove that present CFD simulations with RNG k- model and grid arrangement with the maximum grid size of 5cm is effective [17, 22, 26, 48] and can be adopted in the following simulation of indoor environments.

This study aims to figure out the characteristics of droplet evaporation and dispersion in an enclosed long-route coach bus. A realistic coach bus, with a dimension of 11.63 m×2.6 m×2 m (L×W×H), was adopted to investigate the influence of airconditioning supply directions and indoor relative humidity. The detailed descriptions of enclosed bus are summarized in Table. 1 was about 2, 790, 000, which was determined by refining the mesh until the flow field solution was grid-independent. Zhao et al. [49] found that the dispersion of exhaled particles was easily affected by the size of particles, body thermal plumes and ventilation airflow patterns. So we investigated the particle dispersion and deposition in terms of various initial sizes of droplets, air condition supply directions and RH. 5c ) where located in the air condition vents will be illustrated in the discussion section.

The fate of droplets, including suspended, deposited and escaped, as well as the number concentration of droplets around and on passengers were calculated to quantify the healthy passengers' risk of infection, which can effectively prevent and control the respiratory infectious diseases.

As is well-known, there are two main kinds of airflow patterns in nature, laminar flow and turbulent flow. Indoor airflow is usually turbulent which can be simulated by Large Eddy Simulation (LES) and Reynolds Average Navier-Stokes (RANS) turbulence models. However, the application of LES model requires longer computational time [50] [51] [52] . The Renormalization Group (RNG) k-ε turbulence model which is one of the most widely-adopted RANS models is employed in terms of accuracy, computing efficiency, and robustness for modeling indoor environments J o u r n a l P r e -p r o o f [17, 26, 39, [53] [54] . Thus, we adopted the RNG k-ε model to simulate the airflow pattern in the bus. More details about the governing equations and the turbulence parameters of RNG k-ε model can be found in the literature [17, 53] . The SIMPLE algorithm was adopted to decouple pressure and velocity. The second-order upwind scheme was used to discretize the convection and diffusion-convection terms in the governing equation.

Besides, the Boussinesq model was employed to consider the buoyancy effect, in which the air density was regarded as a constant except in the momentum equation of vertical velocity.

Lagrangian method was used to track respiratory droplets. To simplify the calculation, the following assumptions were used:

(1) the heat and mass transfer between air and droplets were neglected;

(2) the influence of droplets on airflow was also neglected;

(3) no droplet was coagulated in its deposition process;

(4) the droplets were all in ideal sphere shape.

This approach calculates the trajectory of each droplet by solving the individual droplet movement equation whose theory is Newton's second law: (2) and Eq. (3) were respectively adopted to describe the drag force and gravity on the droplet in i direction:

where is the Stoke's drag modification function for large aerosol Reynolds number ( ) which is defined in Eq. (4); is the aerosol characteristics response time, which is defined as Eq. (5); and are respectively the density of droplet and air;

and are respectively the droplet diameter and the turbulent viscosity (kg·m -1 ·s -model was adopted [46] . The droplets evaporate till their inert content (residue) [26, 36] .

The droplet vaporization rate is defined as the following equation:

where is the molar flux of vapor, kg·mol·m -2 ·s -1 , and is related to the gradient of the vapor concentration between the droplet surface and the surrounding air; is the mass transfer coefficient (m/s) that can be obtained using Sherwood relationship [56] ;

, and , are respectively the vapor concentration at the droplet surface and in the surrounding air (both in kg·mol·m -3 ), and can be obtained via the ideal gas relationship and molar fractions of water vapor. Droplet evaporation is influenced by RH in terms of , in Eq. (7).

All boundary conditions for airflow are summarized in Table. 3. The influences of human breathing and heat flux at body surfaces were taken into account. Considering the total heat of 76 W [17] produced by the sleeping manikin with surface area of 1.47 m 2 , the convection heat flux at body surfaces was defined as 26 W/m 2 for passengers assuming they were sedentary and 58.5 W/m 2 for the driver. For simplification, the breathing flow was assumed to be exhaled from the human mouth with the temperature of 303 K. The boundary at mouth openings (~0.0016m 2 ) was set as the mean exhalation velocity of 0.12m/s [16, 17, 57] in the direction paralleling to y-axis.. Our CFD simulation considered only mouth exhalation for all manikins. The air-conditioning vents were also set as velocity inlet, and the wind speed was 3.0m/s (Air change rate per hour=8.6 h -1 ) with the air temperature of 290 K. Non-slip boundary conditions were applied for all walls where isothermal condition was assumed. Table. 4. For solid walls and seats, the trap condition was applied with the assumption that droplets were deposited as soon as they touch the wall surfaces and the trajectory calculation was terminated. While for the ceiling and luggage carriers, the reflect condition was set due to gravity. Escape condition was applied to the exhaust and mouths as well as air-conditioning vents.

Gravity plays a particularly important role for the movement of large droplets (50μm) [16, 31, 33, 38, 40, 42] . Thus, to better reveal the influence of air condition supply wind, the following subsection focuses on the analysis of the 10 μm droplet diffusion in different air condition supply modes as RH = 35%. There are differences between Windnx (Fig. 6c) and Windpx (Fig. 6d ) supply modes as passengers will release heat and affect the flow field. The velocity is larger when air condition supply wind blows to the front of the bus (Windpy), which has the superposition effect with the exhaust (Fig. 6f) . A vortex is formed between the patient and the front seat, where the upward flow is relatively stronger. In addition, there is also airflow across the seat backs and front. Referring to

Windpy mode, almost half of droplets move forwards across the back of the chair, and leave several droplets sink because of small vertical downward force, and then rise up because the upward airflow continues to float to the right of the carriage (Fig. 7e1-e3 and Fig. S1c ). In the process of forward diffusion, some droplets are blocked by the seat backs of V5L, and a great number of droplets move across V4L, sinking at V3L

and V2L due to the obstruction of the seats subsequently. The droplet which isn't trapped in the object keeps on fluttering forwards in higher level. According to the droplet distribution at t=40s, there will be droplet aggregation in the front area on the left side of the bus where the patient is located.

As previously investigated [16, 23, 26, 31, 33, [38] [39] [40] 42] , the particle/droplet dispersion process is greatly determined by the gravity force. In this study, the impacts of different initial droplet sizes and its evaporation rate are discussed. Results show that the diffusion features between 10μm and 50μm droplets are of great variation under the same air condition supply wind direction and RH. In contrast to the initial diameter of 50μm droplets, 10μm droplets tend to move faster, farther and wider at the same time. Hence, the size of droplets determines the dominant force in the diffusion process.

The larger the droplets are, the faster the deposition is, the slower the diffusion is, and the lower the risk is to the driver and passengers.

Relative humidity was proved to be dominant for evaporation time of droplets [41, 43] . Droplets consisting of liquid (H2O) and solid particulate matter (NaCl) was J o u r n a l P r e -p r o o f taken consideration, and the processes of evaporation and diffusion were simulated in this study. After released from patient mouth, the change of droplet size with time was counted. According to our statistics, under RH = 35%, droplets with the initial diameter of 10 μm was evaporated completely within the first 0.2 s. For the condition of RH = 95%, the evaporation time of 10μm droplets hardly change, since they evaporated too fast to be seen any difference [40] . As the ratio of water to sodium chloride in the droplet is set to be 9:1, the final diameter for droplets with the initial size of 10μm and 50 μm is 3.65 μm and 18.26 μm, respectively. In another word, their volumes have been reduced to one tenth of their original size ultimately.

The change of droplet diameter under different RH is shown in Fig. 9 . Results show that high RH can dramatically postpone the process of droplet evaporation, since air with higher RH has a lower potential in absorbing the water vapor [40] . The figure reveals that the droplet size decreases to stable at t=1.8 s and 7 s respectively when RH = 35% and 95%. The larger the RH is, the more time it takes for droplets to evaporate.

Therefore, the effect of buoyancy and gravity forces on the diffusion of droplets will be more obvious for RH=95%.

Nevertheless, as the short time of droplet evaporation, its influence on the diffusion of droplets is limited. Compared to 50 μm droplets, 10 μm droplets evaporate too quick to be seen any difference in the dispersion, thus 50 μm droplets are used to present to discuss as followed. Fig. 10 depicts the distribution of 50 μm droplets at different time under both dry (RH=35%) and wet (RH=95%) environment in the Windny mode. In general, droplets seem to move towards the same direction, and the dispersion range J o u r n a l P r e -p r o o f has no significant variation between them. Actually, as a result of the short evaporation time (1.8 s) in RH=35%, droplets shrink quickly to droplet core whose diameter is 18.26 μm, and subsequently diffuse fast. It is observed in Fig. 10a2, a3 and Fig. 10b2 , b3 that droplets arrive the farther place compared to RH=95%. Besides, it should be mentioned that the number of droplets in RH=95% is fewer than that in RH=35%, because more droplets will deposit in the object surface in the diffusion process, leading to less suspension droplets (e.g. Windpy, Fig. S1d-e) , which will be discussed in section 3.2.

After released from the patient' mouth, droplets begin to evaporate and spread to every corner of the carriage because of the gravity, buoyancy force and airflow of the air-conditioning. In this paper, droplets composed of liquid and solid elements are employed. The solid elements still travel around in the carriage after the liquid is evaporated. During the diffusion process, some droplets' journey will end up when they deposit on the surface of the seats, human bodies or walls, while the others still suspend till they deposit or escape from the exhaust fan which is set on the front of the roof. In general, there are three final statuses of droplets when the calculation stops, named trapped, suspended and escaped, and the total number of them is 130,720. In addition, when the droplet size increases to 50 μm (orange bars), the effect of wind direction becomes smaller than that for 10μm droplets. As a result, more than 91.0% of 50 μm droplets will deposit. The proportion of suspended droplets decreases slightly from 3.5-6.0% (10 μm) to 1.3-4.5% (50 μm) due to the greater gravity force on larger droplets. There is an exception that the proportion of suspended droplets increases from 3.2-3.4% (10 μm) to 6.9-8.5% (50 μm) in the mode of Windpy where droplets are stopped by the V5L seat backs and move towards the aisle with little obstruction.

However, the number of escaped droplets is of dramatically reduction, especially in the Windny mode, which decreases to 0.04%. As the initial diameter increased, droplets are less removed from the carriage, and most of them still stay in the bus, which is a risk to passengers.

When the relative humidity is between 35% and 95%, droplets express similarity in their ultimate fate. There is slight distinction of fate for 50 μm droplets in different conditions of supply wind, which is related to the short evaporation time of 10μm.

Taking 50 μm droplet as an example, in the mode of Windpy, 6.9% and 8.5% of droplets are suspended when RH=35% and 95%, respectively. The relative humidity brings the same function to droplets size. Therefore, the influence of RH on dispersion of droplets depends on the initial size of droplets and the supply wind direction.

The zone, which is more than 10 μm droplets (7.06‰). Droplets mostly suspend above the fifth and sixth row. This result is consistent with the previous droplet diffusion characteristics in subsection 3.1.1.

Passengers whose body surfaces are deposited by droplets exhaled from the source patient are at higher risk to get infected than those whose body surfaces are not diameter is 50 μm compared to 10 μm. More droplets will deposit on the passengers around the patient such as 6C, 7B. In terms of driver and passenger 11C and 11D, the distance between them and patient is more than 4.5 m, which significantly reduce the probability of airborne transmission.

Finally, we recall the facts that no passengers were infected by the source patient with MERS from South Korea. Several reasons can be the most significant. First, although the source patient did not wear any mask, fortunately he did not cough/sneeze or talk with other people. There were only droplets exhaled by breathing activities.

Second, it was lucky that there were no passengers in the adjacent seats in front of or behind this source patient as well as beside his seat which were revealed of the highest risk for droplet transmission. For the other seats, the risk of droplet transmission decreased sharply.

Our study can be further improved in which more processes/parameters are considered. Firstly, we only studied the influence of air-conditioning wind direction and relative humidity on the droplet dispersion. However, in real cases, the location of the infection source relative to the exhaust fan is also an important factor on the droplet diffusion, transmission, and elimination, because the only exhaust fan is of great significance on flow pattern in the enclosed bus. Secondly, as a start, this study only considered exhaled droplet by breathing. Future investigations will consider different respiratory activities (e.g. speaking, coughing, sneezing), which may lead to complex J o u r n a l P r e -p r o o f jet speed and different initial characteristics of droplets (sizes, velocities etc.). Thirdly, the final fate and composition of the droplets are of great significance for the evaluation of the infection risk, and the relationship between them deserves further study.

The enclosed and crowded indoor environments in long-route coach buses usually experience high infection risk of respiratory diseases due to droplet transmissions. In this study, as a novelty, we built a numerical model according to a real case to investigate the influence of ventilation and evaporation of exhaled droplets on their transport. We employed five air supply directions, two kinds of relative humidities (RH=35% and 95%) and initial droplet sizes (10 μm and 50 μm). We summarized the number of droplets/droplet nuclei suspending in different zones and depositing on the body surface of each passenger to show the temporal and spatial characteristics of droplet distributions.

Some meaningful findings are addressed:

(1) Droplets with the initial diameter of 10 μm finish evaporation within the first 0.2 s as RH=35% and 95%, while 50 μm droplets evaporate to pure solid droplet nuclei within 1.8 s and 7.0 s respectively under dry and wet conditions.

(2) Followed by the air supply mode and droplet initial size, droplet evaporation related to relative humidity is the third key factor influencing the droplet diffusion and its final state. RH of 95% tends to attain less risk of droplet transmission than RH of 35% because droplets evaporate slower in wetter air and deposit more quickly onto J o u r n a l P r e -p r o o f wall surfaces.

(3) In general, small droplets (10 μm) diffuse faster, farther and wider compared with large droplets (50 μm). 91%-100% of 50 μm droplets are trapped on the surfaces, which is higher than that of 10 μm (85%-95%) because of the gravity-force effects. 

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Miss J o u r n a l P r e -p r o o f (a) (b) Fig.3 . The computational domain, human models and the schematic structure in the coach bus. 

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