The dispersion of respiratory droplets is strongly influenced by the complex airflow induced by human activities, such as walking in a queue. Understanding the relationship between local airflow disturbances during queue walking and droplet dispersion is crucial. This study investigates the effects of following distance (1.0, 1.5, 2.0, and 2.5 m), walking speed (0.8, 1.0, 1.2, and 1.4 m/s), and droplet diameter (1, 10, 50, 80, and 120 μm) on droplet dispersion. The findings reveal that the interaction between wake vortex and forward airflow provides a foundation for cross-infection among individuals. An increased following distance leads to an initial rise and subsequent decrease in the concentration in the breathing zone of the susceptible individual. The social distances of 1.0 and 1.5 m are insufficient to mitigate the risk of cross-infection, warranting a recommended following distance of at least two meters. The effect of walking speed on droplet dispersion varies depending on the scenario. In cases involving standing and walking cycles, the infection risk of the susceptible individual gradually increases with higher walking speeds. Conversely, when individuals walk continuously in a queue, the infection risk of the susceptible individual decreases with increased walking speed. Moreover, intermediate-sized droplets play a critical role in the transmission of respiratory infectious diseases and demand heightened attention. This study expounds the intricate airflow dynamics during queue walking and emphasizes the significance of following distance, walking speed, and droplet diameter in minimizing the risk of cross-infection.

The novel coronavirus disease 2019 (COVID-19) was first reported in Wuhan, China, in December 2019, and then quickly spread around the world. The emergence of the COVID-19 pandemic has once again drawn public attention to respiratory infectious diseases. Many respiratory infectious diseases (MERS, influenza, COVID-19, etc.) can be spread by aerosols.1 People can exhale droplets of different sizes by coughing, sneezing, breathing, and talking.2,3 Different-sized droplets have distinct dispersion characteristics. Large droplets tend to settle quickly, leading to short-range transmission, while small droplets can remain suspended in the air for an extended period and contribute to long-range airborne transmission. The air distribution around an infectious source significantly influences the dispersion of droplets. Previous studies have extensively investigated the effects of ventilation systems on droplet dispersion mechanisms in various scenarios such as buses,4 aircraft,5,6 hospital wards,7 classrooms,8 and conference rooms.9 Researchers tried to explore new ventilation systems to effectively reduce the risk of cross-infection.10,11 Additionally, some measures, such as air curtains,12 air purification devices,13,14 barriers,15,16 and masks,17,18 have been studied to indirectly modify air distribution and reduce infection risk. However, many studies have primarily focused on scenarios where individuals remain stationary. In reality, human movement can obviously disturb the surrounding airflow field and further impact the dispersion of exhaled droplets.19–21 When people are stationary, although the ambient wind speed is provided at the same speed as that of human walking, the airflow field changes around the human are still very different.22 Therefore, it is essential to study the effects of human movement on airflow and droplet dispersion.

When individuals walk, the air in front of them is pushed away and moves upward, while a strong downward airflow is formed behind them and develops into a vortex.23,24 Walking also alters the lateral airflow within a 1-m range on both sides of the individual.25,26 Although human movement may seem to disturb the local airflow field, it can still have a significant effect on cross-infection, especially in scenarios with inadequate ventilation, limited space, or close social distance. Walking speed plays a role in droplet dispersion, as evidenced by studies on exhaled droplets of patients in airborne infection isolation rooms. Increasing walking speed can reduce the infection risk for medical staff by effectively reducing the number of suspended droplets.19 Even for bacteria-carrying particles generated by moving individuals, walking can entrain and capture them. The lower the walking speed, the higher the infection risk.27,28 However, Liu et al.29 showed that increased walking speed enhances the disturbance of the airflow, suggesting that circulating nurses should walk at a lower speed.

The effect of walking on droplet dispersion is also related to the interactive human movement.30–32 Human movement can significantly disturb the respiratory airflow of nearby stationary individuals. Some droplets exhaled by stationary individuals are wrapped in the wake, enhancing long-range airborne transmission.30,31 The airflow induced by the movement of multiple individuals is more complex than that induced by a single person. The arrangement of moving individuals, such as a ladder or side-by-side distribution, can enhance the mixing of the wake and lateral droplet dispersion.26 Another form of interactive human movement is when individuals walk in a queue. In this case, the droplets exhaled by walking individuals move behind them and are further affected by the wake. Li et al.33 proposed that the droplet dispersion behind an infectious source could be categorized into two modes: the attached mode and the detached mode. The detached mode was formed with high walking speed and limited space, while the attached mode was prevalent in other cases. Zhao et al.32 studied the effects of windward, leeward, and crosswind conditions on the dispersion of droplets exhaled by queuing individuals and emphasized that droplets mainly affected individuals behind infectious source during walking. Li et al.34 mentioned the infection risk of susceptible individuals behind the infection source when riding the escalator. However, the presence of this susceptible individual was fictitious in the study. In order to fully consider the interference of the rear susceptible individual to the wake, Takii et al.35 studied the scenario where ten or five individuals walked in a queue to take the escalator and found that the ascending escalator brought higher exposure risk than the descending escalator.

As mentioned above, the mechanism of droplet dispersion in static environments has been well explored, while little research has been conducted on droplet dispersion in dynamic environment of human movement, especially when walking in a queue. The droplet dispersion in a queue is not well understood yet. Walking in a queue is a common occurrence in daily life, such as waiting for trains in queue at stations, queuing for examination at hospitals, and queuing for shopping at malls. Especially during respiratory infectious diseases outbreaks, individuals are often required to walk in a queue maintaining a certain distance. However, the effect of human behaviors during queue walking has not been focused on. Therefore, it is still impossible to give appropriate recommendations or policies for queue walking scenarios. Further exploration is needed to determine the safe distance and recommended walking speed for individuals walking in a queue.

In this study, the airflow field and droplet dispersion induced by two individuals walking in a queue in a closed room were numerically simulated using ANSYS Fluent. To investigate the coupling effect of wake vortex and forward airflow on droplet dispersion, there was no ventilation system in the closed room. The primary focus of this paper is to examine the effect of different following distances (1.0, 1.5, 2.0, and 2.5 m), walking speeds (0.8, 1.0, 1.2, and 1.4 m/s), and droplet diameters (1, 10, 50, 80, and 120 μm) on the exposure risk of the susceptible individual. The obtained results aim to provide valuable insight for the control and mitigation of respiratory infectious diseases within indoor environments.

In this study, a closed room model with the size of 20 × 6 × 4 m3 was established, as shown in Fig. 1(a). Two humans with a height of 1.75 m were positioned in the room. The susceptible individual (depicted in blue) followed the infectious source (depicted in red) at a distance of D m, walking forward at the same speed v m/s as the infectious source. The walking movement was simplified without considering the effect of arm and leg swing on droplet dispersion. Notably, droplets within a spherical region with a radius of 0.1 m in front of the human face were considered to be directly inhaled. The computational domain mesh was constructed with unstructured tetrahedral cells, as shown in Fig. 1(b). Sufficiently fine cells were arranged in the region near the human body to capture detailed airflow dynamics.

FIG. 1.

(a) Computational domain of two individuals standing in a room. The global origin (x, y, z = 0 m) is between the two heels of the infectious source. At this time, the coordinates of the mouth center of the infectious source are (0, 0.067, and 1.535). (b) Mesh details of 3.70 × 106 cells at plane x = 0 m.

FIG. 1.

(a) Computational domain of two individuals standing in a room. The global origin (x, y, z = 0 m) is between the two heels of the infectious source. At this time, the coordinates of the mouth center of the infectious source are (0, 0.067, and 1.535). (b) Mesh details of 3.70 × 106 cells at plane x = 0 m.

Close modal
To predict the airflow in the room, an incompressible Reynolds-averaged Navier–Stokes model, Re-Normalization Group (RNG) kɛ model was adopted. The RNG kɛ model is the most commonly used turbulence model to calculate the airflow in enclosed environment.36,37 For the RNG k-ɛ model, the transport equations of turbulent kinetic energy k and dissipation rate ɛ are expressed as
( ρ k ) t + ( ρ k u i ) x i = x j ( α k μ eff k x j ) + G k + G b ρ ε + S k ,
(1)
( ρ ε ) t + ( ρ ε u i ) x i = x j ( α ε μ eff ε x j ) + C 1 ε ε k ( G k + C 3 ε G b ) C 2 ε ρ ε 2 k C μ ρ η 3 ( 1 η / η 0 ) 1 + β η 3 ε 2 k + S ε ,
(2)
where ρ is the air density; u i is the velocity component; α k and α ε are the inverse effective Prandtl numbers for k and ɛ, respectively; μ eff is the effective viscosity coefficient; G k and G b are the generation of k due to the mean velocity gradients and buoyancy, respectively; S k and S ε are user-defined source terms; C 1 ε, C 2 ε, C 3 ε, C μ, η 0 and β are constants; and η = S k / ε.
For the droplets, the Lagrangian approach was used to track the movement of released droplets by solving the force balance on the droplets. For a droplet, the force balance equation can be expressed as
u p t = F D ( u u p ) + g ( ρ p ρ ) ρ p + F a ,
(3)
where u and u p are the air velocity and droplet velocity, respectively; F D ( u u p ) is the drag force per unit droplet mass; ρ p is the droplet density; and F a is the additional force per unit mass. In the present study, the Saffman's force and thermophoretic force are incorporated into the analysis. The Saffman's force is expressed as 2 K ν 1 / 2 ρ d i j ρ p d p ( d l k d k l ) 1 / 4 ( u u p ), while the thermophoretic force is expressed as 6 π d p μ 2 C s ( K + C t K n ) ρ ( 1 + 3 C m K n ) ( 1 + 2 K + 2 C t K n ) m p T. K = k a / k p, k a, and k p are the air thermal conductivity and droplet thermal conductivity, respectively; d i j is the deformation tensor; d p is the droplet diameter; μ is the air viscosity; K n is the Knudsen number; m p is the droplet mass; T is the local air temperature; C s, C t, and C m are constants with values 1.17, 2.18, and 1.14, respectively.
The evaporation effect is also important for droplet dispersion. In this study, the heat and mass transfer phenomena of droplets were numerically simulated by solving the heat balance equation of droplets. The heat balance equation can be expressed as
m p c p d T p d t = h p A p ( T T p ) d m p d t h f g ,
(4)
where c p is the droplet heat capacity; T p is the droplet temperature; h p is the convection heat transfer coefficient between droplet and air; A p is the droplet surface area; and h f g is the latent heat.
The evaporation rate of droplets can be expressed as
d m p d t = k c A p ρ p ln ( 1 + B m ) ,
(5)
where k c is the mass transfer coefficient and B m is given by
B m = C s C 1 C s ,
(6)
where C s is the mass fraction of water vapor on the droplets surface and C is the water vapor mass fraction in the air. The validation study of the Lagrangian approach and the evaporation model is presented in the  Appendix.
In order to simulate human walking, it is necessary to use dynamic mesh method. For dynamic meshes, the integral form of the conservation equation for a general scalar ϕ on any control volume V with moving boundary can be written as
d d t V ρ ϕ dV + V ρ ϕ ( u u g ) d A = V Γ ϕ d A + V S ϕ d V ,
(7)
where u is the flow velocity vector; u g is the mesh velocity of the moving mesh; Γ is the diffusion coefficient; S ϕ is the source term of ϕ; and V is used to represent the boundary of the control volume. In this study, smoothing and remeshing methods were used to modify the volume mesh of the deforming region during human walking. The methods have been widely applied to realize human movement.29,30

In this study, no-slip wall boundaries were used for all walls and human surfaces in the computational domain. The temperature of the walls was 293.15 K, while the surface temperature of the human body was set to 304.15 K. According to the previous research,38,39 the breathing process was simplified in this paper. The infectious source was modeled as continuous exhalation with an exhalation speed of 1.25 m/s and an exhalation temperature of 306.15 K, while the susceptible individual was assumed to continue inhaling with an inhalation speed of –1.25 m/s. The droplets exhaled by the infectious source were considered to be composed of water and nonvolatile sodium chloride, with a density of 1010 kg/m3. The droplet mass flow rate was 6.35 × 10−13 kg/s. For all walls and human surfaces, the trap condition was applied, while the escape condition was applied to the mouths of both the infectious source and the susceptible individual. To investigate the effects of following distance, walking speed, and droplet diameter on droplet exposure, a total of eleven cases were calculated in this study, as summarized in Table I. Cases 1–4 focused on the effect of following distance, cases 2, 5–7 studied the effect of walking speed, and cases 2, 8–11 investigated the effect of droplet diameter.

TABLE I.

The list of the cases conducted in this paper.

Case number Following distance D (m) Walking speed v (m/s) Droplet diameter dp (μm)
Case 1  1.2 
Case 2  1.5  1.2 
Case 3  1.2 
Case 4  2.5  1.2 
Case 5  1.5  0.8 
Case 6  1.5  1.0 
Case 7  1.5  1.4 
Case 8  1.5  1.2  10 
Case 9  1.5  1.2  50 
Case 10  1.5  1.2  80 
Case 11  1.5  1.2  120 
Case number Following distance D (m) Walking speed v (m/s) Droplet diameter dp (μm)
Case 1  1.2 
Case 2  1.5  1.2 
Case 3  1.2 
Case 4  2.5  1.2 
Case 5  1.5  0.8 
Case 6  1.5  1.0 
Case 7  1.5  1.4 
Case 8  1.5  1.2  10 
Case 9  1.5  1.2  50 
Case 10  1.5  1.2  80 
Case 11  1.5  1.2  120 

In the study, the numerical simulation was conducted using the SIMPLE (Semi-Implicit-Method for Pressure Linked Equations) scheme for pressure–velocity coupling. The SIMPLE scheme uses the relationship between pressure and velocity corrections to enforce mass conservation and obtain the pressure field. The least squares cell-based method was employed for gradient discretization. The PRESTO! (Pressure Staggering Option) was used for pressure. For tetrahedral meshes in this study, comparable accuracy is obtained using it. To establish the initial conditions for droplet dispersion, a steady-state calculation was performed to obtain the stable distribution of air velocity and temperature. The droplet dispersion was simulated using transient calculations, which included both the standing process and the walking process. In the standing process, the two individuals stood still for 5 s, during which the infectious source continuously exhaled droplets. In the walking process, the infectious source and the susceptible individual walked forward together for 5 s, during which the infectious source continued to exhale droplets.

Mesh size is important for accurately predicting the short-term dispersion of violent respiratory events.40 In order to ensure the accuracy of the computational results, the mesh independence test was conducted with the following distance of 1.5 m. Three different mesh configurations were tested, consisting of 1.65 × 106, 3.7 × 106, and 7.5 × 106 cells. To evaluate the effect of mesh density on the simulation results, the variation of airflow velocity along the horizontal line at z = 1.2 and z = 1.7 m at the time of walking for 2.5 s was analyzed, as shown in Fig. 2. As depicted in the figures, the calculation results of the 3.7 × 106 cells and 7.5 × 106 cells were essentially the same. Therefore, the mesh with 3.7 × 106 cells was chosen for the calculations presented in this paper, as it provided a good balance between computational efficiency and accuracy.

FIG. 2.

Variation of airflow velocity along lines of (a) X = 0 m, Y = 0 m to 4 m, and Z = 1.2 m and (b) X = 0 m, Y = 0 m to 4 m, and Z = 1.7 m.

FIG. 2.

Variation of airflow velocity along lines of (a) X = 0 m, Y = 0 m to 4 m, and Z = 1.2 m and (b) X = 0 m, Y = 0 m to 4 m, and Z = 1.7 m.

Close modal

In this study, the analysis primarily focuses on the variation of airflow velocity on the vertical middle plane. Figure 3 shows the velocity field and vector field on the vertical middle plane when the following distance is 1.5 m and the walking speed is 1.2 m/s.

FIG. 3.

Velocity field and vector field on the vertical middle plane (X = 0 m) at (a) t = 5, (b) t = 5.5, (c) t = 6.0, (d) t = 6.5, (e) t = 7.0, and (f) t = 7.5 s.

FIG. 3.

Velocity field and vector field on the vertical middle plane (X = 0 m) at (a) t = 5, (b) t = 5.5, (c) t = 6.0, (d) t = 6.5, (e) t = 7.0, and (f) t = 7.5 s.

Close modal

As depicted in Fig. 3(a), when the two individuals are stationary, it can be found that there is an obvious thermal plume around the human body. The velocity of the thermal plume reaches 0.2–0.4 m/s, which is similar to the previous findings by Licina et al.41 Once the two individuals begin to walk, the air in front of them is pushed forward, while the following airflow is generated behind them. The velocity of the forward airflow remains relatively low, around 0.2–0.4 m/s in most regions, while the wake velocity reaches 1.6–1.8 m/s. Notably, there is a peak velocity near the back of the human body, as also observed by Tao et al.23 At the same time, under the effect of the pressure difference between front and back, the wake vortex from front to back is generated during walking. According to Figs. 3(c)–3(f), due to the effect of the following airflow and the forward airflow generated by the susceptible individual, the vortex turns back and flows toward the posterior region of the human body. The height at which the wake vortex can descend depends on the walking speed and the following distance, which will be further discussed in subsequent analysis. Notably, when the following distance is 1.5 m, the wake vortex generated by the infectious source can even reach the rear of the susceptible individual. This means that the susceptible individual is enveloped within the wake vortex, potentially increasing the infection risk. Moreover, the velocity contours indicate that the effect of walking on the indoor air cannot be recovered in a short time, which may lead to an increased dispersion range of droplets. Wu et al.30 found that the duration of induced airflow could exceed 20 s, emphasizing the prolonged effects of walking on the air movement.

To analyze the effect of walking on indoor airflow velocity and disturbance range, Fig. 4 compares the variation of airflow velocity along horizontal lines on the middle plane at the height of z = 1.2 m after the two individuals have walked for 2.5 s under different following distances (the fixed walking speed is 1.2 m/s) and walking speeds (the fixed following distance is 1.5 m). The red and blue mannequins represent the position of the infectious source and the susceptible individual, respectively.

FIG. 4.

Variation of airflow velocity along lines of X = 0 m, Y = 0 m to 4 m, and Z = 1.2 m at t = 7.5 s. (a) Different following distances with the fixed walking speed of 1.2 m/s. (b) Different walking speeds with the fixed following distance of 1.5 m.

FIG. 4.

Variation of airflow velocity along lines of X = 0 m, Y = 0 m to 4 m, and Z = 1.2 m at t = 7.5 s. (a) Different following distances with the fixed walking speed of 1.2 m/s. (b) Different walking speeds with the fixed following distance of 1.5 m.

Close modal

In Fig. 4(a), the disturbance of airflow varies depending on the following distance. When the following distance is 1.0 m, the airflow fluctuation between the two individuals is higher than other cases due to the interaction between the wake induced by the infectious source and the forward airflow generated by the susceptible individual. At this time, there is one trough in the airflow velocity between the individuals. As the following distance increases, the effect of the infectious source's wake on the susceptible individual gradually weakens. An additional trough appears between the two individuals. Moreover, according to the variation of airflow velocity behind the susceptible individual, it can be found that when the following distance is 1.0 m, the airflow behind the susceptible individual initially increases and then decreases in the direction away from the individual. There is no airflow fluctuation phenomenon, indicating that the airflow behind the susceptible individual is still affected by the wake of the infectious source. When the following distance is 2.0 m and 2.5 m, the airflow behind the susceptible individual show fluctuations. However, when the following distance is 1.5 m, the fluctuation is not as pronounced, suggesting that the distance of 1.5 m represents a transitional stage.

According to Fig. 4(b), the walking speed has a great effect on the airflow fluctuation between the two individuals. When the speed is low (0.8 and 1.0 m/s), there is a peak and a trough in the airflow between the infectious source and the susceptible individual. As the walking speed increases to 1.2 m/s and 1.4 m/s, the airflow movement between the two individuals becomes more complex, with three peaks and two troughs.

Figure 5 (Multimedia view) illustrates the distribution of 1 μm droplets exhaled by the infectious source when the following distance is 1.5 m and the walking speed is 1.2 m/s.

FIG. 5.

Distribution of 1 μm droplets exhaled by the infectious source with following distance of 1.5 m and walking speed of 1.2 m/s at (a) t = 1.0, (b) t = 2.0, (c) t = 3.0, (d) t = 4.0, (e) t = 5.0, (f) t = 5.5 (g) t = 6.0, (h) t = 6.5, (i) t = 7.0, (j) t = 7.5, (k) t = 8.0, (l) t = 8.5, (m) t = 9.0, (n) t = 9.5, and (o) t = 10.0 s. Multimedia available online.

FIG. 5.

Distribution of 1 μm droplets exhaled by the infectious source with following distance of 1.5 m and walking speed of 1.2 m/s at (a) t = 1.0, (b) t = 2.0, (c) t = 3.0, (d) t = 4.0, (e) t = 5.0, (f) t = 5.5 (g) t = 6.0, (h) t = 6.5, (i) t = 7.0, (j) t = 7.5, (k) t = 8.0, (l) t = 8.5, (m) t = 9.0, (n) t = 9.5, and (o) t = 10.0 s. Multimedia available online.

Close modal

As shown in Figs. 5(a)–5(e), when the infectious source is stationary, the exhaled droplets are captured by the human thermal plume and disperse continuously upward. Under the windless condition, these droplets cannot affect the susceptible individual walking behind the infectious source. When people start walking, some droplets that have dispersed above the height of the human body are induced by the wake vortex and descend to the rear of the infectious source. Figure 5(h) demonstrates the initial formation of a droplet vortex. As the droplet vortex rotates, it is continuously elongated to form an “ellipse”, with fewer droplets in the center and more droplets at the periphery. The forward airflow below the waist height moves downward under the effect of the infection source and the backward airflow between his legs. Therefore, the droplets located in the peripheral region below the droplet vortex are affected by this airflow, causing them to exit the wake vortex and descend further.

In fact, droplets experience various forces in the air, including gravity, drag force, buoyancy, and inertia force. These forces contribute to the differences in droplet dispersion. The magnitude of these forces is closely related to the airflow velocity around the droplets and the droplet diameter. The details of droplet dispersion under different cases are shown in the supplementary material.

In this paper, the dispersion of droplets at different following distances is predicted when the walking speed is 1.2 m/s and the droplet diameter is 1 μm. Figure 6 depicts the effect of the following distance on droplet exposure. Figure 7 shows the vorticity contours induced by human walking at different following distances. It is worth noting that this paper divides the walking process into two stages. The first stage represents the queue walking from stop to start, and the second stage is continuous queue walking.

FIG. 6.

Average droplet concentration in the breathing zone of the susceptible individual under different following distances with the walking speed of 1.2 m/s and the droplet diameter of 1 μm.

FIG. 6.

Average droplet concentration in the breathing zone of the susceptible individual under different following distances with the walking speed of 1.2 m/s and the droplet diameter of 1 μm.

Close modal
FIG. 7.

Vorticity contours at t = 7.5 s for (a) D = 1.0, (b) D = 1.5, (c) D = 2.0, and (d) D = 2.5 m.

FIG. 7.

Vorticity contours at t = 7.5 s for (a) D = 1.0, (b) D = 1.5, (c) D = 2.0, and (d) D = 2.5 m.

Close modal

As shown in Fig. 6, there is a peak in the concentration of droplets in the breathing zone of the susceptible individual during the first stage, occurring near the initial position of the infectious source. During this stage, the concentration in the breathing zone is mainly affected by the droplets exhaled by the infectious source while standing. Before the start of walking, the exhaled droplets cannot be carried away in time by the human thermal plume. The droplets that disperse to a certain height are subsequently drawn downward by the vortex after walking, resulting in a higher infection risk when the susceptible individual walk near the initial position of the infectious source.

In the second stage, the concentration in the breathing zone of the susceptible individual show fluctuations. The droplets exhaled by the infectious source form a droplet vortex between the two individuals due to the effect of human walking. Before the susceptible individual first contacts the droplet vortex, the droplet vortex develops continuously, and the droplet concentration in the center of the droplet vortex is low. Hence, when the susceptible individual is exposed to the droplet vortex, the concentration in the breathing zone initially increases, then decreases in the middle of the droplet vortex, and increases again when moving to the periphery of the droplet vortex. Overall, the infection risk of the susceptible individual is higher in the first stage compared to the second stage.

Furthermore, the concentration in the breathing zone of the susceptible individual initially increases and then decreases with the increase in the following distance in the first stage. The following distance of 1.5 m results in the highest infection risk. Even in the second stage, the concentration at the following distance of 1.5 m is comparable to that at the following distance of 1.0 m. It can be seen from Fig. 7 that when the following distance is 1.0 m, the wake vortex generated by the infectious source fails to develop fully due to the distance between the two individuals, and the lateral length of the wake vortex is 0.858 m. As the following distance increases to 1.5 m, the wake vortex fully develops up to a length of 1.079 m. The lengthening of the wake vortex length means that its area increases. The influence range of the wake vortex expands. Therefore, the number of droplets drawn downward increases with the increase in the following distance, resulting in a higher concentration at the following distance of 1.5 m compared to 1.0 m. As the distance further increases to 2.0 and 2.5 m, the lateral length of the wake vortex behind the infectious source is reduced because the enhancement effect of the forward airflow on the wake vortex weakens. This reduction in the ability to draw in droplets and the increased space and time for droplet dispersion between the two individuals leads to a gradual decrease in concentration with increasing distance. Based on the analysis, the social distance of 1.0 m is not sufficient to reduce cross-infection among individuals and the social distance of 1.5 m can even increase the infection risk of susceptible individuals.

Figure 8 illustrates the effect of walking speed on droplet exposure. At this time, the fixed values of following distance and droplet diameter are 1.5 m and 1 μm, respectively. As shown in the figure, the peak concentration in the breathing zone of the susceptible individual does not increase monotonically with the increase in the walking speed in the first stage. Instead, it decreases at the walking speed of 1.4 m/s. Figure 9 shows the vorticity contours induced by human walking at different speeds. The wake vortex intensity increases with the walking speed, resulting in a greater ability to draw in droplets. Additionally, faster walking speeds allow the susceptible individual to reach the corresponding position in less time, leaving little time for droplet dispersion. This leads to an increase in the concentration with the increase in the walking speed. However, at even faster speeds, the forward airflow near the head of the susceptible individual blew away some droplets that moved downward induced by the wake vortex. Therefore, the peak concentration in the breathing zone of the susceptible individual decreased at the walking speed of 1.4 m/s. This forward airflow also makes the downward moving droplets stay at the mouth height of the susceptible individual for a long time. As a result, there are two high concentration points when the walking speed is 1.4 m/s. Taking into account the total accumulation of suspended droplets in the breathing zone during the first stage, it can be observed that the infection risk increases with walking speed.

FIG. 8.

Average droplet concentration in the breathing zone of the susceptible individual under different walking speeds with the following distance of 1.5 m and the droplet diameter of 1 μm.

FIG. 8.

Average droplet concentration in the breathing zone of the susceptible individual under different walking speeds with the following distance of 1.5 m and the droplet diameter of 1 μm.

Close modal
FIG. 9.

Vorticity contours at t = 7.5 s for (a) v = 0.8, (b) v = 1.0, (c) v = 1.2, and (d) v = 1.4 m/s.

FIG. 9.

Vorticity contours at t = 7.5 s for (a) v = 0.8, (b) v = 1.0, (c) v = 1.2, and (d) v = 1.4 m/s.

Close modal

In the second stage, a significant increase in the breathing zone concentration occurs as walking speed decreases. Slower walking speeds result in shorter longitudinal lengths of the wake vortex and shorter settling distances for droplets under the action of the wake vortex. Moreover, slower speeds allow droplets that were originally below the breathing zone to have time to suspend again, so that more droplets are concentrated at the height of the breathing zone. Figure 10 compares the average height of suspended droplets between the infectious source and the susceptible individual at different walking speeds. At the walking speed of 0.8 m/s, the average height of droplets between the two individuals is 1.5 m, close to the height of human mouth. With the walking speed increasing, the average height of droplets gradually decreases. Furthermore, slower walking speeds result in weaker forward airflow in the front of the susceptible individual, insufficient to blow away droplets between the two individuals. In contrast, it can be seen from the droplet distribution shown in Fig. 10 that when the susceptible individual contacts the droplet vortex at the walking speed of 1.2 m/s, most droplets are still suspended below the breathing zone. As the walking speed increases to 1.4 m/s, the forward airflow blows away the droplets between the two individuals.

FIG. 10.

Average height of suspended droplets between the infectious source and the susceptible individual at t = 9.5 s. The corresponding droplet distribution is shown in the dotted box.

FIG. 10.

Average height of suspended droplets between the infectious source and the susceptible individual at t = 9.5 s. The corresponding droplet distribution is shown in the dotted box.

Close modal

Figure 11 depicts the effect of droplet diameter on droplet exposure. In this section, the following distance is 1.5 m and the walking speed is 1.2 m/s. From Fig. 11, it is observed that the concentration in the breathing zone of the susceptible individual first rises and then declines as the droplet diameter increases. However, there are different inflection points in the two stages, occurring at 80 μm and 50 μm, respectively. Intermediate-sized droplets are subject to more complex forces, whereas small droplets are mainly affected by airflow. Therefore, the variation in concentration is essentially similar for the droplet diameters of 1 and 10 μm.

FIG. 11.

Average droplet concentration in the breathing zone of the susceptible individual under different droplet diameters with the following distance of 1.5 m and the walking speed of 1.2 m/s.

FIG. 11.

Average droplet concentration in the breathing zone of the susceptible individual under different droplet diameters with the following distance of 1.5 m and the walking speed of 1.2 m/s.

Close modal

Furthermore, in the first stage, when the droplet diameters are 50 and 80 μm, the concentration in the breathing zone of the susceptible individual increases by thirty and seventy times, respectively, compared to droplets with diameters of 1 and 10 μm. This significant increase in concentration can be attributed to the enhanced effect of gravity as the droplet diameter increases, resulting in a slower floating speed for the droplets. Consequently, when the susceptible individual walks to the initial position of the infection source, a considerable number of droplets still remain in his breathing zone. From Fig. 12, it can be seen that when the susceptible individual reaches the initial position of the infectious source, the average height of 1 and 10 μm droplets is higher than the height of the mouth, and their overall quantity is relatively less.

FIG. 12.

Average height and number of suspended droplets between the infectious source and the susceptible individual at t = 6.25 s, which is the time when the susceptible individual walks to the initial position of the infectious source.

FIG. 12.

Average height and number of suspended droplets between the infectious source and the susceptible individual at t = 6.25 s, which is the time when the susceptible individual walks to the initial position of the infectious source.

Close modal

Interestingly, in the second stage, the effect of droplet vortex on the susceptible individual disappears for the droplets with the diameter of 80 μm. With increasing droplet diameter, the drag force and gravity become stronger. The droplet vortex, driven by the forward airflow, has a small range and primarily disperses in the shoulder and lower regions of the human body. Therefore, when the exhaled droplets are 80 μm, the infection risk of the susceptible individual is reduced during subsequent walking in a queue, even lower than that posed by 1 and 10 μm droplets. However, when the droplet diameter is 50 μm, the concentration in the breathing zone of the susceptible individual remains higher than that of 1 and 10 μm droplets. The gravity of 50 μm droplets is greater than that of 1 and 10 μm droplets. Therefore, 50 μm droplets are more likely to fall and less likely to float. When affected by the wake, the number of droplets being drawn downward can increase. Consequently, the infection risk when the susceptible individual contacts the droplet vortex is higher.

It is worth noting that when the droplet diameter is 120 μm, the concentration in the breathing zone of the susceptible individual remains consistently zero throughout the process. This is primarily because the droplets are strongly affected by gravity and immediately settle after being exhaled. Some droplets may become trapped by the body of the infectious source, while the remaining droplets settle to the ground. Figure 12 illustrates that when the droplet diameter is 120 μm, the number of droplets between the two individuals decreases significantly. The settling behavior of droplets larger than 100 μm is similar to the research findings of Trivedi,42 Wei,43 and Liu44 regarding stationary states of individuals.

This study aims to explore two scenarios: the cycle of standing and walking, and continuous walking in a queue. It is necessary to examine these scenarios since the cycle of standing and walking always occurs in many events such as checkout processes in shopping malls or ticket checking processes in waiting rooms. The above-mentioned analysis demonstrates that the cycle of standing and walking poses a higher infection risk compared to continuous walking in a queue. The following distance between the two individuals seems to have a similar effect in both stages. However, walking speed and droplet diameter have different effects on the concentration in the breathing zone during these two stages. In addition, the social distance of 1.5 m did not produce good results in these two stages. The risk of infection also increases significantly during the continuous queue walking stage when the walking speed is slowed down. The following distance of 1.5 m cannot mitigate the effect of intermediate-sized droplets. Therefore, in the queue walking scenario, the following distance needs to be larger. Based on the research findings, it may be possible to provide more scientific and effective epidemic prevention measures for the scenario of walking in a queue. For example, the recommended following distance should be at least two meters.

In this study, the velocity field and droplet dispersion during the two individuals walking in a queue are investigated under windless conditions. In fact, there is generally an air conditioning system running and providing a certain background wind speed indoors. Especially during respiratory infectious disease epidemics, measures to increase ventilation rate are often taken to reduce the risk of cross-infection. These circumstances necessitate consideration of the background wind speed. However, it is important to note that the walking direction of individuals in a queue is generally random, except for specific instances such as queueing for checkout or ticket check-in. Therefore, it is not feasible to precisely define the background airflow direction in the research process. By conducting the study under windless conditions, the interaction between wake vortex and forward airflow can be more clearly observed. This is advantageous for understanding droplet dispersion during human walking in a queue. Furthermore, the findings from windless conditions can provide valuable insight for windy conditions. For example, it has been found that the recommended safe distance of 1.0 m may not effectively reduce the infection risk in windless conditions. The situation could be even more severe in windward conditions, indicating that a further social distance is necessary. In contrast, leeward and crosswind conditions are effective in dispersing droplets suspended between the infectious source and the susceptible individual, thereby reducing the risk of cross-infection during walking in a queue. Based on the research findings, a bottom-up background airflow is recommended. Implementing a bottom-up airflow can weaken the wake vortex induced by walking and reduce the number of droplets that would be drawn downward.

The investigation of droplet diameter reveals that the infection risk associated with large droplets during walking in a queue is negligible, indicating a lack of droplet transmission. In contrast, intermediate-sized and small droplets play a critical role in the transmission of respiratory infectious diseases, underscoring the significance of aerosol transmission that cannot be ignored. The force exerting on intermediate-sized droplets is more complex. This complexity makes the control of intermediate-sized droplets more challenging. The study emphasizes the importance of wearing masks during an epidemic. Researches conducted by Liu17 and Coyle45 indicate that wearing a mask can reduce the diameter of droplets released into the air to approximately 1 μm. The infection risk caused by small droplets during walking in a queue is 3.3%–1.4% of that caused by intermediate-sized droplets, even without considering the effective reduction in the number of droplets leaking into the air due to mask usage. In addition, considering the importance of droplet diameter, the formation mechanism of droplets in respiratory tract needs to be further explored. With the development of computational fluid dynamics, abundant theories46 and related numerical studies47,48 on droplet formation provide the possibility for the study of the coupling between respiratory tract and indoor space.

In this study, the validated droplet evaporation dispersion model and the dynamic mesh method were used to obtain the airflow field and droplet distribution caused by human walking in a queue. The analysis focused on the interaction between the wake vortex and the forward airflow, with the aim of exploring the effect of various factors such as following distances, walking speeds, and droplet diameters on the infection risk of the susceptible individual. The main conclusions are as follows:

  1. Human walking obviously disturbs the local velocity field, generating forward airflow in front and a wake behind the body. A front-to-back vortex is formed above the body due to the pressure difference. The airflow between the two individuals is significantly affected by the following distance and walking speed. Shorter distances and faster speeds result in complex fluctuations of airflow velocity.

  2. The concentration in the breathing zone of the susceptible individual initially increases and then decreases as the following distance increases. This trend is related to the intensity of the wake vortex between the two individuals. At the following distance of 1.5 m, the wake vortex reaches its full development with a length of 1.079 m, resulting in an increased number of induced droplets. The research results indicate that the social distance of 1.0 m is insufficient to effectively reduce cross-infection and the social distance of 1.5 m may even increase the infection risk of the susceptible individual. The recommended walking distance in a queue should be at least two meters.

  3. The effect of walking speed on the infection risk of the susceptible individual depends on queuing scenarios. In scenarios involving alternating cycles of standing and walking, the infection risk gradually rises as walking speed increases. However, in continuous queue walking scenarios, the infection risk decreases with the increase in the walking speed.

  4. As droplet diameter increases, the concentration in the breathing zone of the susceptible individual first rises and then decreases. Small droplets are more significantly affected by airflow, easily floating up with the human thermal plume and being induced when the thermal plume is destroyed by wake vortex disruptions. Intermediate-sized droplets are strongly affected by gravity. Therefore, during alternating cycles of standing and walking, intermediate-sized droplets cause virus concentrations surpassing small droplets by 30 to 70 times. However, the rapid settlement of large droplets has minimal effect on the susceptible individual following behind.

See the supplementary material for the details of droplet dispersion under different cases.

The authors would like to acknowledge the support provided by the Research Fund of Key Laboratory of Aircraft Environment Control and Life Support, MIIT, Nanjing University of Aeronautics and Astronautics (Grant No. KLAECLS-E-202201).

The authors have no conflicts to disclose.

Benben Kong: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Writing – original draft (equal). Yu Li: Formal analysis (equal); Investigation (equal); Validation (equal); Writing – review & editing (equal). Mengmeng Cheng: Validation (equal); Writing – review & editing (equal). Caiyue Song: Writing – review & editing (equal). Yitao Zou: Writing – review & editing (equal). Hong Shi: Conceptualization (equal); Funding acquisition (equal); Methodology (equal); Supervision (equal); Writing – review & editing (equal). Yanlong Jiang: Conceptualization (equal); Methodology (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal).

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

The mathematical model used was validated by comparing the computational results with the experimental data conducted by Lu et al.49 The experiment was performed in a two-zone room with internal circulation, as depicted in Fig. 13. The room dimensions were 5 × 2.4 × 3 m3. The air supply diffuser and the air exhaust diffuser were, respectively, arranged on the sidewall of zone 1 and zone 2. The air change rate per hour (ACH) was set to 9.216 h−1. To conduct the experiment, smoke particles with a density of 865 kg/m3 and sizes ranging from 1 to 5 μm were injected and evenly distributed in zone 1. Subsequently, these particles were dispersed into zone 2 through the supplied fresh air and eventually discharged through the exhaust diffuser. Figure 14 compares the present study results with the experimental and simulation data of Lu et al. As can be seen, the present computational results show a good agreement with the mentioned experiment.

FIG. 13.

The schematic of the two-zone room and initial positions of sample droplets.49 

FIG. 13.

The schematic of the two-zone room and initial positions of sample droplets.49 

Close modal
FIG. 14.

Comparison between the present computations and data of Lu et al.

FIG. 14.

Comparison between the present computations and data of Lu et al.

Close modal

Furthermore, to validate the evaporation model used, the computational results were compared with the experimental data obtained by Hamey.50 Hamey studied the evaporation process of free-falling droplets in windless environment. The comparisons of present computational results with experimental data are shown in Fig. 15. The prediction of the evaporation model used agrees well with the experimental data.

FIG. 15.

Comparison of the present computational droplet diameter change and the experimental data obtained by Hamey. The free-falling droplet temperature is 289 K. The air temperature and humidity are 293 K and 70%, respectively.

FIG. 15.

Comparison of the present computational droplet diameter change and the experimental data obtained by Hamey. The free-falling droplet temperature is 289 K. The air temperature and humidity are 293 K and 70%, respectively.

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Supplementary Material