## 3 Results and Discussion  
### Effect of Various Initial Conditions on Droplet Diffusion  
To comprehensively reveal the movement patterns of droplets inside the subway carriage, this study considered some primary factors, including the initial droplet size, release location, release velocity (corresponding to different breathing activities), passenger density, and _RH_. The airflow primarily influences the dispersion and movement of the droplets within the carriage. As shown in Figure 6, three cross-sections (y = 1.29 m, x = 2.95 m, and x = 5.93 m) are selected to show the flow field characteristics inside the carriage. Figure 7 illustrates the flow field inside the carriage when the passenger density is 2 p/m\({}^{2}\). Figure 8 presents the diffusion characteristics of the droplets under different initial conditions under this flow field. Figure 5: Droplet evaporation validation. The ventilation mode significantly influences the air distribution in enclosed spaces [71; 72]. The overall flow field characteristics inside the subway carriage are depicted in Figure 7a. Due to the return air volume inside the carriage accounting for a large proportion of the total supply air volume, the two centralized return air vents dominate the airflow movement. The airflow primarily moves toward these two centralized return air vents, creating a noticeable longitudinal flow (x-direction) between pillars a and c. Under this airflow pattern, the droplets released by the infected passenger at position D1 tend to move toward return air vent I, as shown in Figure 8. However, several passengers standing near pillars a and c obstruct the airflow movement, resulting in the airflow near two ends of the carriage not flowing noticeably toward the nearest return air vent. Figure 7b displays a cross-sectional airflow field at the location of the infected passenger (D1). The airflow generated by the infected passenger's mouth interacts with the downward airflow from the supply air grille, forming a strong counterclockwise vortex between the infected passenger and the right-side wall (y = 2.5 m). The movement characteristics of the released droplets are closely related to this counterclockwise vortex. Figure 7c shows the airflow field around return air vent I. The flow velocity near return air vent I exceeds 1m/s and the airflow within this section all flows toward the return air vent. Figure 6: The schematic of selected planes: (**left**) y = 1.29 m; (**middle**) x = 2.95 m; (**right**) x = 5.93 m.  
Figure 7: The airflow distribution within the carriage under passenger density 2 p/m\({}^{2}\): (**a**) plane y = 1.29 m; (**b**) plane x = 2.95 m; (**c**) plane x = 5.93 m.  
Figure 8: Droplet diffusion inside the carriage at different times: (**a**) case 1; (**b**) case 2; (**c**) case 3; (**d**) case 4; (**e**) case 5. Many studies have reported on the influence of the initial droplet size on the diffusion of droplets in different settings [23; 28; 33; 72; 73; 23], and the consensus is that the droplets' size determines the diffusion process's dominant force. Figure 8a-c show the diffusion processes of droplets of three different initial sizes (10 \(\upmu\)m, 50 \(\upmu\)m, and 100 \(\upmu\)m). Under the same \(RH\) condition, droplets of smaller sizes require less time to complete the evaporation process [41]. During the evaporation process, the volume of droplets decreases to around 2% of the original volume after complete evaporation [29]. Small droplets are more susceptible to the influence of the airflow during their movement, and the diffusion range of 10 \(\upmu\)m and 50 \(\upmu\)m droplets is much larger than that of 100 \(\upmu\)m droplets. The 10 \(\upmu\)m droplets tend to follow the airflow inside the carriage within 0-10 s after release (as shown in Figure 7b). Although the diffusion speed of the 50 \(\upmu\)m droplets within 0-10 s is slower than that of 10 \(\upmu\)m droplets, the diffusion trends of both sizes of droplets are generally consistent at 30 s and 60 s (Figure 8a,b).