## 3 Results and Discussion
### Effect of Various Initial Conditions on Droplet Diffusion
When the initial size is 100 \(\upmu\)m, the released droplets quickly settle on the floor due to gravity. As the initial size of the droplets increases, the larger the droplets, the faster the deposition, and the slower the diffusion. Considering the differences in airflow patterns between the middle and the ends of the subway carriage, the dispersion of droplets is investigated when the infected passenger stands in the middle of the carriage, as shown in Figure 8d. Despite the similar distance of the infected passenger from return air vents I and II, the droplets primarily move toward return air vent I, with only a tiny portion directed toward return air vent II. This dispersion pattern aligns with the airflow shown in Figure 7a. The streamlines near the right side of the central pillar b point toward return air vent I rather than the closer return air vent II. Based on the results from Figure 8a,d, whether the infected passenger stands at positions D1 or D2, most droplets accumulate near return air vent I, and are subsequently expelled from the carriage through it. Therefore, the passengers standing near return air vent I are at a higher probability of ingesting virus-laden droplets. When passengers can choose their standing positions inside the carriage, they should look for a non-crowded area or avoid standing directly beneath concentrated return air vents [74]. Figure 8e illustrates the diffusion results for droplets released at an initial velocity of 1 m/s. Passengers may release virus-laden droplets into the subway carriage with different breathing patterns, such as breathing (1 m/s), coughing (10 m/s), or sneezing (\(\geq\)20 m/s) [15]. Comparing Figure 8a,e, when droplets are released at 10 m/s, within the first 0-10 s, droplets enter the carriage environment in a jet-like manner and rush toward the floor near the carriage wall; when droplets are released at 1 m/s, the jet-like effect is significantly weakened. These released droplets are firstly dragged by the airflow toward return air vent I and then diffuse near the carriage wall. At 30 and 60 s, it can be noticed that the higher the droplet release velocity, the larger the diffusion area of the droplets, and the higher the probability of encountering droplets for passengers standing or sitting between the infected passenger and return air vent I. The \(RH\) inside the carriage dominates the speed of droplet evaporation [29; 75]. Air with a higher \(RH\) has a lower potential to absorb water vapor, resulting in a longer time being required for droplet evaporation. To ensure passengers' thermal comfort, the \(RH\) inside the subway carriage should be controlled within 90% [69]. Figure 9 illustrates the diffusion process of droplets under 35% and 70% \(RH\) conditions, respectively. A previous study [41] showed that at an \(RH\) of 35%, it takes approximately 1.8 s for a droplet (initial size = 50 \(\upmu\)m) to complete the evaporation process, while at an \(RH\) of 70%, it takes less than 7 s to complete the evaporation process. In the present work, under the condition of \(RH\) = 35%, the droplets have already diffused after 10 s of release, while under the condition of \(RH\) = 70%, most droplets have not started to diffuse and are still concentrated near the floor. However, when comparing the diffusion results at 30 s and 60 s under both \(RH\) conditions, the diffusion area of the droplets and the concentration distribution inside the carriage are essentially the same. In addition to the \(RH\), the passenger density is significantly different inside the subway carriage during peak and off-peak hours. As the number of passengers increases, their obstruction to the airflow inside the carriage becomes more pronounced. Figure 10 shows the effect of varying the passenger density on the diffusion of droplets with an initial velocity of 1 m/s.