## 3 Results and Discussion
### Droplet Distribution at Different Times within the Carriage  
After droplets enter the carriage and undergo diffusion, their ultimate destinations are as follows: remaining suspended in the air (suspended), settling on the carriage's surfaces (deposited), being trapped in passengers' bodies (trapped), or being expelled by the ventilation system (escaped) [25; 41]. Figure 11 illustrates the time-dependent proportions of droplets under the various conditions mentioned in Section 3.1. Gravity plays a crucial role in the movement of large droplets [23; 28; 33], while for the diffusion of tiny droplets (less than 5 \(\upmu\)m), the drag force of airflow becomes the dominant factor. As shown in Figure 11b, for droplets with an initial diameter of 100 \(\upmu\)m (case 3), 98% of them have settled on the carriage floor within 10 s after release, and these droplets have not completed the evaporation process before settling on the floor. For droplets with an initial diameter of 50 \(\upmu\)m (case 2), approximately 20% of them have settled on the floor within the first 10 s. As mentioned in a previous study [41], droplets with a 50 \(\upmu\)m diameter can complete the evaporation process within 10 s. Before the evaporation finishes, gravity dominates the droplets' downward movement; after evaporation, the airflow inside the carriage will dominate their movement. As a result, the proportion of deposited droplets increases rapidly within the first 10 s, increasing only by approximately 10% over the remaining 50 s. For droplets with a diameter of 10 \(\upmu\)m (case 1), less than 10% have been deposited on the carriage surfaces within 60 s. Regarding the diffusion of droplets of different sizes in the subway carriage, the driving forces for the diffusion processes of large and tiny droplets are relatively more straightforward. The evaporation process causes medium-sized droplets to transform from medium-sized into tiny droplets, leading to a more complex driving force for their movement and diffusion inside the subway carriage. Furthermore, based on Formulas (6)-(9) for risk assessment, it is evident that medium-sized droplets carry much larger virus particles than tiny droplets. The diffusion characteristics of medium-sized droplets require more attention. Figure 10: The effect of passenger density on droplet diffusion: (**a**) case 5; (**b**) case 7. The flow field characteristics in various indoor environments are crucial in determining the motion of tiny droplets [33; 34; 35; 36; 41; 42; 43]. Due to the differences in airflow fields at positions D1 and D2 in the carriage (Figure 7a), the speed of droplet removal from the carriage varies significantly (case 1 and case 4 in Figure 11d). When droplets are released at position D2, the ventilation system exhausts 60% of the droplets from the carriage within 20 s (the total expelled droplets from the return air vents and exhaust air outlets), and over 80% of the droplets can be expelled within 60 s. When droplets are released at position D1, the escape speed of the droplets is relatively slower compared to position D2. The proportion of escaped droplets gradually increases to approximately 55% within 60 s. The main reason for this is that the longitudinal airflow generated by return air vent 1 at position D2 is stronger than at position D1. Therefore, when droplets are released at D2, they are swiftly carried by the airflow toward the vicinity of air supply air vent I (Figure 8d), thereby accelerating the process of droplet removal from the carriage. Comparing case 1 and case 5, we can see that as the initial release velocity decreases from 10 m/s to 1 m/s, the proportion of suspended droplets rapidly decreases. When the droplets are released at an initial velocity of 1 m/s, the longitudinal flow inside the carriage exerts a stronger dragging effect relative to the jet flow from the infectious passenger, causing the droplets to be more rapidly carried toward the region near the return air vent I (Figure 8e).