# Study on the Impact of Ventilation Methods on Droplet Nuclei Transmission in Subway Carriages
## 2 Materials and Methods
### Evaluation Criteria  
Airflow distribution under different ventilation methods, air supply velocities, and air supply temperatures significantly impacts infection risk. When evaluating subway ventilation systems during a pandemic, deposition rate and suspension rate are commonly used to assess their effectiveness. The deposition rate is defined as the ratio of the total number of exhaled droplets to the number of droplets deposited on various indoor surfaces. The suspension rate is defined as the ratio of the number of suspended droplets inside the subway car to the total number of exhaled droplets. The system's effectiveness is evaluated by measuring the instantaneous mass of particles escaping through the return air vents and the average instantaneous mass of infectious particles inhaled by passengers. Additionally, the risk of cross-infection can be determined by examining the concentration of contaminants in the breathing zones of the infected individual and other passengers. To guide public policy on social distancing, it is essential to measure the dispersion of cough particles, quantified by the average contamination range and the maximum reach of the droplets. In this study, the average concentration of tracer gas N\({}_{2}\) in the entire car was used for calibration. The first two terms refer to one type of evaluation definition, while the latter can be expressed as a volume-weighted average concentration. The formulas for calculating deposition rate (DER), suspension rate (SR), weighted average contamination range (CR), and particle reach probability (PRP) are as follows:  
\[DER=\frac{Ntrap}{Ns}\times 100 \tag{8}\]  
\[SR=\left(1-\frac{Nscape+Ntrap}{Ns}\right)\times 100 \tag{9}\]  
where _Nscape_ represents the number of droplets discharged from the exhaust louvers (EA), \(Ntrap\) is the number of droplets deposited on each surface in the ward, and \(Ns\) is the total number of droplets produced by the patient's exhalation. \[CR=\frac{\sum_{i=0}^{n}x_{i}d_{i}}{\sum_{i=0}^{n}x_{i}} \tag{10}\]  
where \(xi\) represents the particle mass or count and \(di\) denotes the distance the particle travels in the streamwise direction from the mouth. Droplets may collide with one another, either adhering together or bouncing off during transportation. High slip velocity or particle acceleration can also cause the droplets to break apart. Additionally, droplet evaporation occurs, influenced by the Sherwood number of the droplets. The results revealed all three phenomena, with droplet coalescence being \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case No.** & \begin{tabular}{c} **Supply Air** \\ **Temperature (°C)** \\ \end{tabular} & \
\begin{tabular}{c} **Supply Air Velocity** \\ **(m/s)** \\ \end{tabular} &
\begin{tabular}{c} **Ventilation Method** \\ \end{tabular} \\ \hline Case 1 & 25 & 0.2 & SFRC \\ Case 2 & 25 & 0.3 & SFRC \\ Case 3 & 25 & 0.4 & SFRC \\ Case 4 & 25 & 0.8 & MV \\ Case 5 & 25 & 1.2 & MV \\ Case 6 & 25 & 1.6 & MV \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Air supply parameters and ventilation method. the most prominent. The droplets expelled from the mouth had sizes varying from 0.1 um to 50 um. We assume that the mass-weighted CR was influenced by larger (heavier) particles, while the count-weighted CR was affected by the smallest particles due to their higher quantity. Therefore, the CR was calculated using both mass-weighted and count-weighted averages to assess its sensitivity to these two metrics. The maximum range of the particles refers to the farthest distance from the origin (mouth) in the direction of the cough where droplets are deposited. An alternative approach to quantifying contamination spread is to estimate the percentage of particles within a defined distance from the coughing individual. Therefore, the 2-3 m thresholds are used to determine the percentage of particles that settle on the ground within these distances. Following a forceful expiratory event, like a cough, particles of different sizes are expelled into the environment.