# Simulation of Aerosol Evolution within Background Pollution for Nucleated Vehicle Exhaust via TEMOM
## 4 Results and Discussion
As shown in Figure 4, on the sampling line, x = 0.1 m and x = 0.25 m, the nucleation rate under the nonpolluted condition is greater than the nucleation rate under the polluted condition. On the sampling line, x = 0.5 m and x = 0.75 m, the nucleation rate in the second half of the nonpolluted situation is greater than the nucleation rate in the polluted condition, and the opposite is the case in the first half. Since the ordinate axis is a logarithmic coordinate, at  
Figure 2: No polluted flow field data in 2004.  
x = 0.1 m and x = 0.5 m, the part where no pollution exceeds the pollution is much larger than the difference between x = 0.5 m and x = 0.7 m. The situation has been the same for three years. The lower nucleation rate under the polluted condition is the direct cause of the lower \(m_{0}\) under the polluted condition. As for why the nucleation rate is lower under polluted conditions, it needs to be analyzed by other physical quantities. Figure 3: Every distance of polluted and nonpolluted \(m_{0}\) over three years. Figure 4: Every distance of polluted and nonpolluted \(J\) in three years. The value of each moment in the moment method contains the physical properties of the particles, such as surface area, volume, and diameter, and these physical quantities are not independent of each other. For the same volume of particle population, the smaller the particle size, the larger the total surface area of the particle population. For the particle population of the same volume, the larger the particle size, the fewer the particles. The correlation between these variables can be used to infer the mechanism of their evolution. As shown in Figure 5, it is the volume average particle diameter of the particles, defined as \((6m_{1}/\pi m_{0})\). It can be seen that the particle size under the pollution condition in three years is always larger than the particle size under the no pollution condition. A large particle size means a larger surface area, which is suitable for condensation. Under polluted conditions, water molecules and sulfuric acid molecules are more involved in condensation, so the critical molecular clusters involved in nucleation are reduced, resulting in a lower nucleation rate. This conclusion needs to be corroborated. First, introduce another physical quantity. In the log-normal theory, the geometric mean volume for particles is:  
\[v_{g}=\frac{m_{1}^{2}}{m_{0}^{3/2}m_{2}^{1/2}} \tag{22}\]  
From the area formula of the sphere, \(s=\pi d^{2}\) and volume formula of the sphere, \(v_{g}=(\pi/6)d^{3}\) the relationship between area and volume is:  
\[S=(36\pi)^{1/3}v^{2/3} \tag{23}\]  
Substituting Equation (22) into Equation (23) is the surface area of the particles, and multiplying by the number of particles, \(M_{0}\), we can get the total particle surface area. Figure 6 compares the total particle surface area in the case of pollution and no pollution. Under pollution conditions, the volume average diameter is larger, but the number concentration is minor. If the total volume of particulate matter under polluted and no polluted conditions is equal, then the smaller the number concentration, the smaller the particulate matters's total area. However, it can be seen from Figure 6 that the total area of particulate matter is larger under polluted conditions. This means that the total volume of particulate matter in a polluted condition is greater than the total volume of particulate matter in a no polluted condition. This is confirmed in the data of \(m_{1}\) in Figure 7. At the same time, it should be noted that the nucleation rate is higher under no polluted conditions. The higher nucleation rate increases the total volume while increasing the total area. The total volume of particulate matter reflects the mass concentration of particulate matter, which is an index used to measure the degree of pollution. On this index, the total volume of particulate matter under no polluted conditions is always less than the total volume under polluted conditions.