## 2 Model and Process  
### Motion Equation  
The deposition of aerosol particles near the photovoltaic (PV) module was the interaction result of the particle collision, airflow, and gravity. The deposition process of aerosol particles belongs to the typical gas-solid two-phase flow category, constrained by the continuity equation, momentum equation, and Reynold's stress equation [24]. The continuity equation of the gas phase and solid phase can be expressed as Equations (1) and (2), respectively. \[\frac{\partial(\varphi_{\text{f}}\rho_{\text{f}}u_{x})}{\partial x}+\frac{ \partial(\varphi_{\text{f}}\rho_{\text{f}}u_{y})}{\partial y}=0 \tag{1}\]  
where \(\varphi_{\text{f}}\) is the volume fraction of air, and \(\rho_{\text{f}}\) is the density (kg/m\({}^{3}\)) of air. \[\frac{\partial(\varphi_{\text{p}}\rho_{\text{p}}u_{x})}{\partial x}+\frac{ \partial(\varphi_{\text{p}}\rho_{\text{p}}u_{y})}{\partial y}=0 \tag{2}\]  
where \(\varphi_{\text{p}}\) is the volume fraction of aerosol particles, and \(\rho_{\text{p}}\) is the density (kg/m\({}^{3}\)) of aerosol particles. The momentum equations of the gas phase and solid phase were obtained by Equations (3) and (4), respectively. \[\frac{\partial}{\partial t}\big{(}\varphi_{\rm f}\varphi_{\rm f}\varphi_{\rm p} \big{)}+\
abla(\varphi_{\rm f}\varphi_{\rm f}\varphi_{\rm f}\varphi_{\rm f})=- \varphi_{\rm f}\
abla p+\
abla\tau_{\rm p}+\varphi_{\rm f}\varphi_{\rm f}\varphi _{\rm f}+f \tag{3}\]  
where \(v_{\rm f}\) is the velocity (m/s) of air, \(v_{\rm p}\) is the velocity (m/s) of aerosol particles, \(p\) is the pressure (Pa) of air-solid two-phases flow, \(\tau_{\rm f}\) is the stress tensor (N/m\({}^{2}\)) of air, \(\tau_{\rm p}\) is the stress tensor (N/m\({}^{2}\)) of aerosol particles, \(g\) is the acceleration of gravity (m/s\({}^{2}\)), and \(f\) is the force (N/m\({}^{2}\)) between air and aerosol particles calculated by Equation (3). \[\frac{\partial}{\partial t}\big{(}\varphi_{\rm p}\varphi_{\rm p}\varphi_{\rm p }\big{)}+\
abla\big{(}\varphi_{\rm p}\varphi_{\rm p}\varphi_{\rm p}\varphi_{ \rm p}\big{)}=-\varphi_{\rm p}\
abla p-\
abla p_{\rm p}+\
abla\tau_{\rm p}+ \varphi_{\rm p}\rho_{\rm p}g+f \tag{4}\]  
where \(p_{\rm p}\) is the pressure of aerosol particles (Pa). \[f=\frac{C_{\rm D}Re}{24} \tag{5}\]  
where \(C_{\rm D}\) is the resistance coefficient calculated by Equation (5), and \(Re\) is the Reynolds number. \[C_{\rm D}=\frac{24}{Re}\cdot 10^{\alpha} \tag{6}\]  
where \(\alpha\) is a dimensionless parameter related to the particle morphology [25]. The \(\psi\) is the ratio of the surface area of spherical particles to the actual surface area of particles with the same volume, which is used to quantify the morphology of aerosol particles. The relationship between \(\alpha\) and \(\psi\) can be calculated by Equation (7), and \(\psi\) can be expressed by Equation (8). \[\alpha=\frac{1}{4}\sqrt{\psi\frac{d_{v}}{d_{n}}}\cdot\left(\frac{d_{v}}{d_{n}} -1\right)-log_{10}\left(\frac{d_{v}}{d_{n}}\sqrt{\psi}\right) \tag{7}\]  
where \(d_{v}\) is the equivalent diameter (m) of the equal volume sphere of aerosol particles, and \(d_{n}\) is the equivalent diameter (m) of the equal area projection circle along the settlement direction of aerosol particles. \[\psi=\frac{4\pi\left(\frac{3V_{\rm p}}{4\pi}\right)^{\frac{2}{3}}}{S_{\rm p}} \tag{8}\]  
where \(V_{\rm p}\) is the actual volume (m\({}^{3}\)) of aerosol particles, and \(S_{\rm p}\) is the actual area (m\({}^{2}\)) of aerosol particles. The typical turbulence model of gas-solid two-phase flow can use the standard k-\(\varepsilon\) equation, where the governing equations of \(k\) and \(\varepsilon\) are Equations (9) and (10), respectively.