## 2 Atmospheric Particulate Matter Separation Principle  
The working principle of atmospheric particulate separation matter based on the compound electric field is shown in Figure 1. The separation system is mainly composed of air inlet, charge room, acceleration room, and separation room. Firstly, the particles enter the room at a speed from the entrance. In the charge room, the anode corona discharge ionizes the air, producing a lot of free electrons and ions. As the particles pass through the ionization zone, electrons are attached to the particles, which make the particles charged by collision and diffusion, and finally reach a saturated state [31]. Then the particles slowly enter the acceleration room, all of them are accelerated by the electric field. Finally, the particles enter the separation room, and particles of different diameters carry different charges. Through the action of the composite electric field, their motion trajectories are different. Therefore, the separation of particulate matter can be achieved. In the charge room, the particles enter a space where a large amount of ions and electrons exist, and the charges are obtained by collision and diffusion, and reach a saturated state. The diffusion charges are derived from the thermal motion of the particles. The principle is shown in Figure 2. The particles gain total charge can be defined by [31]:  
\[q_{0}=\frac{3\varepsilon_{r}}{\varepsilon_{r}+2}\pi\varepsilon_{0}d_{p}^{2}E_{ 0}+\frac{2\pi\varepsilon_{0}d_{p}kT}{q_{\varepsilon}}ln\left(1+\frac{q_{ \varepsilon}^{2}N_{0}d_{p}}{2\varepsilon_{0}\sqrt{2m\pi kT}}t\right), \tag{1}\]  
where \(\varepsilon_{r}\) is relative dielectric constant; \(\varepsilon_{0}\) is vacuum dielectric constant; \(d_{p}\) is particle diameter; \(E_{0}\) is electric field intensity in the charged region; \(k\) is Boltzmann constant; \(q_{\varepsilon}\) is unit charge; \(T\) is absolute temperature; \(m\) is the mass of the particle; \(N_{0}\) is the number of space ions; \(t\) is particle movement time. Figure 1: Proposition of composition and principle of atmospheric particulate separation matter based on the compound electric field. Figure 2: Simplified scheme of composition and principle of charged room. In the acceleration room, the force between the particles is very small, as atmospheric particles are relatively sparse and the distance between particles is large. Therefore, interactions between particles can be ignored. In the gas-solid two-phase flow, particles are subjected to drag, Basset force, encapsulation mass force, gravity and electric field force, and move under the action of various forces. In a gas-solid two-phase flow, the definition and measurement of the drag force at different stages are critical. The drag force of particles is defined by [32]:  
\[F_{D}=\frac{1}{8}\pi d_{p}^{2}\rho_{g}C_{D}\big{|}v_{p}-v_{g}\big{|}\big{(}v_{ p}-v_{g}\big{)}, \tag{2}\]  
\[\left\{ \begin{array}{ll}C_{D}=\frac{24}{Re_{t}},&Re_{t}<2\\ C_{D}=\frac{18.5}{Re_{t}^{3}b.a},&2<Re_{t}<500\\ C_{D}=0.44,&Re_{t}>500\end{array} \right., \tag{3}\]  
\[Re_{t}=\frac{\big{|}v_{p}-v_{g}\big{|}d_{p}\rho_{g}}{\mu_{g}}, \tag{4}\]  
where \(C_{D}\) is drag coefficient; \(Re_{t}\) is the particle Reynolds number; \(\rho_{g}\) is air density; \(v_{g}\) is gas velocity; \(v_{p}\) is particle velocity; \(\mu_{g}\) is hydrodynamic viscosity. As the particles accelerate first and then drive the surrounding fluid to accelerate, the Bassett force is produced by the viscous effect of the fluid. In the acceleration room, charged particles are accelerated. When the acceleration is large, the Basset forces become important. When particles are accelerating in a stationary fluid, the Bassett force can be derived according to the Stokes region.