## 3 Theoretical Analysis
### Pulsed Corona Discharge Field  
In the monodisperse aerosol system, although the particles are mainly concentrated around a certain size, the pulsed corona discharge process is an intermittent discharge process. In the pulsed corona discharge period, the voltage is considerably high, and an electron avalanche occurs. When the electric field intensity is sufficiently large, a large number of free electrons can negatively charge the fine particles. During the intermission period, the positive ion diffusion charge dominates the whole space. In the entire particle movement process, charged particles move toward the electrode plate with the presence of the electric field force during the discharge period, and the particles with opposite charges collide under Coulomb forces.  
Due to the influence of electric field force, the movement of particles to the plate is similar to that in the direct current discharge. The particles can, however, achieve a larger charge because of the high pulse voltage. The electric field force in this process can be expressed as follows:  
\[F_{e}=E_{a}q, \tag{5}\]  
where \(E_{a}\) is the average electric field intensity inside ESP, and q is the particle charge.  
Owing to the presence of mean free path, [PERSON] [26] combined the traditional field charge and diffusion charge to derive the overall expression of particle charge in the electric field as follows:  
\[q=\pi\varepsilon_{0}\Bigg{[}\bigg{(}1+\frac{2\lambda}{d}\bigg{)}^{2}+\bigg{(} \frac{2}{1+\frac{2\lambda}{d}}\bigg{)}\bigg{(}\frac{\varepsilon-1}{\varepsilon +2}\bigg{)}\bigg{]}E_{a}d^{2}, \tag{6}\]  
where \(\varepsilon_{0}\) is the permittivity of vacuum, and \(\varepsilon\) is the relative permittivity of particles.  
In the process of moving toward the dust collector plate, the particles are also subject to viscous resistance. The particles are in the Stokes motion zone, and it can, therefore, be known from [PERSON]'s second law that  
\[m\frac{dv}{dt}=E_{a}q-\frac{6\pi\eta_{g}Rv}{C_{c}}, \tag{7}\]  
Figure 4: Schematic of acoustic wake effect.  
where \(v\) is the velocity of particles moving toward the dust collector plate. This velocity is also the migration velocity in the ESP.  
By solving Equation (6) and Equation (7) and ignoring the exponential term, the migration velocity formula can be obtained as follows:  
\[v=\frac{E_{\mathrm{z}}q\mathrm{\Omega}_{C}}{6\pi\eta_{S}R}. \tag{8}\]  
In this study, monodisperse particles did not have an absolute single particle size. Particles with various sizes and opposite charges agglomerated because of the Coulomb force in the entire pulsed corona discharge process. Some scholars [22] believe that there is a distinct critical point between the electric field charge and diffusion charge in the pulsed corona discharge process. Regardless of whether it is the discharge period or the intermission period, even particles of the same size may be oppositely charged, and the process becomes relatively complex. When considering particle charge, the approximate expression is that of Equation (8). The mathematical expression of Coulomb force in the pulsed corona discharge is as follows:  
\[F_{c}=\frac{q_{1}q_{2}}{4\pi\varepsilon_{0}r^{2}}, \tag{9}\]  
where \(r\) is the center distance between two particles, and \(q_{1}\) and \(q_{2}\) are the particle charges.  
The acoustic wave and pulsed corona discharge coupling field can increase the probability of collision and agglomeration of fine particles. Some of these fine particles are collected by the dust collector plate, thus effectively reducing their number. [PERSON] et al. [27] used a numerical calculation to analyze the agglomeration coefficient of the acoustic and electricity coupling field; they drew a conclusion that the existence of the coupling field increased the agglomeration coefficient of particles compared with that in the single external field, and they also verified the theoretical analysis and results of this paper.