## 4 Results and Discussion
### Effects of Coupling Field on Particle Number Concentration  
In order to verify whether the acoustic wave and pulsed corona discharge coupling field can effectively further increase the reduction ratio of particles with three sizes, the selected acoustic wave parameters were 143 dB and 1600 Hz, and the selected pulse input voltage was 50 kV. The effect of the coupling and single fields on the PNC is demonstrated in Figure 15.  
As demonstrated in Figure 15, the particle number concentration reduction ratios of three sizes in the single and coupling fields were significantly different. Under the three conditions, the reduction ratio in the coupling field was greater than that in the acoustic wave field, which was also greater than the reduction ratio in the pulsed corona discharge field. When the particle size was adjusted to 0.5 \(\upmu\)m, the effect of the coupling field was considerably better than that of the two single fields. The corresponding reduction ratio of particles could reach 0.464, which was more than twice that in the pulsed corona discharge field (i.e., 0.226). As mentioned above, the 0.5-\(\upmu\)m particles are in the critical region of field charge and diffusion charge, and they are the most difficult to remove using traditional ESPs. This shows that the effect of coupling field on the reduction of the PNC in small-sized segments was remarkable. With the increase in particle size, the reduction effect of the three types of external fields on particles increased. In particular, when the particle size was 4 \(\upmu\)m, the reduction ratio in the coupling field could reach 0.918. Since, in this study, only agglomeration effect was considered and there was no collection effect, the agglomeration efficiency was still higher than the 90% of Xu [22] and 75.3% of Liu [23]. The reduction ratios in the acoustic wave field and pulsed corona discharge field could reach 0.814 and 0.794, respectively. The differences among the reduction ratios of these fields were smaller than those when the particle size was adjusted to 0.5 \(\upmu\)m. The effect of the three external fields on the 2-\(\upmu\)m particles was similar to their effect on the two other sizes. The reduction ratios were 0.526 (coupling field), 0.438 (acoustic wave field), and 0.385 (pulsed corona discharge field). The results also definitely indicate that, with the increase in particle size, the particles had a greater tendency to agglomerate, and the coupling field facilitated submicron particle agglomeration and reduction. Owing to the limit of the experimental set-up, the evaporation of DEHs in the monodisperse aerosol generator was constant, and the larger particles had lower number concentration. Some scholars [28; 29] found that a higher number concentration of particles led to a better agglomeration effect, but the number concentration must be less than \(4.1\times 10^{6}\) cm\({}^{-3}\). Firstly, particles with larger concentration are more likely to be broken up by acoustic waves; secondly, since the charge concentration generated by corona  
Figure 14: Number concentration of 4-\(\upmu\)m particles at different voltages.  
discharge remains unchanged, the charge of each fine particle decreases correspondingly. In this experimental study, the number concentration of particles was less than \(4.1\times 10^{6}\) cm\({}^{-3}\). We choose the N/N\({}_{0}\) values to compare the results in order to reduce the influence of original number concentration. According to the results, as the particles with lowest number concentration, the agglomeration effect on 2-\(\upmu\)m particles was better than that on the two other sizes. It can be seen that the influence of particle size distribution on agglomeration was far greater than the influence of number concentration. If the original number concentration of the three sizes was adjusted to be the same, the results would be more pronounced.