## 5 Simulation Results and Analysis
### Simulation of the Effect of Nanoparticles on Charged Particles  
The method of adding nanoparticles to transformer oil can effectively improve the breakdown voltage of transformer oil. Nanoparticles have a larger specific surface area, which leads to adsorption forces between them and the liquid phase medium molecules. In other words, nanoparticles provide \"shallow traps\" that can effectively capture charged particles in the oil, thereby reducing their migration rate and energy [52; 53].  
Under the influence of an external electric field, nanomaterials become polarized. The negatively charged particles in the nanoparticles move in a directed manner under the external electric field and accumulate on one side of the nanoparticles. Correspondingly, an equal amount of positive charge appears on the other side, which is distributed on the surface of the nanoparticles as surface charges. This results in one end of the nanoparticles exhibiting positive polarity and the other end exhibiting negative polarity. To study this phenomenon, a modeling approach using COMSOL was employed to simulate the migration process of negatively charged particles in nanoparticles under the influence of an external electric field (Figure 20), as well as the migration process of positively charged particles in nanoparticles under the influence of an external electric field (Figure 21). As time progresses, the trajectory of charged particles evolves from figure (a) to figure (f). The arrows in the figures indicate the direction of the electric field.  
Figure 19: Motion trajectories of charged particles after being adsorbed by nanoparticles between a sphere plate electrode configuration.  
Figure 18: Motion trajectories of charged particles between a sphere plate electrode configuration.  
Under the action of an electric field, the migration path of charged particles in transformer oil is generally from the negative plate to the positive plate. The polarized nanoparticles, due to the accumulation of surface charges, exhibit an external electric field and have a certain adsorption effect on the negatively charged particles moving in the oil. The simulation results of the time-varying adsorption process are shown in Figure 22. However, due to the limited surface charge of the nanoparticles, the adsorption of negatively charged particles is also limited. When the nanoparticles reach saturation in terms of adsorbing negatively charged particles, the charged particles will escape from the surface of the nanoparticles. Subsequently, under the action of the applied electric field, they continue to move toward the positive plate. From the simulation results, it can be concluded that the nanoparticles were first polarized in the electric field, and then affected the motion trajectory of the charged particles, obstructing the directed motion of the charged particles in the oil.  
Nanoparticles are too large for electrons, which suggests that they can only play a certain role in hindering and adsorbing electrons, thereby reducing the density of free electrons in the oil. The charged particle capture model proposed in this study is more suitable for larger-sized positive and negative ions. Due to the extremely microscopic scale of the study, direct observation is not possible. At this stage, the construction of this model remains largely speculative and hypothetical. Therefore, further research is needed to elucidate the specific mechanisms involved.  
Figure 21: Polarization processes in nanoparticles under a uniform electric field (II).  
Figure 20: Polarization processes in nanoparticles under a uniform electric field (I).