## 3 Experiment and Analysis of Carbon Particle Adhesion Under Different Electric Field Strengths  
Due to the fact that electric field force is the main driving force for particle movement in oil, the strength of the electric field will affect the adhesion degree of carbon particles on the surface of epoxy resin. To study the influence of electric field strength on the degree of particle adhesion, this paper conducted carbon particle adhesion experiments under different electric field strengths. Carbon particles with a median particle size of 11.00 \(\upmu\)m were taken as samples, and the control of electric field strength was achieved by changing the output voltage of the DC high-voltage generator. The corresponding carbon particle adhesion images are shown in Figure 8, and the calculated average proportion of adhesive area of each group of experiments is shown in Figure 9.  
The data in Figure 9 indicates that the magnitude of the electric field strength can have a significant impact on the adhesion degree. When the electric field strength is low, the proportion of carbon particle adhesion area is also low, with only 0.27% of the particle adhesion area under an electric field of 0.17 kV/mm; as the electric field strength increases, the proportion of carbon particle adhesion area also increases. When the electric field strength increases to 0.86 kV/mm, the proportion of carbon particle adhesion area reaches its maximum, reaching 2.24%; as the electric field strength further increases, the proportion of carbon particle adhesion area no longer increases, but shows a decreasing trend. When  
Figure 8: Carbon particle adhesion images with different electric field strengths. Figure 9: The relationship between the adhesion degree of carbon particles and the electric field strength. the electric field reaches 2.06 kV/mm, the proportion of particle adhesion area decreases to 0.36%. Therefore, the adhesion degree of carbon particles increases first and then decreases with the increase in electric field strength; that is, there exists a specific field strength that causes the adhesion degree of carbon particles to reach peak value. This field strength is referred to as the peak adhesion field strength in this article. Due to the fact that the migration and adhesion behavior of carbon particles in insulating oil is determined by their stress conditions, this article discusses the adhesion characteristics of particles through force analysis. The force situation of particles in fluids is relatively complex, and the main forces are shown in Table 5[3; 22]. Among them, due to the approximately uniform electric field between the plate electrode and the internal electric field gradient being about zero, the dielectrophoresis force of the particles can be ignored. There is no temperature gradient inside the container used in the experiment, so the thermophoretic force exerted on the particles is zero. After being charged, particles are driven by electric field force to move in transformer oil. Ignoring the brief acceleration process after the particles are pulled away from the solid surface, there is no relative acceleration between the particles and the fluid. Therefore, the additional quality force and Basset force exerted on the particles are both zero. Due to the polarization effect of the particles and friction with fluids, particles generally do not rotate, so the Magnus force of the particles is also zero. Due to the insulation oil remaining stationary during the experiment, the Saffman force acting on the particles is also zero. In summary, the main forces acting on the particles in the insulation oil are gravity and buoyancy, oil drag force, and electric field force. In addition, after the particles adhere to the solid surface, they will also be subjected to the forces generated by the solid material, including adhesion force and elasticity.