## 1 Introduction  
The converter transformer is the core piece of electrical equipment of the ultra-high voltage direct current transmission system. The valve-side bushing, as a key component connecting the converter transformer and the valve hall converter, carries the AC/DC composite voltage and plays an important role in the safety and stability of the ultra-high voltage direct current transmission function [1]. The oil end of the valve-side bushing is located inside the rising seat of the converter transformer, and its main insulation is generally made of epoxy-resin-impregnated insulation paper, which is wrapped in several layers of insulation screens. The insulation structure and electromagnetic environment are relatively complex, and insulation oil is required to achieve its heat dissipation and partial insulation functions [2]. However, transformer oil is prone to contamination during the manufacturing, operation, and maintenance stages of the converter [3], resulting in micrometer-sized impurity particles, such as cellulose, carbon particles, metals, and their oxides, in the oil. Due to the poor conductivity of cellulose and relatively low content of metal particles, carbon particles are the most abundant conductive particles in insulating oil [4]. Carbon particles in oil not only have a certain impact on the physical and chemical properties of transformer oil itself, but also aggregate, adhering to the surface of solid insulating materials under the influence of factors such as electric field and oil flow, causing distortion of the electric field. In severe cases, it will induce partial discharge and cause local damage to the insulating surface [5], which is an important reason for the decrease in internal insulation performance and the increase in the risk of surface flashover in converter flow. In recent years, multiple incidents of valve-side bushing breakdown and explosion caused by local electric field distortion have occurred, posing a serious threat to the safe operation of the power system [6]. Therefore, the impact of carbon particle adhesion on the insulation inside the valve-side bushing of transformers cannot be ignored. It is necessary to study the adhesion characteristics and influencing factors of carbon particles in insulation oil on the surface of epoxy resin under DC electric field and provide empirical support for the evaluation of the internal insulation performance and pollution risk of converter transformers. At present, some scholars have conducted extensive research on the motion behavior of impurity particles in oil and their impact on internal insulation performance. [PERSON] et al. [7] compared and analyzed the migration and aggregation characteristics of metal and cellulose particles in oil under direct current voltage. The results showed that impurity particles would move back and forth between electrodes after being charged, and the aggregation degree of metal particles was smaller than that of fiber impurities. [PERSON] et al. [8] studied the bridging characteristics of cellulose particles in flowing transformer oil, and the results showed that when a direct current voltage is applied, low-speed oil flow can accelerate the formation of cellulose bridges, while high-speed oil flow can delay or prevent the formation of full bridges. The above research mainly focuses on cellulose and metal particles, while there is relatively little research on carbon particles. [PERSON] et al. [9] tested the breakdown voltage of transformer oil containing carbon particles under different conditions and found that its breakdown voltage approximately conforms to the Weibull distribution commonly used in reliability analysis and life testing. The breakdown voltage gradually decreases with the increase of carbon particle concentration and particle size, but the influence of particle adhesion behavior on the surface insulation performance of solid materials was not considered.