Abstract
Based on the fractal geometry science and the model of flow friction resistance when fluid flows through rough microcapillaries, the formula of diffusion layer thickness and the spatial charge density distribution of the pipe were derived. The relationship between the amount of space charge and the structural parameters of rough elements, relative roughness, liquid conductivity, pipeline diameter, and other physical quantities was discussed. It was found that the height of rough elements is directly proportional to the thickness of the diffusion layer, and also positively proportional to the amount of current. The predicted results of the model are in good agreement with existing models and various published experimental data, verifying the accuracy and reliability of the model.
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