A NOVEL MODEL FOR THE ELECTRICAL CONDUCTIVITY OF WATER-SATURATED TREE-LIKE BRANCHING NETWORK WITH FRACTAL ROUGH SURFACES

Tree-like branching networks play a critical role in various natural and engineering systems. In this work, a novel model for the electrical conductivity of water-saturated tree-like branching networks with fractal rough surfaces is derived. The proposed model is expressed in terms of relative roughness, length ratio, diameter ratio, total number of branching levels, branching number, branching angle, pore water conductivity, and porosity. The effects of these structural parameters on electrical conductivity are systematically investigated. It is found that electrical conductivity decreases with increasing relative roughness and length ratio, while it increases with increasing porosity and pore water conductivity. Additionally, electrical conductivity increases, reaches a maximum, and then decreases as the diameter ratio increases. The electrical conductivity predictions are compared with those from existing models and Archie’s law, showing good agreement and validating the proposed model. The present model has no empirical constants and all parameters have clear physical meaning, thus providing deeper insight into the electrical properties of tree-like branching networks.