Unified mixed conductivity model

Abstract

Matter conductivities are crucial physical properties that directly determine the engineering application value of materials. In reality, the majority of materials are multiphase composites. However, there is currently a lack of theoretical models to accurately predict the conductivities of composite materials. In this study, we develop a unified mixed conductivity (UMC) model, achieving unity in three aspects: (1) a unified description and prediction for different conductivities, including elastic modulus, thermal conductivity, electrical conductivity, magnetic permeability, liquid permeability coefficient, and gas diffusion coefficient; (2) a unified-form governing equation for mixed conductivities of various composite structures, conforming to the Riccati equation; (3) a unified-form composite structure, i.e., a three-dimensional multiphase interpenetrating cuboid structure, encompassing over a dozen of typical composite structures as its specific cases. The UMC model is applicable for predicting the conductivity across six different types of physical fields and over a dozen different composite structures, providing a broad range of applications. Therefore, the current study deepens our understanding of the conduction phenomena and offers a powerful theoretical tool for predicting the conductivities of composite materials and optimizing their structures, which holds significant scientific and engineering implications.