Quantitative relationships between microstructure and effective transport properties based on virtual materials testing

The microstructure influence on conductive transport processes is described in terms of volume fraction ε, tortuosity τ, and constrictivity β. Virtual microstructures with different parameter constellations are produced using methods from stochastic geometry. Effective conductivities σeff are obtained from solving the diffusion equation in a finite element model. In this way, a large database is generated which is used to test expressions describing different micro-macro relationships such as Archie's law, tortuosity, and constrictivity equations. It turns out that the constrictivity equation has the highest accuracy indicating that all three parameters (ε,τ,β) are necessary to capture the microstructure influence correctly. The predictive capability of the constrictivity equation is improved by introducing modifications of it and using error-minimization, which leads to the following expression: σeff=σ02.03ε1.57β0.72/τ2 with intrinsic conductivity σ0. The equation is important for future studies in, for example, batteries, fuel cells, and for transport processes in porous materials.