Predicting effective conductivities based on geometric microstructure characteristics

Empirical relationships between effective conductivities in porous and composite materials and their geometric characteristics such as volume fraction ε, tortuosity τ and constrictivity β are established. For this purpose, 43 virtually generated 3D microstructures with varying geometric characteristics are considered. Effective conductivities σeff are determined by numerical transport simulations. Using error-minimization the following relationships have been established: σeff=σ0ε1.15β0.37τgeod4.39 and σeff=σ0εβ0.36τgeod5.17 (simplified formula) with intrinsic conductivity σ₀, geodesic tortuosity τgeod and relative prediction errors of 19% and 18%, respectively. We critically analyze the methodologies used to determine tortuosity and constrictivity. Comparing geometric tortuosity and geodesic tortuosity, our results indicate that geometric tortuosity has a tendency to overestimate the windedness of transport paths. Analyzing various definitions of constrictivity, we find that the established definition describes the effect of bottlenecks well. In summary, the established relationships are important for a purposeful optimization of materials with specific transport properties, such as porous electrodes in fuel cells and batteries.