Effective conductivity in random porous media with convex and non-convex porosity

A fundamental study on the effective conductivity in random porous media is presented in this paper. Porous media are distinguished based on the convexity of the insulating porous phase: microstructures with convex porosity are representative of foams and sponges, while non-convex porosity includes granular and particulate materials. This distinction allows us to identify two limit cases within which the effective conductivity of an isotropic porous medium lies. The effective conductivity is evaluated through a random walk method, applied on structures numerically reconstructed with packing algorithms which use spheres to represent convex elements. Simulation results are compared with theoretical relations and experimental data in a range of 0-40% in porosity, wherein the solid phase is entirely connected and not suspended in the porous phase. This study shows that, given the porosity, structures with convex porosity are more conducting than structures with non-convex pores, because the bottlenecks for conduction are narrower in the second case. These situations identify two limit cases for the effective conductivity in a random isotropic porous medium, as confirmed by experimental data of structures with partly convex and partly non-convex porosity. In addition, for convex porosity the effective conductivity is larger when pores are isolated, attaining the Hashin-Shtrikman upper bound, while when pores are overlapped the effective conductivity is well described by the Archie power law