Rigorous bounds on the fluid permeability: Effect of polydispersivity in grain size

Abstract

Rigorous bounds on the fluid permeability (on resistance) of porous media composed of spherical grains with a continuous size distribution are computed. For any finite degree of polydispersivity, scaling the resistance bound by the square of the specific surface (relative to the monodisperse case) yields effectively universal behavior at a fixed sphere volume fraction. A new proposition regarding an exact relationship between the permeability and another effective parameter, the trapping constant associated with diffusion‐controlled reactions among traps, is employed to assess the accuracy of the rigorous bound.