Sandstone, granular media, bone, wood, and cell membranes are just a few examples of porous media that abound in Nature and in synthetic situations. Two important effective properties of fluid-saturated porous media that have been extensively studied are the trapping constant γ and scalar fluid permeability k. Exact expressions for the "void" bounds on γ and k for coated-spheres and coated-cylinders models of porous media are derived. In certain instances, the bounds are shown to be optimal, i.e., the void bounds coincide with the corresponding exact solutions of γ and k for these coated-inclusions models. In the optimal cases, we obtain exact expressions for the relevant length scale that arises in the void bounds, which depends on a two-point correlation function that characterizes the porous medium. By contrast, optimal bounds on the effective conductivity and elastic moduli of composite media have long been known.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)