Optimal Bounds on the Trapping Constant and Permeability of Porous Media

Abstract

We derive exact expressions for so-called ``void'' bounds on the trapping constant $\gamma$ and fluid permeability $k$ for coated-spheres and coated-cylinders models of porous media. We find that in some cases the bounds are optimal, i.e., the void bounds coincide with the corresponding exact solutions of $\gamma$ and $k$ for these coated-inclusions models. In these instances, exact expressions are obtained for the relevant length scale that arises in the void bounds, which depends on a two-point correlation function that characterizes the porous medium. In contrast to bounds on the effective conductivity and elastic moduli of composite media, this is the first time that model microstructures have been found that exactly realize bounds on either the trapping constant or fluid permeability.

Cited by in corpus (9)

• Modeling Heterogeneous Materials via Two-Point Correlation Functions: I. Basic Principles
• Hyperuniformity and its Generalizations
• Disordered Hyperuniform Heterogeneous Materials
• Toward an Ising Model of Cancer and Beyond
• Geometrical Ambiguity of Pair Statistics. II. Heterogeneous Media
• New Tessellation-Based Procedure to Design Perfectly Hyperuniform Disordered Dispersions for Materials Discovery
• Methodology to Construct Large Realizations of Perfectly Hyperuniform Disordered Packings
• Microstructural and Transport Characteristics of Triply Periodic Bicontinuous Materials
• Low-cost approximate reconstructing of heterogeneous microstructures