Geometrically Exact Calculation of Percolation Threshold through Voids around Impermeable Polyhedral Grains

Void percolation, in which fluid or charge transport is through connected volumes around impenetrable grains, serves as a model for flow through strongly disordered porous materials. However, the irregularly shaped void volumes among impermeable inclusions pose a challenge in the determination of the percolation threshold inclusion concentration, in which critical densities of grains interrupt connected void networks to the degree that a macroscopic level system spanning path through void volumes no longer exists. We discuss results for a method which, for sample realization of disorder made up of randomly placed faceted grains, determines whether navigable network of contiguous voids exists in the sample. The technique addresses void geometry directly by taking into account the concave shapes of the irregulary spaced volumes between inclusions; the method scales directly as the system size. As a test case, we consider systems comprised of random assemblies of impenetrable regular polyhedra (e.g. tetrahedra, cubes, octahedra, dodecahedra, and icosadera). For the latter, we consider both aligned and randomly oriented grains. In this manner, we revisit an early result in which percolation thresholds were found to differ for aligned versus randomly oriented cases only fore cube shaped impermeable grains.