Percolation through Voids around Structurally Disordered Impermeable Inclusions

The permeability of porous media with respect to fluid flow is contingent on the availability of channels comprised of connected voids among the particles making up the medium. If the density of the latter exceeds a critical value, known as the percolation threshold, fluid flow on macroscopic scales is blocked. To account for the high degree of irregularity of grains in realistic systems, we provide a geometrically exact treatment of percolation phenomena involving strongly disordered barrier particles. On the one hand, we randomly perturb the shapes of grains (e.g. for cubes, tetrahedra, and icosahedra), with an insensitivity of the critical volume fraction to weak disorder giving way to a monotonic rise for moderate to strong structural distortions. On the other hand, to examine assemblies formed from grains created by agressive fragmentation processes, we examine both aligned and randomly oriented cubes fragmented by randomly placed slicing planes with isotropically sampled orientations. For both the former and the latter, we find a convergence of percolation thresholds to a common critical void volume fraction for a mean number of sustained stochastically chosen slices on the order of 10. We also discuss the effect of weathering on the critical grain concentration.