Percolation through Porous Media comprised of Axially Symmetric Grains

The permeability of porous materials to fluid or charge flow is of fundamental and industrial relevance. The density of impenetrable grain or inclusions making up a medium determines if fluid flow occurs on large scales or if transport is not possible in the bulk limit. In the thermodynamic limit, the shift with increasing grain concentration between the former and latter scenarios is known as a percolation transition. In the case of fluid flow through irregular spaces between impenetrable grains, percolation phenomena are a class of continuum percolation known as void percolation. With a dynamic infiltration algorithm in which statistics are accumulated on virtual tracer particles navigating spaces between inclusions to find the critical grain concentration ρ_c, we have calculated percolation thresholds for randomly placed and randomly oriented axially symmetric grains for broad range of aspect ratios (from highly oblate plate-like to highly prolate needle-like inclusions), for a variety of shapes. Critical concentrations for the latter (including, e.g., ellipsoids, cylinders, and cones) appear to converge to a common geometry independent asymptotic value in the large aspect ratio limit.