Percolation through Voids around Randomly Oriented Faceted Inclusions

Abstract

We give a geometrically exact treatment of percolation through voids around assemblies of randomly placed impermeable barrier particles, introducing a computationally inexpensive approach to finding critical barrier density thresholds marking the transition from bulk permeability to configurations which do not support fluid or charge transport in the thermodynamic limit. We implement a dynamic exploration technique which accurately determines the percolation threshold, which we validate for the case of randomly placed spheres. We find the threshold densities for randomly oriented hemispherical fragments and tablets with flat and curved surfaces derived from a sphere truncated above and below its equator. To incorporate an orientational bias, we consider barrier particles with dipole moments along the symmetry axis; the extent of the alignment is then tuned with uniform electric fields of varying strengths. The latter compete with thermal fluctuations which would eliminate orientational bias in the absence of an applied field.