Percolation through Voids around Randomly Oriented Faceted Inclusions

TL;DR

This paper presents a geometrically exact and computationally efficient method to determine percolation thresholds around randomly oriented faceted inclusions, validated for spheres and extended to biased orientations with electric fields.

Contribution

Introduces a new exact geometric approach and exploration technique for percolation thresholds around complex, oriented barrier particles, including effects of electric field bias.

Findings

Accurately determines percolation thresholds for spheres and faceted particles.

Develops a method to incorporate orientational bias via electric fields.

Validates the approach against known sphere percolation cases.

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.