Percolation through Voids around Randomly Oriented Polyhedra and Axially Symmetric Grains.

Area of Science:

• Physics
• Materials Science
• Chemical Engineering

Background:

• Porous materials with impermeable grains restrict fluid flow to interstitial spaces.
• Percolation transitions define the density thresholds for bulk transport versus flow blockage.

Purpose of the Study:

• To calculate the critical number density for percolation (ρc) across diverse grain geometries.
• To investigate how grain shape and orientation influence fluid transport in porous media.

Main Methods:

• Dynamical infiltration of void spaces using virtual tracer particles.
• Exact treatment of inclusion geometries for various shapes, including axially symmetric and faceted solids.
• Calculation of percolation thresholds for platonic solids and truncated icosahedra.

Main Results:

• Percolation thresholds were determined for cylinders, ellipsoids, cones, and tablet-shaped grains.
• A common asymptotic value for percolation was observed for faceted solids, similar to aligned cylinders.
• Distinct percolation thresholds for aligned versus randomly oriented grains were found only for cubes.
• Anomalous diffusion exponents differed from those in standard 3D lattice models.

Conclusions:

• Grain geometry and orientation significantly impact fluid flow and percolation in porous materials.
• The study provides precise percolation data for complex and polyhedral grain shapes.
• Findings offer a more nuanced understanding of transport phenomena in disordered media.