Percolation through Voids around Toroidal Inclusions

Abstract

In the case of media comprised of impermeable particles, fluid flows through voids around impenetrable grains. For sufficiently low concentrations of the latter, spaces around grains join to allow transport on macroscopic scales, whereas greater impenetrable inclusion densities disrupt void networks and block macroscopic fluid flow. A critical grain concentration ${\rho }_c$ marks the percolation transition or phase boundary separating these two regimes. With a dynamical infiltration technique in which virtual tracer particles explore void spaces, we calculate critical grain concentrations for randomly placed interpenetrating impermeable toroidal inclusions; the latter consist of surfaces of revolution with circular and square cross sections. In this manner, we study for the first time continuum percolation transitions involving non-convex grains. As the radius of revolution increases relative to the length scale of the torus cross section, the tori develop a central hole, a topological transition accompanied by a cusp in the critical porosity for percolation. With a further increase in the radius of revolution, as constituent grains become more ring-like in appearance, we find that the critical porosity converges to that of high aspect ratio cylindrical counterparts only for randomly oriented grains.

arXiv comment10 pages, 10 figures

References in corpus (10)

• Localization Transition of the Three-Dimensional Lorentz Model and Continuum Percolation
• Bond and Site Percolation in Three Dimensions
• The Localization Transition of the Two-Dimensional Lorentz Model
• Critical dynamics of ballistic and Brownian particles in a heterogeneous environment
• Splitting of the universality class of anomalous transport in crowded media
• Cluster-resolved dynamic scaling theory and universal corrections for transport on percolating systems
• Percolation of overlapping squares or cubes on a lattice
• Anomalous transport of a tracer on percolating clusters
• Critical pore radius and transport properties of disordered hard- and overlapping-sphere models
• Percolation through Voids around Randomly Oriented Platonic Solids