Differences between Lattice and Continuum Percolation Transport Exponents

Abstract

We use a scaling analysis to estimate critical exponents for the electrical conductivity, elastic constants, and fluid permeability near the percolation threshold of a class of disordered continuum systems (Swiss-cheese models), where the transport medium is the space between randomly placed spherical holes. We find that the exponents are significantly larger than their counterparts in the standard discrete-lattice percolation networks, except for the case of electrical conductivity in two dimensions, where they are equal.