Network Approach to Void Percolation in a Pack of Unequal Spheres

A procedure is developed to map the void space in a packing of unequal spheres onto a network. This enables one to use random networks to study problems with no underlying network defined a priori. The procedure is used to calculate the continuum percolation threshold for void space percolation in sets of randomly located, overlapping spheres with unequal radii. Within the statistical uncertainty, this threshold appears to be universal: 0.159 ±{} 0.002 in two dimensions and 0.030 ±{} 0.002 in three dimensions. As a possible application, the permeability of a bead pack is discussed.