Voronoi tessellation of packings of spheres: Topological correlation and statistics

Abstract

We describe three-dimensional froths obtained by the Voronoi tessellation of monosize packings of spheres at different packing fractions C from C = 0 toC = 0·58. The packings are built numerically. The distribution p(f) of the number f of faces of a cell is well approximated by a Gaussian. The average number m(f) of faces of the neighbours of a f-faceted cell follows the three-dimensional equivalent of the Aboav-Weaire law. The Lewis and the Deschlaws can be generalized to the three-dimensional case to describe the metricproperties of the froths. The distribution of the volumes of the cells is wellfitted by a gamma law at low packing fractions but becomes narrower and more symmetric at higher concentrations.