The porosity and contact points in multicomponent random sphere packings calculated by a simple statistical geometric model

Abstract

The structure of a random packing of spheres with different sizes is reduced to an amenable system composed of known subunits by making one simplifying assumption: that all spheres touch their neighbors. A simple theory involving statistics and geometry is presented by which the frequency distribution of these subunits can be calculated from the sphere size distribution and hence the structure of the packing can be determined. Results are presented for the porosities of binary and ternary sphere packings which bear a qualitative similarity to previously published experimental results. After defining the coordination numbers which are involved in multicomponent packings, results are presented for the contacts in such a packing. These results give more detail and a more comprehensive description of the structure of these packings than is possible to obtain by experiment. The model is proposed as providing a general idealized framework for the description and further investigation of multicomponent packings.