Statistical geometry of particle packings. I. Algorithm for exact determination of connectivity, volume, and surface areas of void space in monodisperse and polydisperse sphere packings

Packings of spheres serve as useful models of the geometry of many physical systems; in particular, the description of the void region in such packings (the region not occupied by the spheres) is crucial in many studies. The void region is, in general, composed of disconnected cavities. We present an algorithm for decomposing void space into cavities and determining the exact volumes and surface areas of such cavities in three-dimensional packings of monodisperse and polydisperse spheres.