Specific surface area and volume fraction of the cherry-pit model with packed pits

This paper investigates volume fraction φ and specific surface area s for statistically homogeneous systems of partially penetrating spheres, i.e. so-called 'cherry-pit models'. In contrast to the version where the pits form an equilibrium system of hard spheres, here pits or hard spheres are considered which are packed, can be in direct contact, and form a nonequilibrium distribution. For this kind of system, new formulas for φ and s are given, which yield values in good agreement with the ones for large models constructed from hard sphere packings generated both experimentally and numerically. Surprisingly, the existing formulas for φ and s in the equilibrium cherry-pit model lead to values which deviate substantially from the values obtained here.