Surfaces of hard-sphere systems

Abstract

In various situations surfaces appear that are formed by systems of hard spheres. Examples are porous layers as surfaces of sand heaps and biofilms or fracture surfaces of concrete. The present paper uses a model where a statistically homogeneous system of hard spheres with random radii is intersected by a plane and the surface is formed by the spheres with centers close to this plane. Formulae are derived for various characteristics of such surfaces: for the porosity profile, i.e., the local porosity in dependence on the distance from the section plane and for the geometry of the sphere caps that are located above the section plane. It turns out that these characteristics only depend on the first-order characteristics of the sphere system, its sphere density and the sphere radius distribution. Comparison with empirically studied biofilms shows that the model is realistic.