On the two-point correlation functions in random arrays of nonoverlapping spheres

Abstract

For a random dispersion of identical spheres, the known two-point correlation functions like "particle-center", "center-surface", "particle-surface", etc., are studied. Geometrically, they give the probability density that two points, thrown at random, hit in various combinations a sphere's center, a sphere, or a sphere's surface. The basic result of the paper is a set of simple and integral representations of one and the same type for these correlations by means of the radial distribution function for the set of sphere's centers. The derivations are based on the geometrical reasoning, recently employed by Markov and Willis when studying the "particle-particle" correlation. An application, concerning the effective absorption strength of a random array of spherical sinks, is finally given.