Distribution of Nearest Neighbors in Dilute Suspensions of Monodisperse Spheres

Abstract

A model is proposed to describe the distribution of distances between nearest neighbors in random-packed low-density assemblies of equal-sized spheres. The model is based on the probability of not finding any sphere center in an arbitrary volume of a given size. This probability contains a limiting packing density, φ_m, as a fitting parameter. The physical meaning of φ_m is the solids concentration above which every particle in the suspension is in contact with at least one of its neighbors. It means that at solids concentration φ = φ_m the fraction of particles whose motions are constrained by the presence of any other contacting particles becomes unity. The value of φ_m is evaluated from nearest neighbor distributions in random assemblies of spheres obtained by computer simulation. The closeness of the resulting value, φ_m = 0.52, to that reported by Probstein et al. (1994) from viscosity measurements leads to the possibility of interpreting the empirical viscosity correlations in terms of the local arrangement of particles in the suspension.