Average nearest-neighbor distances between uniformly distributed finite particles

Abstract

The average center-to-center distance (and hence the average free distance) between a finite particle and its nearest neighbor is calculated for three problems involving monodisperse particles uniformly distributed in space. These are: (1) the nearest-neighbor distance in a three-dimensional distribution of finite spheres; (2) the nearest-neighbor distance in a plane section normal to the axes of finite parallel cylinders; (3) the nearest-neighbor distance in a plane section through the three-dimensional array of spheres. Our calculations are compared with their well-known point-particle counterparts; they show that the average free distances obtained from the point-particle approximations are reasonable only at small volume fractions (less than 0.05 in the more favorable two-dimensional problems). For each case considered, the range of volume fractions over which our calculations should be valid is discussed. The applicability of our results to various problems involving dispersions of a second phase is also discussed.