The distribution of kth nearest neighbours and its application to cluster settling in dispersions of equal spheres

The spatial distribution of spheres in a very dilute suspension is described approximately by a Poison distribution, but much better approximations result when the volume of the spheres is taken into account. For solids fractions up to 0.32, the distribution of kth nearest neighbours calculated from the radial distribution function for a hard-sphere gas agreed closely with that determined from a computer simulation. This distribution provides insight into the concentration threshold for cluster settling and the increase in sedimentation rate with time in dilute dispersions. Two models provide rough explanations for the maintenance of cluster velocities greater than the Stokes velocity.