The instability of a dispersion of sedimenting spheroids

Abstract

It is shown that hydrodynamic interactions between non-Brownian, non-spherical, sedimenting particles give rise to an increase in the number of neighbouring particles in the vicinity of any given particle. This result suggests that the suspension is unstable to particle density fluctuations even in the absence of inertia; a linear stability analysis confirms this inference. It is argued that the instability will lead to convection on a lengthscale (nl)−½, where l is a characteristic particle length and n is the particle number density. Sedimenting suspensions of spherical particles are shown to be stable in the absence of inertial effects.