Gravitational Instability in Suspension Flows

The gravity-driven flow of non-neutrally buoyant suspensions is shown to be unstable to spanwise perturbations when the shearing motion generates a density profile that increases with height. The instability is simply due to having heavier material over light. The wavelength of the perturbation is found to be on the order of the thickness of the suspension layer. The parameters important to the problem are the angle of inclination of the layer relative to gravity, the relative density difference between the particles and fluid, the ratio of the particle size to the suspension layer, and the bulk volume fraction of particles. An example showing the growth rate as a function of wave number is shown.