Interfacial instabilities in sediment suspension flows

We report the existence of interfacial instability in the two-dimensional channel flow of a sediment suspension whose particles diffuse in the carrier fluid due to shear-induced collisions. We derive partial differential equations that govern the deformations of the interface between the sediment suspension and the clear fluid, and devise a perturbation method that preserves the positivity of the particle volume fraction. We solve perturbed momentum, particle transport and deforming interface equations to show that a Kelvin Helmholtz-type unstable wave develops at the interface for wavelengths longer than a critical value. Short-wavelength oscillations of the interface are damped due to shear-induced diffusion of particles. We also show that the lowest critical Reynolds number, above which the interface is unstable, occurs for intermediate values of the total volume fraction of particles.