Shear-flow and material instabilities in particulate suspensions and granular media

This article is a review of recent theoretical work on shear flow instabilities of particulate suspensions and dry granular medium. Attention is devoted largely to steady homogeneous unbounded simple shearing flows, as a generalization of the classical Kelvin problem for Newtonian fluids, with a View towards identifying material or constitutive instabilities arising from the coupling of stress to particulate concentration and temperature fields. After reviewing the most common constitutive models, a unified linear-stability treatment is given for suspensions and granular media, based on an assumed 'short-memory' response of stress and various fluxes to perturbations on materially steady and uniform base states. A two-dimensional stability analysis of inertialess suspension flow indicates the possibility of particle-depleted sheer bands. A comprehensive three-dimensional analysis of rapid granular flow reveals transverse 'layering' and spanwise 'corrugations' as possible modes of instability. The latter appear to result from a kind of material instability, although not the simple short-wavelength instability found for suspensions. Based on the current theoretical treatments, several new studies are recommended, including the effects of granular dilatancy and yield stress, three-dimensional disturbances in suspensions and the effects of gravity in granular flow.