Instabilities of fully developed rapid flow of a granular material in a channel

Abstract

The equations of motion for ‘rapid’ flow of a granular material have fully developed solutions representing flow driven by a body force, such as gravity, along a channel bounded by plane parallel walls. The stability of these solutions to small perturbations is investigated. For given properties of the particles and the channel walls it is found that the condition of critical stability is a relation between the mean concentration of the particles and the width of the channel. When the base state is unstable the fastest growing modes are travelling waves propagating in the axial direction and these induce characteristic patterns of variations in particle concentration, as well as velocity. These instabilities are contrasted with those found for Couette shearing in an earlier publication.