Segregation in inclined flows of binary mixtures of spheres

Abstract

We outline the equations that govern the evolution of segregation of a binary mixture of spheres in flows down inclines. These equations result from the mass and momentum balances of a kinetic theory for dense flows of inelastic spheres that interact through collisions. The theory employed for segregation is appropriate for particles with relatively small differences in size and mass. The flow of the mixture is assumed to reach a fully developed state much more rapidly than does the concentrations of the two species. We illustrate the predictions of the theory for a mixture of spheres of the same diameter but different masses and for spheres of different diameters but nearly the same mass. We show the evolution of the profiles of the concentration fractions of the two types of spheres and the profiles in the final, steady state. The latter compare favourably with those obtained in discrete-element numerical simulations.