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.
Highlights
Larcher & Jenkins [1] predict the evolution of concentration profiles in dry flows of a binary mixture of inelastic spheres in dense inclined flows
We compare the steady states obtained with the profiles measured by Tripathi & Khakhar [6] in discrete numerical simulations
We have outlined a theoretical model for the time evolution of particle segregation of dense, collisional channel flows driven by gravity in the absence of sidewalls
Summary
Larcher & Jenkins [1] predict the evolution of concentration profiles in dry flows of a binary mixture of inelastic spheres in dense inclined flows. For the mixture, they employed the extension of kinetic theory for identical, inelastic spheres developed by Garzo & Dufty [2], modifying the expression for energy dissipation to take in to account the formation of particle clusters [3-5]. The theory employed for segregation is appropriate for particles with relatively small differences in size and mass In doing this, they assumed that the flow of the mixture reaches a fully developed state much more rapidly than does the concentrations of the two species. We compare the steady states obtained with the profiles measured by Tripathi & Khakhar [6] in discrete numerical simulations
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