Surface flows of inelastic spheres

Abstract

We study flows of inelastic spheres on the surface of an erodible bed between frictional sidewalls and distinguish two regions in such flows: a dilute, diffuse region, neighboring the free surface, for which we solve a boundary-value problem based on the kinetic theory, and a dense algebraic layer, in which there is an approximate algebraic balance between production and dissipation of fluctuation energy. We take into account correlated motions between the particles at high volume fractions and employ the trapezoidal rule to solve, in an approximate way, for the flow quantities in the diffuse layer. Using boundary conditions of no-slip and yield at the bed and vanishing of the stresses and the energy flux at the free surface, we obtain analytical predictions of flow depth and mass flow rate that compare favorably with the results of experiments performed on glass spheres flowing on the surface of a heap and in half-filled rotating drums.