Kinetic Theory applied to Inclined Flows

We apply the continuum equations of a kinetic theory to predict the features of uniform, steady, inclined flows of identical, frictional, inelastic spheres over a rigid, bumpy base between vertical, frictional side walls. Numerical solutions of these equations over a range of mass flow rates exhibit features seen in physical experiments and numerical solutions in the absence of side walls. For the densest flows, we employ a phenomenological extension of kinetic theory that involves a length scale associated with particle correlations. When a dense flow is thick enough, an algebraic balance between the production and dissipation of fluctuation energy reproduces the relation between mass flow rate and mass hold-up obtained when solving the boundary-value problem of the extended theory