Approximate analytical solutions in a model for highly concentrated granular-fluid flows

We extend a simple two-phase model for a steady, fully-developed flow of particles and water over an erodible, inclined bed to situations in which the water and particles do not have the same depth. The rheology of the particles is based on recent numerical simulations and physical experiments, the rheology of the fluid is based on an eddy viscosity, and the interaction between the particles and the fluid is through drag and buoyancy. Simple approximations permit analytical expressions for the flow velocities and the depth of flow to be obtained that satisfactorily reproduce those measured in experiments.