A theoretical analysis of free-surface flows of saturated granular-liquid mixtures

A simple two-phase model for a steady, fully developed flow of particles and water over an erodible, inclined bed is developed for situations in which the water and particles 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. Numerical solution of the resulting differential equations and boundary conditions provide velocity profiles of the fluid and particles, the concentration profile of the particles, and the depth of the flow at a given angle of inclination of the bed. Simple approximations permit analytical expressions for the flow velocities and the depth of flow to be obtained that agree with the numerical solutions and those measured in experiments.