Abstract
Kinetic theory is used to propose and solve boundary value problems for fully developed, steady, dense gravity-driven flows of mixtures composed of identical inelastic spheres and water over both inclined erodible beds and rigid, bumpy bases confined by vertical sidewalls. We solve the boundary value problems assuming values of the mass density and of the size of the spheres typical of natural materials and show the numerical solutions for the profiles of the mean velocities of the particles and fluid, the intensity of the particle velocity fluctuations, and the granular concentration. In addition, we indicate how the features of the grain velocity fluctuations profile would influence segregation in three situations when the particle phase consists of two sizes of spheres: (1) the spheres are of the same material, and only gradients of temperature influence their segregation; (2) the mass densities of the material of the spheres are such that only gravity influences segregation; and (3) the mass densities are such that the coefficients of the temperature gradients and gravity segregation mechanisms are equal. For spheres of the same material, over a rigid bumpy base, the concentration of larger spheres increases from zero at the bed to the maximum value at the top of the flow; while over an erodible bed, this concentration has its maximum value at both the bed and the top of the flow.