A Semi-Analytical Description of the Flow of Unidirectional, Collisional Suspensions via Extended Kinetic Theory

We address the collisional transport of cohesionless sediments over a particle bed driven by a gravitational turbulent stream under steady and fully developed flow conditions. The sediment-laden flow forms self-equilibrated resistance mechanisms at the bed surface, below which the sediments are at rest. The principle of mass, momentum, and energy conservation, for both the fluid and the particle phases, gives rise to a challenging set of differential equations, demanding closures for stresses, interaction forces and exchange of energy among the phases and energy dissipation in particle–particle encounters. We introduce a semi-analytical solution of steady, unidirectional collisional suspensions in the framework of the kinetic theory of granular gases, extended to deal with a high volumetric concentration of frictional, nonspherical sediments and the influence of the fluid drag in between collisions. We supplement the extended kinetic theory with a single-parameter and depth-adaptive, although arbitrary, concentration profile. Then, the set of nonlinear differential equations can be solved in a straightforward fashion. As part of the analytical procedure, the concentration parameter is determined without data fitting. The agreement with laboratory experiments performed with mixtures of plastic cylinders in water, in a range of strength of the turbulent shearing fluid and angle of inclination of the flow, is remarkable in terms of profiles of particle mean velocity, velocity fluctuations, and concentration, at least in the part of the flow where the length of the particle trajectories in between successive collisions can be considered unaffected by gravity and buoyancy.