Analytical Solution of Collisional Sheet Flows

Abstract

This work focuses on the sediment transport that is dominated by collisional exchange of momentum between particles and can be identified as the transition regime between bed-load and suspended-load transport. Idealizing the particles as inelastic frictional spheres and accounting for the role of the interstitial fluid on particle collisions, three regions characterize such flows: a diffuse collisional layer neighboring the free surface, in which a simple trapezium rule is employed to solve a boundary-value problem based on the kinetic theory; a dense, algebraic layer, in which there is an algebraic balance between production and dissipation of particle fluctuation energy, the concentration is approximately constant, and correlated motion between the particles exists; and a macroviscous layer, close to the erodible bed, in which the collisions are inelastic and the fluid viscous force dominates the momentum exchange. Using boundary conditions of no-slip and yielding at the erodible bed and vanishing of the particle stresses and energy flux at the top of the sediments, an analytical description of the flow field is obtained. After a sensitivity analysis of the approximate theoretical solution to the model parameters—only one of them has a phenomenological origin and cannot be directly measured—comparisons with experiments performed on sheet flows of water and plastic cylinders, sand, or gravel assess the validity of the theory.