The motion of Brownian particles and sediment on an inclined plate

The gravitational settling of a homogeneous suspension of Brownian particles on an inclined plate is considered. The hindered settling towards the wall and the viscous, buoyancy-driven bulk motion of the sediment are considered assuming steady conditions and accounting for the effects of Brownian diffusion, shear-induced diffusion and migration of particles due to a gradient in shear stress. Generally, the results show the development of a sediment boundary layer where the settling towards the wall is balanced by Brownian diffusion at the beginning of the plate and by shear-induced diffusion further downstream. Compared to previous results in the literature, the present theory allows steady-state solutions for extended values of the plate inclination and particle volume fraction above the sediment; upon reconsidering the case with non-Brownian particles, a new similarity solution, with a stable shock in particle density, is developed.