A linear model of the motion of a low-concentration suspension of monodisperse Stokes particles in a flat channel

In the framework of the convection-diffusion approach to the monodisperse low-concentration solid phase sedimentation in a suspension moving in a flat horizontal channel, we obtain a linear boundary value problem for a parabolic equation on the local concentration of particles. We impose boundary conditions of the third kind using the condition that the flux of particles on the wetted surface is proportional to their concentration at the wall. Integral transformations yield an analytical solution of the stated boundary value problem, which we use to find the relations to determine the thickness of sediment on the bottom and top walls of the channel. Simulations show that the kinetics of the solid phase settling from a flowing suspension, as well as the sediment formation rate and its distribution on the botton and top walls of the flat channel, substantially depend on the degree of mixing of the dispersion medium and the absorption capacity of wet surfaces. We establish that for walls with low absorption capacity a decrease in the mixing intensity reduces the rate of particle sedimentation on the walls, but increases it in the case of high absorption capacity.