Two-dimensional viscous flow of a suspension due to particle settling in a vertical vessel

Summary This paper investigates the influence of the viscosity of the suspension together with wall friction on sedimentation in vessels with vertical walls. The settling process is described by four basic equations, i.e. two continuity and two momentum equations. Assuming a very dilute suspension, an asymptotic expansion for small particle concentration is carried out. To first order, the well-known one-dimensional solution is recovered. The motion of the liquid, however, is a second-order effect governed by the biharmonic equation. In order to find a solution satisfying the boundary conditions, harmonic expansions are used. Thus the problem is reduced to a system of linear algebraic equations. Solutions for the two-dimensional flow of the liquid and the motion of the particles are given, and the influence on the shape of the interface between the suspension and the clear liquid is discussed.With 7 Figures