The sedimentation of polydisperse suspensions in vessels having inclined walls

A theory is presented for describing the sedimentation of polydisperse suspensions in two-dimensional channels having walls that are inclined to the vertical. The theory assumes that the flow is laminar and that the suspension consists of spherical beads having small particle Reynolds numbers. The suspension may consist of either $\text{N}$ distinct species of particles or of a continuum of particle sizes and densities. For the sake of simplicity, the analysis is mostly confined to the case in which the hindered settling velocity of each particle is given by its Stokes settling velocity multiplied by a function of the total local solids concentration. Under these conditions, results are developed that are useful for the design of either batch or continuous settling devices. Experimental observations were found to be in good agreement with the predictions of the present theory.