Mathematical model and numerical simulation of the settling of flocculated suspensions

Thickeners for solid-liquid separation are still designed and controlled empirically in the mining industry. Great efforts are being made to develop mathematical models that will change this situation. Starting from the basic principles of continuum mechanics, the authors developed a phenomenological theory of sedimentation for flocculated suspensions which takes the compressibility of the flocs under their own weight and the permeability of the sediment into consideration. This model yields, for one space dimension, a first-order hyperbolic partial differential equation for the settling and a second-order parabolic partial differential equation for the consolidation of the sediment, where the location of the interface with the change from one equation to the other is, in general, unknown beforehand. This initial-boundary value problem was analyzed mathematically, and transient solutions are obtained for several continuous feed and discharge hows. A finite difference numerical method is used to calculate concentration profiles of the transient settling process, including the filling up and emptying of a thickener. (C) 1998 Elsevier Science Ltd. All rights reserved.