We formulate a mathematical model for continuous sedimentation-consolidation processes of flocculated suspensions in clarifier-thickener units. The governing equation of this model is a scalar, strongly degenerate parabolic equation in which both the convective flux and the diffusion term depend on parameters that are discontinuous functions of the depth variable. A simple finite-difference scheme for the numerical solution of the model is introduced. We perform a limited analysis of steady states as desired stationary modes of operation. Finally, numerical examples illustrate that the model realistically describes the dynamics of flocculated suspensions in clarifier-thickeners. (c) 2005 Elsevier B.V. All rights reserved.