This paper presents a unified theory of solid-liquid separation of flocculated suspensions including sedimentation-thickening, centrifugation and filtration. After identifying the variables and equations for each of the operations, thickening, centrifugation and filtration, and establishing the compatibility between them, we show that these processes can be described by variants of one scalar hyperbolic-parabolic strongly degenerate partial differential equation with appropriate initial and boundary conditions. To complete the description, constitutive equations should be postulated for the solid-fluid interaction forces in the suspension and for the permeability and the compressibility of the porous medium, which is either a sediment or a filter cake. A particular unit operation can then be simulated by solving these equations numerically. The mathematical analysis of the resulting model confirms the well-posedness of the mathematical model and support the design of robust numerical simulation methods. These methods are employed to calculate a variety of examples from thickening, centrifugation and filtration, which illustrate the theory. (C) 2003 Elsevier B.V. All rights reserved.