Phenomenological foundation and mathematical theory of sedimentation-consolidation processes

The phenomenological theory of sedimentation describes a flocculated suspen sion as a mixture of the solid and the fluid as two superimposed continuous media. Starting from the mass and linear momentum balances for each compon ent, this theory yields, through constitutive assumptions and an order-of-m agnitude analysis, three coupled partial differential equations describing the sedimentation-consolidation behaviour of the suspension in several spac e dimensions. The study and numerical solution of this system of equations has started only recently, but results are available for the one-dimensiona l case, in which these modelling equations reduce to a scalar hyperbolic-pa rabolic strongly degenerate partial differential equation with appropriate initial and boundary conditions. In this contribution, the research work pe rformed by several groups of mathematicians on the formulation, analysis an d numerical solution of mathematical sedimentation models is reviewed, with an emphasis on theoretical and numerical results for the simulation of the behaviour of compressible slurries. (C) 2000 Elsevier Science B.V. All rig hts reserved.