Model equations for gravitational sedimentation-consolidation processes

We develop a general phenomenological theory of sedimentation-consolidation processes of flocculated suspensions, which are considered as mixtures of two superimposed continuous media. Following the standard approach of conti nuum mechanics, we derive a mathematical model for these processes by apply ing constitutive assumptions and a subsequent dimensional analysis to the m ass and linear momentum balance equations of the solid and liquid component . The resulting mathematical model can be viewed as a system of Navier-Stok es type coupled to a degenerating convection-diffusion equation by singular perturbation terms. In two or three space dimensions, solvability of these equations depends on the choice of phase and mixture viscosities. In one s pace dimension, however, tills model reduces to a quasilinear strongly dege nerate parabolic equation, Sor which analytical and numerical solutions are available. The theory is applied to a batch sedimentation-consolidation pr ocess.