Model equations for gravitational sedimentation-consolidation processes

Abstract

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 continuum mechanics, we derive a mathematical model for these processes by applying constitutive assumptions and a subsequent dimensional analysis to the mass and linear momentum balance equations of the solid and liquid component. The resulting mathematical model can be viewed as a system of Navier-Stokes 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 space dimension, however, this model reduces to a quasilinear strongly degenerate parabolic equation, for which analytical and numerical solutions are available. The theory is applied to a batch sedimentation-consolidation process.