On the modeling of sedimentation of a suspsension

Wolfgang Wendland
Mathematisches Institut A
University of Stuttgart

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. In two of three space dimensions, solvability of the resulting 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.