Abstract

Mathematical models for sedimentation processes are needed in numerous industrial applications for the description, simulation, design and control of solid-liquid separation processes of suspensions. The first simple but complete model describing the settling of a monodisperse suspension of small rigid spheres is the kinematic sedimentation model due to Kynch [93], which leads to a scalar nonlinear conservation law. The extension of this model to flocculated suspensions, pressure filters, polydisperse suspensions and continuously operated clarifier-thickener units give rise to a variety of time-dependent partial differential equations with intriguing non-standard properties. These properties include strongly degenerate parabolic equations, free boundary problems, strongly coupled systems of conservation laws which may fail to be hyperbolic, and conservation laws with a discontinuous flux. This contribution gives an overview of the authors' research that has been devoted to the mathematical modeling of solid-liquid separation, the existence and uniqueness analysis of these equations, the design and convergence analysis of numerical schemes, and the application to engineering problems. Extensions to other applications and general contributions to mathematical analysis are also addressed. © Springer-Verlag Berlin Heidelberg 2006.