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Mathematical Models for the Sedimentation of Suspensions

  • Chapter
Multifield Problems in Solid and Fluid Mechanics

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 28))

Summary

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.

Research Project A2 “Sedimentation with Compression”

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Authors and Affiliations

  1. Institute for Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Stefan Berres & Wolfgang L. Wendland

  2. Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Raimund Bürger

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  1. Stefan Berres
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  2. Raimund Bürger
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  3. Wolfgang L. Wendland
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Editors and Affiliations

  1. Institut für Wasserbau, Hydromechanik und Hydrosystemmodellierung, Universität Stuttgart, Pfaffenwaldring 61, 70569, Stuttgart, Germany

    Rainer Helmig

  2. Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117, Berlin, Germany

    Alexander Mielke

  3. Institut für Angewandte Analysis und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Barbara I. Wohlmuth

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© 2006 Springer-Verlag Berlin Heidelberg

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Berres, S., Bürger, R., Wendland, W.L. (2006). Mathematical Models for the Sedimentation of Suspensions. In: Helmig, R., Mielke, A., Wohlmuth, B.I. (eds) Multifield Problems in Solid and Fluid Mechanics. Lecture Notes in Applied and Computational Mechanics, vol 28. Springer, Berlin, Heidelberg . https://doi.org/10.1007/978-3-540-34961-7_1

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  • DOI: https://doi.org/10.1007/978-3-540-34961-7_1

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