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Models for the two-phase flow of concentrated suspensions

Published online by Cambridge University Press:  04 June 2018

TOBIAS AHNERT ,
ANDREAS MÜNCH  and
BARBARA WAGNER
TOBIAS AHNERT
Affiliation:
Institute of Mathematics, Technische Universität Berlin, Strasse des 17. Juni 136, Berlin 10623, Germany emails: ahnert@math.tu-berlin.de, muench@maths.ox.ac.uk, bwagner@math.tu-berlin.de
ANDREAS MÜNCH
Affiliation:
Mathematical Institute, 24–29 St Giles, Oxford OX1 3LB, UK email: muench@maths.ox.ac.uk
BARBARA WAGNER
Affiliation:
Institute of Mathematics, Technische Universität Berlin, Strasse des 17. Juni 136, Berlin 10623, Germany emails: ahnert@math.tu-berlin.de, muench@maths.ox.ac.uk, bwagner@math.tu-berlin.de
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Abstract

A new two-phase model for concentrated suspensions is derived that incorporates a constitutive law combining the rheology for non-Brownian suspension and granular flow. The resulting model exhibits a yield-stress behaviour for the solid phase depending on the collision pressure. This property is investigated for the simple geometry of plane Poiseuille flow, where an unyielded or jammed zone of finite width arises in the centre of the channel. For the steady states of this problem, the governing equations are reduced to a boundary value problem for a system of ordinary differential equations and the conditions for existence of solutions with jammed regions are investigated using phase-space methods. For the general time-dependent case a new drift-flux model is derived using matched asymptotic expansions that takes into account the boundary layers at the walls and the interface between the yielded and unyielded region. The drift-flux model is used to numerically study the dynamic behaviour of the suspension flow, including the appearance and evolution of an unyielded or jammed regions.

Keywords

Suspensionsjammingyield stressaveragingmultiphase modelphase-space methodsmatched asymptoticsdrift-flux
Type
Papers
Information
European Journal of Applied Mathematics , Volume 30 , Issue 3 , June 2019 , pp. 585 - 617
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

AM is grateful for the support by KAUST (Award Number KUK-C1-013-04). TA and BW gratefully acknowledges the support by the Federal Ministry of Education (BMBF) and the state government of Berlin (SENBWF) in the framework of the program Spitzenforschung und Innovation in den Neuen Ländern (Grant Number 03IS2151).

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