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Journal of Engineering Mathematics

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21-02-2018

Stability of concentrated suspensions under Couette and Poiseuille flow

Authors: Tobias Ahnert, Andreas Münch, Barbara Niethammer, Barbara Wagner

Published in: Journal of Engineering Mathematics | Issue 1/2018

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Abstract

The stability of two-dimensional Poiseuille flow and plane Couette flow for concentrated suspensions is investigated. A linear stability analysis of the two-phase flow model for both flow geometries shows the existence of a convectively driven instability with increasing growth rates of the unstable modes as the particle volume fraction of the suspension increases. In addition it is shown that there exists a bound for the particle phase viscosity below which the two-phase flow model may become ill-posed as the particle phase approaches its maximum packing fraction. The case of two-dimensional Poiseuille flow gives rise to base state solutions that exhibit a jammed and unyielded region, due to shear-induced migration, as the maximum packing fraction is approached. The stability characteristics of the resulting Bingham-type flow is investigated, and the connections to the stability problem for the related classical Bingham flow problem are discussed.

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Title: Stability of concentrated suspensions under Couette and Poiseuille flow
Authors: Tobias Ahnert
Andreas Münch
Barbara Niethammer
Barbara Wagner
Publication date: 21-02-2018
Publisher: Springer Netherlands
Published in: Journal of Engineering Mathematics / Issue 1/2018
Print ISSN: 0022-0833
Electronic ISSN: 1573-2703
DOI: https://doi.org/10.1007/s10665-018-9954-x

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