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arXiv · 1801.02038

Stability of concentrated suspensions under Couette and Poiseuille flow

Tobias Ahnert·Andreas Münch·Barbara Niethammer·Barbara Wagner
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Abstract

The stability of two-dimensional Poiseuille flow and plane Couette flow for concentrated suspensions is investigated. 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 connections to the stability problem for the related classical Bingham-flow problem are discussed.

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Tobias Ahnert, Andreas Münch, Barbara Niethammer, Barbara Wagner. 2018-01-06. Stability of concentrated suspensions under Couette and Poiseuille flow. https://arxiv.org/abs/1801.02038

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