WIAS Preprint No. 2159, (2015)

Stability of concentrated suspensions under Couette and Poiseuille flow



Authors

  • Ahnert, Tobias
  • Münch, Andreas
  • Niethammer, Barbara
  • Wagner, Barbara

2010 Mathematics Subject Classification

  • 76E17 76E15 76T20

2008 Physics and Astronomy Classification Scheme

  • 83.80.Hj

Keywords

  • stability analysis, suspensions, yield stress, multiphase flow model

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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