Stability of concentrated suspensions under Couette and Poiseuille flow
- Ahnert, Tobias
- Münch, Andreas
- Niethammer, Barbara
- Wagner, Barbara
2010 Mathematics Subject Classification
- 76E17 76E15 76T20
2008 Physics and Astronomy Classification Scheme
- stability analysis, suspensions, yield stress, multiphase flow model
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.
- J. Engrg. Math., 111 (2018), pp. 51--77, DOI 10.1007/s10665-018-9954-x .