Author(s) :
Tobias Ahnert
,
Andreas Münch
,
Barbara Niethammer
,
Barbara Wagner
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 21-2015
MSC 2000
- 76T20 Suspensions
-
35Q35 Other equations arising in fluid mechanics
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.
Keywords :
stability analysis, suspensions, yield stress, multiphase flow model, Bingham flow