Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Doi
Abstract
The stability of two-dimensional Poiseuille flow and plane Couette flow
for concentrated suspensions is investigated. Linear stability analysis of
the twophase 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
