  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.
