Stability of concentrated suspensions under Couette and Poiseuille flow

TL;DR

This paper analyzes the stability of concentrated suspensions in Couette and Poiseuille flows, revealing convective instabilities, potential ill-posedness, and jammed states near maximum packing, with implications for flow behavior and modeling.

Contribution

It introduces a stability analysis of concentrated suspensions in two flow geometries, highlighting instability mechanisms and conditions for flow ill-posedness and jamming.

Findings

Convective instability increases with particle volume fraction.

Existence of a viscosity bound for well-posed flow models.

Jammed regions form near maximum packing due to shear migration.

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.