Stability of concentrated suspensions under Couette and Poiseuille flow

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 twodimensional 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.

Self-similar velocity profiles and mass transport of grains carried by fluid through a confined channel

“…Treatments of such geometries have also been carried out using theories of granular rheology including those relating to the viscous number and kinetic theory [24][25][26][27][28][29][30][31] . Study of Poiseuillestyle flow of grains on the other hand is somewhat limited to being either driven by gravity, for instance dry grains falling through a channel 32,33 , or in the complete absence of it, where pressure-driven density-matched grains in suspension exhibit Bingham-style plug flow velocity profiles similar to yield stress fluids 26,34,35 .…”

Roll of Newtonian and Non-Newtonian Motion in Analysis of Two-Phase Hepatic Blood Flow in Artery during Jaundice

“…International Journal of Mathematics and Mathematical Sciences Using (21), equation ( 48) can be written as follows:…”

“…e precarious and incompressible stream of non-Newtonian liquid through composite stenosis was also considered [19]. e two phases Bingham model was proposed by Ahnert et al [20,21]. ey used the differential equation for solutions and solve the mathematical problems.…”