Particle migration in circular Couette-Poiseuille flows of non-colloidal suspensions

Abstract

The particle migration in circular Couette-Poiseuille flows of non-colloidal suspensions is theoretically studied to elucidate the effects of the coupled Couette and Poiseuille flows on the particle distribution. The flow is driven by both simple shear imposed on the inner cylinder and an axial pressure gradient between two infinite co-axial cylinders. We consider concentrated suspensions with bulk particle volume fractions ranging from \({\phi }_{\mathrm{b}}\)= 0.2 ~ 0.4, a ratio of the annular gap to the particle radius of \(\epsilon \mathrm{ = 60}\), and a radius ratio (i.e., the ratio of inner and outer radii) of \(\eta \mathrm{ = 0.877}\). The suspension-balance model is employed with rheological constitutive laws to describe the particle dynamics and predict the particle distributions. The axial flow rate is varied while maintaining a constant shear rate to examine its influence on particle migration. The parabolic axial velocity enhances the local shear rate near the inner and outer walls, causing particles to migrate to the middle of the gap undergoing shear-induced migration. As the axial flow rate increases, an increasing number of particles are transferred to the middle from near the walls. However, a sharp peak, which has been observed in Poiseuille flows, does not appear in the particle distribution. In addition, friction coefficients, which measure the torque acting on the inner cylinder, are evaluated as the axial flow rate is varied. The results reveal that friction coefficients only depend on the axial flow rate.