Numerical simulations of concentrated suspensions of monodisperse particles in a Poiseuille flow

Abstract

The dynamics of concentrated suspensions of non-colloidal, monodisperse particles in plane Poiseuille flows are investigated by fully three-dimensional numerical simulations for bulk volume fractions of 0.20–0.40 of neutrally-buoyant particles. The ensemble averages of the volume fraction and particle velocity profiles are consistent with previous experiments. A statistical analysis indicates that there is an intermediate region between particle layers near the wall and a plug region in the core, in which the behaviour of ensemble-averaged suspension field can be approximated by a continuum theory. In the intermediate region, the wall-normal and spanwise velocity fluctuations, angular velocity in the vorticity direction and particle shear stress are found to be linear functions of the distance from the wall. The particle normal stresses in the intermediate region are almost uniform, consistent with the concept of normal-stress-driven particle migration. The intermediate region decreases in extent and the width of the core region increases for larger bulk volume fractions. There is a remarkable similarity between the particle–phase pressure profiles scaled by the local shear rate for different bulk volume fractions. The particle pressure profiles in the intermediate region are compared with the rheological model proposed by Morris & Boulay (1999). The effective viscosity, evaluated from the ratio of the total shear stress to the fluid-phase shear stress, shows a good agreement with empirical viscosity relations in Couette-flow suspensions. In the present study, both non-local dynamics and finite-size effects of the particles are evident in the core of the channel. These effects are more pronounced at larger volume fractions.