Particle migration and suspension structure in steady and oscillatory plane Poiseuille flow

A structure-tensor-based model is used to compute the microstructure and velocity field of concentrated suspensions of hard spheres in a fully developed, pressure-driven channel flow. The model is comprised of equations governing conservation of mass and momentum in the bulk suspension, conservation of particles, and conservation of momentum in the particle phase. The equations governing the relation between structure and stress in hard-sphere suspensions were developed previously and were shown to reproduce quantitatively results obtained by Stokesian dynamics simulations of linear shear flows. In nonhomogeneous, pressure-driven flows, the divergence of the particle contribution to the stress is nonzero and acts as a body force that causes particles to migrate across streamlines. Under steady conditions, the model predicts that the resulting migration causes particles to move to the center of the channel, where the concentration approaches the maximum packing for hard-sphere suspensions. In oscillatory flow, the behavior depends strongly on the amplitude of the strain. For oscillations with large strains, the particles migrate to the channel center. However, when the strain is small, the maximum concentration is located either at a position between the channel center and walls or, in the limit of very small strains, at the wall. The migration to the wall induced by small-strain oscillation occurs in conjunction with the suspension microstructure becoming ordered. This behavior agrees qualitatively with experimental observations reported in the literature. However, the predicted rate of migration toward the wall in the simulations is significantly slower than what is observed experimentally.