Particle migration in planar die-swell flows

We present a numerical study on particle migration in a planar extrudate flow of suspensions of non-Brownian hard spheres. The suspension is described as a Newtonian liquid with a concentration-dependent viscosity, and shear-induced particle migration is modelled according to the diffusive flux model. The fully coupled set of nonlinear differential equations governing the flow is solved with a stabilized finite element method together with the elliptic mesh generation method to compute the position of the free surface. We show that shear-induced particle migration inside the channel leads to a highly non-uniform particle concentration distribution under the free surface. It is found that particle migration dramatically changes the shape of the free surface when the suspension is compared to a Newtonian liquid with the same bulk properties. Remarkably, we observed extrudate expansion in the Newtonian and dilute suspension flows; in turn, at high concentrations, a die contraction appears. The model does not account for normal stress differences, and this result is a direct consequence of variations in the flow stress field caused by shear-induced particle migration.