On the pressure-driven flow of suspensions: Particle migration in apparent yield-stress fluids

Suspensions of particles with viscoplastic characteristics are often found both in nature and industrial applications. However, in contrast with the case of suspensions in Newtonian fluids, the dynamics of shear-induced particle migration in yield-stress suspending materials is not yet fully understood. In this work, we present a numerical study of particle migration in pressure-driven, tube flows of suspensions of non-colloidal, spherical particles dispersed in apparent yield-stress fluids. The suspension viscosity is modeled using the classical Krieger-Dougherty equation with a novel regularized viscosity function for viscoplastic materials as the suspending medium viscosity, and the dynamics of shear-induced particle migration is described with the Diffusive Flux Model. The resulting fully coupled, non-linear, one-dimensional model is solved with a second-order finite difference scheme coupled with Newton's method. We present a parametric study that elucidates the role played by the suspension bulk concentration, Plastic number, and power-law index on the velocity profile and particle concentration distribution in the flow. Remarkably, the results show that particle migration in apparent yield-stress fluids leads to a strikingly different pattern of velocity and particle distribution profiles relative to the case of suspensions in Newtonian liquids and true yield-stress materials.