Dynamics and rheology of particles in shear-thinning fluids

Particle motion in non-Newtonian fluids can be markedly different than in Newtonian fluids. Here we look at the change in dynamics for a few problems involving rigid spherical particles in shear-thinning fluids in the absence of inertia. We give analytical formulas for sedimenting spheres, obtained by means of the reciprocal theorem, and demonstrate quantitatively the differences in comparison to a Newtonian fluid. We also calculate the first correction to the suspension viscosity, the Einstein viscosity, for a dilute suspension of spheres in a weakly shear thinning fluid.