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 number of problems involving rigid spherical particles in shear-thinning fluids in the absence of inertia. We give a number of analytical formulas for sedimenting spheres, obtained by means of the reciprocal theorem, and demonstrate quantitively differences in comparison to a Newtonian fluid. We also calculate the first correction to the suspension viscosity for a dilute suspension of spheres in a weakly shear-thinning fluid.