  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 quantitively 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.
