Flow around a squirmer in a shear-thinning fluid

Microorganisms often swim in biological fluids displaying shear-thinning rheology. Although previous analyses exploited the reciprocal theorem to calculate the propulsion speed of a squirmer in a shear-thinning fluid, this approach does not provide information on the flow surrounding the squirmer. In this work, we fill in this missing information by calculating the non-Newtonian correction to the flow in the small Carreau number limit analytically. Our detailed flow analysis allows us to physically interpret how shear-thinning rheology alters swimming performance at low Reynolds numbers.