  Shear-thinning is an important rheological property of many biological
fluids, such as mucus, whereby the apparent viscosity of the fluid decreases
with shear. Certain microscopic swimmers have been shown to progress more
rapidly through shear-thinning fluids, but is this behavior generic to all
microscopic swimmers, and what are the physics through which shear-thinning
rheology affects a swimmer's propulsion? We examine swimmers employing
prescribed stroke kinematics in two-dimensional, inertialess Carreau fluid:
shear-thinning "Generalized Stokes" flow. Swimmers are modeled, using the
method of femlets, by a set of immersed, regularized forces. The equations
governing the fluid dynamics are then discretized over a body-fitted mesh and
solved with the finite element method. We analyze the locomotion of three
distinct classes of microswimmer: (1) conceptual swimmers comprising sliding
spheres employing both one- and two-dimensional strokes, (2) slip-velocity
envelope models of ciliates commonly referred to as "squirmers" and (3)
monoflagellate pushers, such as sperm. We find that morphologically identical
swimmers with different strokes may swim either faster or slower in
shear-thinning fluids than in Newtonian fluids. We explain this kinematic
sensitivity by considering differences in the viscosity of the fluid
surrounding propulsive and payload elements of the swimmer, and using this
insight suggest two reciprocal sliding sphere swimmers which violate Purcell's
Scallop theorem in shear-thinning fluids. We also show that an increased flow
decay rate arising from shear-thinning rheology is associated with a reduction
in the swimming speed of slip-velocity squirmers. For sperm-like swimmers, a
gradient of thick to thin fluid along the flagellum alters the force it exerts
upon the fluid, flattening trajectories and increasing instantaneous swimming
speed.
