  Swimming cells often have to self-propel through fluids displaying
non-Newtonian rheology. While past theoretical work seems to indicate that
stresses arising from complex fluids should systematically hinder low-Reynolds
number locomotion, experimental observations suggest that locomotion
enhancement is possible. In this paper we propose a physical mechanism for
locomotion enhancement of microscopic swimmers in a complex fluid. It is based
on the fact that micro-structured fluids will generically phase-separate near
surfaces, leading to the presence of low-viscosity layers which promote slip
and decrease viscous friction near the surface of the swimmer. We use two
models to address the consequence of this phase separation: a nonzero apparent
slip length for the fluid and then an explicit modeling of the change of
viscosity in a thin layer near the swimmer. Considering two canonical setups
for low-Reynolds number locomotion, namely the waving locomotion of a
two-dimensional sheet and that of a three-dimensional filament, we show that
phase-separation systematically increases the locomotion speeds, possibly by
orders of magnitude. We close by confronting our predictions with recent
experimental results.
