  Microswimmer suspensions in Newtonian fluids exhibit unusual macroscale
properties, such as a superfluidic behavior, which can be harnessed to perform
work at microscopic scales. Since most biological fluids are non-Newtonian,
here we study the rheology of a microswimmer suspension in a weakly
viscoelastic shear flow. At the individual level, we find that the viscoelastic
stresses generated by activity substantially modify the Jeffery orbits
well-known from Newtonian fluids. The orientational dynamics depends on the
swimmer type; especially pushers can resist flow-induced rotation and align at
an angle with the flow. To analyze its impact on bulk rheology, we study a
dilute microswimmer suspension in the presence of random tumbling and
rotational diffusion. Strikingly, swimmer activity and its elastic response in
polymeric fluids alter the orientational distribution and substantially amplify
the swimmer-induced viscosity. This suggests that pusher suspensions reach the
superfluidic regime at lower volume fractions compared to a Newtonian fluid
with identical viscosity.
