  Low Reynolds number swimmers frequently move near boundaries, such as
spirochetes moving through porous tissues and sperm navigating the reproductive
tract. Furthermore, these microorganisms must often navigate non-Newtonian
fluids such as mucus, which are typically shear-thinning and viscoelastic.
Here, we experimentally investigate such a system using the model biological
organism \textit{C. elegans} swimming through microfluidic channels containing
viscous Newtonian fluids and viscoelastic fluids. Swimmer kinematics and
resulting flow fields are measured as a function of channel width and therefore
the strength of confinement. Results show that, for viscoelastic fluids, weak
or moderate confinement can lead to enhancement in propulsion speed but for
strong confinement this enhancement is lost and the swimming speed is slower
than for an unconfined nematode. We use theory developed for bending elastic
filaments in viscoelastic fluids to show that while (weak) confinement leads to
increases in swimming speed there is a, $De-$ dependent, $Wi$ (Weissenberg
number) number transition from a linear stress response regime to a nonlinear
(or exponential) stress response regime. The experimentally obtained velocity
fields are used to calculate a Weissenberg number to show that the decrease in
swimming speed with confinement is likely related to growth in elastic stresses
around the swimmer.
