Undulatory swimming in viscoelastic fluids under confinement

Abstract: 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.