Swimming with small and large amplitude waves in a confined liquid crystal

Boundaries can have a significant impact on the physics of microorganism locomotion. Here we examine the effects of confinement by a rigid boundary or symmetric channel on undulatory locomotion in an anisotropic fluid, treated as a nematic liquid crystal. The competition between hydrodynamics, fluid elasticity, and anchoring conditions results in a complex locomotion problem with unique transport properties. We examine this problem analytically using a well-known mathematical model, an infinite swimming sheet with small wave amplitude, and numerically for large amplitude waves using a modification of the immersed boundary method. For a prescribed stroke and strong planar anchoring in the narrow channel, we demonstrate that the swimming speed approaches its Newtonian value, though the power required to maintain the swimmer's speed depends on the properties of the liquid crystal. We also show that an unusual prograde swimming (in the direction of transverse wave propagation) theorized to exist at small wave amplitude persists at large amplitude, and that the presence of a sufficiently close boundary returns the swimming behavior to the more standard retrograde motion (opposite the direction of the traveling wave).