Microscopic lifeforms rarely locomote in an unconfined liquid. Solid boundaries representing biological membranes, other swimmers, or filaments much larger than the swimmer can represent elements of confinement. Due to the long range of hydrodynamic forces at this scale, the boundaries often have a dominant impact on the physics of locomotion. Here we extend previous work on locomotion of a swimmer with a prescribed stroke in confined isotropic fluids to anisotropic fluids, using the model of a nematic liquid crystal. The competition between elasticity, hydrodynamics, and anchoring conditions leads to a complex locomotion problem with unique transport properties. We examine this problem analytically and numerically for a model swimmer near a bounding wall which can itself also be elastic. For strong planar anchoring at a rigid wall, we find that the swimming speed goes to the isotropic Newtonian limit as the swimmer gets close to the wall, although the power required to maintain the swimmer’s speed depends on liquid crystal properties. We also report new findings on the swimming speed due to large-amplitude waveforms in unbounded liquid crystals.
Madison S. Krieger, Saverio E. Spagnolie and Thomas R. Powers, “Swimming in a confined liquid crystal”, arXiv, PDF