Microscale locomotion in a nematic liquid crystal

Microorganisms often encounter anisotropy, for example in mucus and biofilms. We study how anisotropy and elasticity of the ambient fluid affects the speed of a swimming microorganism with a prescribed stroke. Motivated by recent experiments on swimming bacteria in anisotropic environments, we extend a classical model for swimming microorganisms, the Taylor swimming sheet, actuated either by transverse or longitudinal traveling waves in a three-dimensional nematic liquid crystal without twist. We calculate the swimming speed and entrained volumetric flux as a function of the swimmer's stroke properties as well as the elastic and rheological properties of the liquid crystal. The behavior is quantitatively and qualitatively well-approximated by a hexatic liquid crystal except in the cases of small Ericksen number and in a nematic fluid with tumbling parameter near the transition to a flow-aligning nematic, where anisotropic effects dominate. We also propose a novel method of swimming or pumping in a nematic fluid by passing a traveling wave of director oscillation along a rigid wall.