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 by small-amplitude 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. These results are then compared to previous results on an analogous swimmer in a hexatic liquid crystal, indicating large differences in the cases of small Ericksen number and in a nematic fluid when the tumbling parameter is near the transition to a shear-aligning nematic. 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.