  Several recent experiments investigate the orientational and transport
behavior of self-driven bacteria and colloidal particles in nematic liquid
crystals. Correspondingly, we study theoretically the dynamics of a minimal
model microswimmer in a uniaxially anisotropic fluid. As a first step, the
hydrodynamic Green's function providing the resulting fluid flow in response to
a localized force acting on the anisotropic fluid is derived analytically. On
this basis, the behavior of both puller- and pusher-type microswimmers in the
anisotropic fluid is analyzed. Depending on the propulsion mechanism and the
relative magnitude of different involved viscosities, we find alignment of the
swimmers parallel or perpendicular to the anisotropy axis. Particularly, also
an oblique alignment is identified under certain circumstances. The observed
swimmer reorientation results from the hydrodynamic coupling between the
self-induced fluid flow and the anisotropy of the surrounding fluid, which
distorts the self-generated flow field. We support parts of our results by a
simplified linear stability analysis. Our theoretical predictions are in
qualitative agreement with recent experimental observations on swimming
bacteria in nematic liquid crystals. They support the objective of utilizing
the, possibly switchable, anisotropy of a host fluid to guide individual
microswimmers and active particles along a requested path, enabling controlled
active transport.
