  The swimming behavior of bacteria and other microorganisms is sensitive to
the physical properties of the fluid in which they swim. Mucus, biofilms, and
artificial liquid-crystalline solutions are all examples of fluids with some
degree of anisotropy that are also commonly encountered by bacteria. In this
article, we study how liquid-crystalline order affects the swimming behavior of
a model swimmer. The swimmer is a one-dimensional version of G. I. Taylor's
swimming sheet: an infinite line undulating with small-amplitude transverse or
longitudinal traveling waves. The fluid is a two-dimensional hexatic
liquid-crystalline film. We calculate the power dissipated, swimming speed, and
flux of fluid entrained as a function of the swimmer's waveform as well as
properties of the hexatic film, such as the rotational and shear viscosity, the
Frank elastic constant, and the anchoring strength. The departure from
isotropic behavior is greatest for large rotational viscosity and weak
anchoring boundary conditions on the orientational order at the swimmer
surface. We even find that if the rotational viscosity is large enough, the
transverse-wave swimmer moves in the opposite direction relative to a swimmer
in an isotropic fluid.
