  We study ionic and mass transport in a liquid crystalline fluid film in its
nematic phase under an applied electrostatic field. Both analytic and numerical
solutions are given for some prototypical configurations of interest in
electrokinetics: Thin films with spatially nonuniform nematic director that are
either periodic or comprise a set of isolated disclinations. We present a
quantitative description of the mechanisms inducing spatial charge separation
in the nematic, and of the structure and magnitude of the resulting flows. The
fundamental solutions for the charge distribution and flow velocities induced
by disclinations of topological charge $m=-1/2, 1/2$ and $1$ are given. These
solutions allow the analysis of several designer flows, such as "pusher" flows
created by three colinear disclinations, the flow induced by an immersed
spherical particle (equivalent to an $m=1$ defect) and its accompanying $m=-1$
hyperbolic hedgehog defect, and the mechanism behind nonlinear ionic mobilities
when the imposed field is perpendicular to the line joining the defects.
