Electrokinetic flows in liquid crystal thin films with fixed anchoring.

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.