Electrokinetic flows in liquid crystal thin films with fixed anchoring

TL;DR

This paper investigates ionic and fluid flow behaviors in nematic liquid crystal thin films under electric fields, providing analytical and numerical solutions for various defect configurations and their induced electrokinetic flows.

Contribution

It offers new analytical solutions for charge distribution and flow in nematic films with defects, enhancing understanding of electrokinetic phenomena in liquid crystals.

Findings

Charge separation mechanisms in nematics are characterized.

Flow structures induced by disclinations are quantitatively described.

Solutions for flows around topological defects are provided.

Abstract

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.