Hele-Shaw flow of a nematic liquid crystal

TL;DR

This paper develops a theoretical model for nematic liquid crystal flow in a Hele-Shaw cell, analyzing two limiting cases to understand flow behavior and director alignment, with applications to LCD manufacturing processes.

Contribution

It formulates the thin-film Ericksen-Leslie equations for nematic Hele-Shaw flow and analytically explores the dominant effects of elasticity and viscosity.

Findings

Elasticity-dominated case yields fixed director and anisotropic viscosity guiding flow.

Viscous-dominated case results in isotropic flow with flow-determined director behavior.

Application to the One Drop Filling method illustrates flow differences in limiting regimes.

Abstract

Motivated by the variety of applications in which nematic Hele-Shaw flow occurs, a theoretical model for Hele-Shaw flow of a nematic liquid crystal is formulated and analysed. We derive the thin-film Ericksen-Leslie equations that govern nematic Hele-Shaw flow, and consider two important limiting cases in which we can make significant analytical progress. Firstly, we consider the leading-order problem in the limiting case in which elasticity effects dominate viscous effects, and find that the nematic liquid crystal anchoring on the plates leads to a fixed director field and an anisotropic patterned viscosity that can be used to guide the flow of the nematic. Secondly, we consider the leading-order problem in the opposite limiting case in which viscous effects dominate elasticity effects, and find that the flow is identical to that of an isotropic fluid and the behaviour of the director is determined by the flow. As an example of the insight which can be gained by using the present approach, we then consider the flow of nematic according to a simple model for the squeezing stage of the One Drop Filling method, an important method for the manufacture of Liquid Crystal Displays, in these two limiting cases.