The governing equations for a nematic liquid crystal Hele-Shaw cell #

Joseph Cousins, Stephen Wilson, Nigel Mottram

10:30 Tuesday in 3E11.

Part of the Liquid crystals and transport models session.

Abstract #

Much of the previous work on Hele-Shaw flow has focused on isotropic fluids. Strangely, there has been relatively little work in the theory of Hele-Shaw cells filled with nematic liquid crystals (nematics), despite their relevance to the liquid crystal display (LCD) industry, where thin-film flows of nematic are a key element of LCD manufacturing and recent work on nematic microfluidics. In the present work, we formulate and analyse a theoretical model for a nematic Hele-Shaw cell bounded between parallel plates with a free fluid boundary. In particular, we derive the thin-film Ericksen–Leslie equations, which govern the behaviour of nematic Hele-Shaw flow, and subsequently, consider the thin-film Ericksen-Leslie equations in the limiting case in which nematic elasticity effects dominate viscous effects and the limiting case in which viscous effects dominate nematic elasticity effects. In these limiting cases, the thin-film Ericksen–Leslie equations reduce, much like the well-studied isotropic problem, to classical well-studied partial differential equations, namely Poisson’s equation and Laplace’s equation, which allow analytical solutions to be obtained in many situations. We demonstrate the use of the derived governing equations by analysing a common LCD manufacturing method called the One-Drop-Filling (ODF) method. In the ODF method, an array of nematic drops are squeezed between parallel plates inducing a thin-film flow which ultimately fills the device. In particular, we consider a two-droplet ODF setup and obtain the nematic pressure, velocity and average molecular orientation (commonly called the director) in the limiting cases. We expect many other systems involving thin-film flows of nematics, including experiments on nematic viscous fingering and nematic microfluidics, can also be analysed with the reduced models obtained.