The aim of our work is to describe the behaviour of a liquid crystal when we coat a layer of it onto a substrate in a manner designed to optimise the optical properties of the final film. These optical properties are directly related to the orientation of the director in the film. Specifically we consider steady, two-dimensional coating of a thin film of liquid crystal onto a planar substrate, firstly by moving the substrate to the right with speed U beneath a fixed blade of prescribed shape and secondly by applying different pressure between the ends of the blade (see figure below).
The Eriksen-Leslie equations describing the velocity, pressure and director orientation under the blade are coupled and involve three elastic coefficients and five effective viscosities. We used a combination of analytical and numerical techniques to analyse these equations in the case of a small director angle and small flow alignment angle.
We are particularly interested in the effects of the shape of the blade, how big the applied pressure can be or how fast the bottom surface can be moved without affecting the stability of the flow, and how well ordered the final liquid crystal film is (i.e. how uniform the director orientation is).
Analytical solutions can be obtained in the limit of strong elasticity in which the variation of the director orientation is small. In the limit of weak elasticity the solution for the director exhibits a uniform orientation in the bulk of the channel underneath the blade and interesting boundary-layer behaviour near the channel walls, as well as an internal layer that has to be computed numerically.
References:
J. Quintans Carou, B. R. Duffy, N. J. Mottram and S. K. Wilson, Flow of a nematic liquid crystal in a slowly vaarying channel, to appear in Molecular Crystals and Liquid Crystals (2005). [pdf]
J. Quintans Carou, B. R. Duffy, N. J. Mottram and S. K. Wilson, Shear-driven and pressure-driven flow of a nematic liquid crystal in a slowly varying channel, submitted to Physics of Fluids (2005).