Fingering instabilities in driven thin nematic films

Motivated by experimental work (Cazabet , unpublished), we consider the pos sibility of fingering instabilities in thin films of nematic liquid crystal s. We use lubrication theory on the flow equations for nematic liquid cryst als to derive a simple model describing the evolution of the film height. A s far as we are aware, this is the first time such a systematically derived , time-dependent thin film model for nematics has been presented. Simple "l eading-order" solutions (depending on only one spatial coordinate) are foun d for two different flow driving mechanisms: (i) gravity perpendicular to t he film and (ii) gravity parallel to the film (capillarity is also included in both cases). The effect of imposing two-dimensional perturbations to th ese solutions is studied. We find that for case (i) instability is possible , depending on whether or not there is complete wetting (i.e., whether or n ot the equilibrium contact angle of the droplet with the substrate is zero) . For case (ii) we always have instability, as we would expect from the ana logous result for Newtonian fluids [Phys. Fluids 8, 460 (1996); Europhys. L ett. 10, 25 (1989)]. (C) 2001 American Institute of Physics.