Evolution of a thin film of nematic liquid crystal with anisotropic surface energy

We use lubrication theory on the flow equations for nematic liquid crystals to derive a simple model describing the evolution of the film height under gravity, in the case of finite surface "anchoring energy" at the free surface and at the rigid substrate. This means that the molecules of the nematic have a preferred alignment at interfaces, modelled by a single-well potential surface energy (first introduced by Rapini & Papoular [9]). This paper generalises the earlier work of Ben Amar & Cummings, in which the orientation of the nematic liquid crystal molecules is effectively specified at both surfaces (strong anchoring; isotropic surface tension). Additional terms, analogous in some sense to Marangoni terms, are introduced into the PDE governing the film height evolution. The stability of the derived model is considered, and stability criteria are presented and discussed. The existence of static, drop-like solutions to the model is also briefly considered.