Dewetting and pattern formation in ultra-thin films of nematic liquid crystal: effects of variable substrate anchoring

We consider free surface flow of ultra-thin films of nematic liquid crystal (NLC) on a solid planar substrate. NLCs typically consist of rod-like molecules, which align with their neighbors, imparting effective elasticity and anisotropy. NLC molecules also have a preferred alignment at boundaries, a phenomenon known as anchoring. We study flows where the free surface anchoring is perpendicular to the surface (homeotropic anchoring), and parallel to the substrate (planar anchoring), and we focus particularly on cases where the planar substrate anchoring is spatially inhomogeneous. We use lubrication theory to formulate a long-wave model for the 3D flow of NLCs under these conditions. Our model accounts for the anisotropic stress tensor of NLCs (Leslie-Ericksen theory); for van der Waals' interactions between the NLC molecules and the substrate; and for the inhomogeneous strong planar substrate anchoring, as well as weak homeotropic anchoring at the free surface. We present simulations showing how the details of the substrate anchoring can strongly influence the dewetting patterns observed.