A mathematical model for blade coating of a nematic liquid crystal

The standard industrial process of blade-coating is now being used to produce new liquid crystal displays (LCDs) in which a liquid crystal and optical layers are coated onto a substrate. Motivated by this new LCD manufacturing process, we use the Ericksen-Leslie equations to develop a simple mathematical model for blade coating of a nematic liquid crystal. The direction and uniformity of the director are important factors for the performance of the displays, particularly when this alignment is 'frozen in' within optical layers. For this reason we investigate the flow and director within a liquid crystal film both after emerging from the region under a blade (the so-called 'drag-out' problem) and before entering the region under a blade (the so-called 'drag-in' problem). We restrict our attention to thin films and small director angles, and we study two particular cases in which either orientational elasticity effects or flow effects dominate the alignment of the liquid crystal. We find that there is a unique solution of the drag-out problem, whereas there may be multiple solutions of the drag-in problem. When orientational elasticity effects dominate we obtain a simple analytical solution for the director. When flow effects dominate we find that the director is uniform in the bulk of the liquid crystal, which exhibits thin orientational boundary layers near the substrate and the free surface, within which the director orientation changes rapidly from its prescribed boundary value to the flow alignment angle. These boundary layers may be potential locations for the nucleation of defects.