Asymptotic and numerical analysis of a simple model for blade coating

Motivated by the industrial process of blade coating, the two-dimensional flow of a thin film of Newtonian fluid on a horizontal substrate moving parallel to itself with constant speed under a fixed blade of finite length in which the flows upstream and downstream of the blade are coupled via the flow under the blade is analysed. A combination of asymptotic and numerical methods is used to investigate the number and nature of the steady solutions that exist. Specially, it is found that in the presence of gravity there is always at least one, and (depending on the parameter values) possibly as many as three, steady solutions, and that when multiple solutions occur they are identical under and downstream of the blade, but differ upstream of it. The stability of these solutions is investigated, and their asymptotic behaviour in the limits of large and small flux and weak and strong gravity effects, respectively, determined

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

Steady flow of a nematic liquid crystal in a slowly varying channel

We consider steady, two-dimensional flow of a thin film of a nematic liquid crystal between a fixed blade of prescribed shape and a planar substrate moving parallel to itself with a constant velocity. We use a combination of analytical and numerical techniques to analyse the Ericksen-Leslie equations governing the fluid velocity and pressure and the director orientation when both the aspect ratio of the slowly varying channel formed between the blade and the substrate and the distortion of the director field are small. We demonstrate that, in the limit of small orientational elasticity, orientational boundary layers occur close to the substrate and close to the blade, and that, in addition, an orientational internal layer may also occur within which the director orientation changes from + Θ0 to − Θ0, where Θ0 is the flow--alignment angle