Mathematical modelling of curtain coating

We present a simple mathematical model for the fluid flow in the curtain coat-ing process, exploiting the small aspect ratio, and examine the model in the large-Reynolds-number limit of industrial interest. We show that the fluid is in free fall except for a region close to the substrate, but find that the model can not describe the turning of the curtain onto the substrate. We find that the inclusion of a viscous bending moment close to the substrate allows the curtain to “turn the corner”. 1 The industrial method of curtain coating Curtain coating is an industrial process, traditionally used to coat photographic film, which is now beginning to be used by the paper industry. A reservoir of coating mix, typically an aqueous solution containing 20-50 % solids and surfactants, is formed into a curtain of fluid using either a slot or a slide as shown in Figure 1. This curtain falls under gravity until it hits the substrate or “web ” to be coated, which is conveyed quickly underneath. The coated substrate is passed through driers to evaporate off the water and thus the finished paper is left with a, hopefully uniform, solid coating. The coater machines hav