Mathematical modelling of curtain coating

We present a simple mathematical model for the fluid flow in the curtain coating process, exploiting the small aspect ratio, and examine the model in the largeReynolds-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 have edge guides with water running in them to fix the width of the curtain as, without them, the curtain is observed to “neck in” laterally. In the paper industry this technology is run at much higher web speeds, and with fluids of very different rheologies, than in the photographic industry. 1.1 Advantages and disadvantages of curtain coating Methods currently used to coat paper include blade coating and air-knife coating, where a thick layer of fluid is applied and scraped off to leave the desired thickness. This, however, places a constraint on the speed of coating since, when operated at high speeds, Figure 1: The slot and slide coaters.