A mathematical model of roll-to-web kiss coating

A mathematical model is presented for equilibrium flow in the coating bead of a roll-to-web kiss coater, operating in reverse mode with the web, tension T, wrapped over the applicator roll at a small angle, beta. The lubrication approximation is introduced and predictions presented for the him thicknesses on both the web and applicator roll, which move with peripheral speeds U-1 and U-2 respectively, the gap thickness commensurate with the position of the applicator roll centre, the fluid pressure as a function of the web-to-roll speed ratio, S = U-1/U-2, capillary number, Ca, and applied load, T beta, for the case S < 1. In particular, the ratio of web film thickness to applicator roll radius is found to be directly proportional to Ca and (1 - S)(2) and inversely proportional to T beta. A comparison with experimental data confirms that this ratio is proportional to Ca, that the pressure maximum lies downstream of the applicator rolls central position, and that a sub-ambient loop exists close to the downstream meniscus.