A Mathematical Model of Roll-to-Web Kiss Coating

Abstract

Amathematical 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, β. The lubrication approximation is introduced and predictions presented for the film thicknesses on both the web and applicator roll, which move with peripheral speeds U1 and U2 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 = U1/U2, capillary number, Ca, and applied load, Tβ, for the case S < 1. In particular, the ratio of web film thickne ss to applicator roll radius is found to be directly proportional to Ca and (1 – S)2 and inversely proportional to Tβ. 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.