Lubrication theory as a means of unravelling flow structure in thin film roll coating systems

Abstract The aim of this paper is to demonstrate that lubrication theory provides a simple, yet powerful, means for understanding a wide variety of complex flow phenomena inside the bead of roll coating systems. Attention is focussed on the forward regime, with rollers moving in the same direction through the nip, and analytical predictions are obtained over a wide range of low flux (meniscus roll coating) situations. Although the full flow field within the coating bead is often quite complex due to the existence of eddies and transfer-jets, it is shown that the structure can be classified analytically according to the nature of the stagnation points within the flow. The analytical predictions axe compared with those from a full numerical solution of the flow field, which incorporates the effects of the upstream and downstream free surfaces. The agreement between the analytical and numerical results is extremely good in all instances, a fact which clearly demonstrates that much of this complex flow behaviour can be well understood without having to resort to complex numerical solutions.