A two-scale model for discrete cell gravure roll coating

A two-dimensional model for predicting the fluid pickout and coated film thickness characteristics of a discrete cell direct gravure roll coater operating in reverse mode is derived. A novel multiscale approach is adopted for this purpose and the resulting equations solved numerically for inertia-less flow conditions. A system of stiff ordinary differential equations is found to be sufficient to capture the major gross flow features, while at the cell level the analysis is based on a finite element solution of the momentum and continuity equations. It represents the first such predictive model of its kind, with particular interest placed on the nature of both the pressure distribution and web-to-roll gap profile spanning the coating bead. The effect of key operating parameters, web-to-roll speed ratio, web-tension, wrap-angle, capillary number and cell-geometry, on the degree of fluid pickout from gravure cells and the coated film thickness is explored. Although an idealised model, the trends observed show qualitative agreement with existing experimental data collected on a small-scale gravure coating rig and point the way forward to the eventual formulation of a full three-dimensional predictive model of the process.

► Multiscale method applied to analyse discrete cell gravure roll coating.
► The most important operating parameter is the web-to-roll speed ratio: increase in speed ratio increases pickout.
► An increase in capillary number leads to an increase in pickout (and coated film thickness).
► An increase in web tension leads to a small decrease in pickout (and coated film thickness).
► The effects of cell geometry are also demonstrated.