A two-scale model for discrete cell gravure roll coating

Abstract

A two-dimensional model for predicting the fluid pick-out and coated film thickness characteristics of a discrete-cell direct gravure roll coater operating in reverse mode is derived. A novel multi-scale 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 pick-out 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.

A predictive model for discrete cell gravure roll coating

“…At web tensions less than points A2 and B2 in Figure 14 there is no contact pressure component ( Figure 15a) and a positive non-zero minimum gap is maintained throughout the coating bead, creating a region of constant pressure (Figure 14a). This is a similar pressure profile found by Hewson et al (2011) who modelled low tension gravure coating. Pickout ratio is only sensitive to changes in web tension below this point because it leads to changes in minimum gap, thereby adjusting flow rate through the coating bead.…”

“…The method here builds on the multiscale approach for analyzing gravure rolls by Hewson et al (2011), extending it beyond the two-dimensional test case to real roll geometries and …”

“…Hewson et al (2011) was the first to adopt the HMM for the analysis of gravure coating, however their model was restricted to a two dimensional topography. The present study expands this model to investigate three dimensional topography, industrially representative web tensions and web-to-roll contact.…”

“…The assumption is made that the meniscus radius of curvature is related to the gap, g (Hewson et al, 2011). …”

Two-scale EHL: Three-dimensional topography in tilted-pad bearings

“…Flow factors were introduced to account for the small scale simulations but micro-EHL effects were not considered. A similar model was developed for discrete cell gravure roll coating by Hewson et al [33]. A relationship was derived linking homogenised results of Stokes flow simulations at the small scale to a pressure gradient -mass flow rate relationship at the large scale.…”