Numerical modelling of liquid withdrawal from gravure cavities in coating operations
Schwartz LW, Moussalli P, Campbell P, Eley RR
Chemical Engineering Research & Design, 76: (A1) 22-28 JAN 1998

A numerical model is presented for the simulation of cell emptying behaviour when an engraved roller is used to transfer a liquid coating onto a moving substrate. The three-dimensional unsteady liquid motion is calculated where the flow domain is bounded above by a stress-free surface and bounded below by a moving substrate with a complex pattern of indentations. The physical model is simplified through use of the long-wave or lubrication approximation appropriate to flow in thin liquid layers. Specific predictions are made for particular cells and patterns. Cell size is found to be the principal determinant of emptying behaviour with larger cells emptying more completely. Modelling is currently restricted to the flow domain beneath the receding meniscus and drainage due to gravity. There are limitations on the dimensionless measures of coating speed. It is found that both surface tension and cell orientation are also significant in controlling the rate of drainage. Both Newtonian and shear-thinning flows are considered.