MULTIPLE STATES OF A VISCOUS FREE-SURFACE FLOW - TRANSITION FROM PREMETERED TO A METERING INFLOW

In a forward-roll coating gap or nip, steady laminar flow of liquid be tween counter-rotating cylinders or rolls is used to split the flow in to a coated layer on one roll and a rejected layer on the other. Both layers have free surfaces in contact with air. Liquid may be carried i nto the gap as a layer on one or both rolls. If the arriving layer is not too thick, all of the Liquid flows through the gap, a situation ca lled pre-metered. If the arriving layer is too thick, part of the liqu id is rejected and runs back down the lower roll. The flow rate throug h the gap is said to be metered and is not known a priori. The transit ion from a pre-metered regime to the metered situation was examined by solving the Navier-Stokes system for steady, two-dimensional flow in a domain bounded by free surfaces, two rigid roll surfaces and chosen inflow and outflow surfaces. The free boundary condition, as described by Papanastasiou et al. (Int. j. numer methods fluids, 14, 587 (1992) ), was explored and proved to accommodate both the pre-metered and met ered regimes. A run-back flow state across the synthetic inlet plane w as obtained, provided a condition on the thickness of the arriving lay er was replaced by a kinematic condition at a certain stage. The coupl ed equation system was solved by Galerkin's method with finite element basis functions. The resulting non-linear algebraic system was solved by Newton's method with initialization by pseudo-arc-length continuat ion and automatic parameter step adjustment. Results show the existenc e of multiple solutions which can lead to hysteresis. Flow regime maps were constructed to portray the operating parameter range in which a coating bead can exist and the ranges in which a coating gap operates in either the pre-metered or the metering regime. (C) 1997 by John Wil ey & Sons, Ltd.