FLOWS IN FORWARD DEFORMABLE ROLL COATING GAPS - COMPARISON BETWEEN SPRING AND PLANE-STRAIN MODELS OF ROLL COVER

Roll coating is distinguished by the use of one or more gaps between r otating cylinders to meter a continuous liquid layer and to apply it t o a continuous flexible substrate. Of the two rolls that make a forwar d-roll coating gap, one is often covered by a layer of deformable elas tomer. Thin films can be obtained without the risk of clashing two har d rolls. Liquid carried into the converging side of the gap can develo p high enough pressure to deform the resilient cover, which changes th e gap geometry and thus alters the velocity and pressure fields. The c omplete understanding of the flow in this situation is vital to the op timization of this widely used coating method; however, this elastohyd rodynamic action is not well understood. The situation is similar to w hat is called the Soft-Elastohydrodynamic Lubrication regime (Soft EHL ); however, the range of minimum distance between the rotating rolls, roll speed, and therefore flow rate through the gap in the roll coatin g process is one to three orders of magnitude larger than the typical values reported in previous work on Soft EHL. Earlier works on deforma ble roll coating analyzed the action with both the lubrication approxi mation and the full Navier-Stokes solution and different one-dimension al models of roll cover deformation. In order to test the accuracy of the past approaches, and to evaluate the relationship between the empi rical constant used in the one-dimensional model to the relevant physi cal parameters, a complete, two-dimensional formulation has to be empl oyed for both the liquid flow and the solid deformation. In this work, the flow between a rigid and a deformable rotating roll was examined by solving the complete Navier-Stokes system coupled with a non-linear plane-strain model of the roll cover deformation. The approximate and computationally cheaper approach is evaluated in which the compliant wall is represented by an array of radially-oriented Hookean springs. The equation system was solved by the Galerkin/finite element method; the resulting set of non-linear algebraic equations of the fully coupl ed problem was solved by Newton's method with initialization by pseudo -arc-length continuation as parameters were varied, Results show how r oll deformation affects the total flow rate and forces on the rolls an d illustrate how a deformable roll can be used to obtain thin coated l ayers with much less sensitivity to roll runout than those obtained wi th rigid rolls. (C) 1997 Academic Press.