Elastohydrodynamics of a moving substrate over a curved plate

Conventional drying of coated substrates usually uses air impingement to support and heat the coated web. Because of the high-velocity air flow, most of the heat is transferred by convection and the heat transfer coefficient is not uniform, leading to drying defects. To overcome this and obtain a high uniform heat transfer coefficient, the energy is supplied to the backside of the substrate by conduction through a thin air-layer between a heated plate and the moving substrate. To obtain heat transfer coefficients comparable to those from air impingement, the distance between the web and plate has to be very small, yet not touch the plate. It is essential to form and control a thin, uniform and stable air layer between the substrate and heating plate by wrapping the moving web over a plate with a large radius of curvature. Air-layer thickness entrained between the web and plate is related to the air flow rate between the two surfaces. The flow between a moving flexible substrate and curved solid surface was analyzed by theory and experiments to examine this elastohydrodynamic action and changes in air-layer thickness with the plate geometry, substrate material, and operating conditions. The theoretical model consisted of the Navier–Stokes equation to describe the air motion and cylindrical shell approximation to model the web deformation. Differential equations describing the problem were solved by the Galerkin's/finite-element method. The nonlinear algebraic system was solved by Newton's method with initialization by pseudo-arc-length continuation. In experiments, the distance between the moving web and curved plate was measured at different operating conditions. The predicted air-layer thicknesses agreed well with experimental measurements. The air-layer thickness is controlled by the flow in the plate entrance.