| In every coating application there is an initial transient stage before the establishment of steady state. Although usually brief, start-up stages are of major concern because they often leave defects in the coating, resulting in significant waste of material and time. Obviously, discontinuous operations like patch coating that include a succession of start-ups and stop-downs, are troubled the most. The emergence of discontinuous coating operations in the manufacturing of modern products like LCD displays and silicon wafers increases the need for smooth, straight start-ups. This work investigates, through theoretical modeling, the full sequence of events during start-up of slot coating. The objective is guidelines for optimal start-ups.; Based on distinctions in time and length scales, the process is divided into three stages: approaching of the liquid to the substrate, wetting of the substrate by the liquid, and spreading towards a steady-state configuration. Approaching is modeled as coupled two-dimensional transient flows of liquid and air, whereas during spreading the focus in solely on the liquid. In each case, the resulting Navier-Stokes equations are solved by the Galerkin method with finite element basis functions on a deformable mesh, using DASSL for integration in time. These two transient stages are bridged by the discontinuous wetting stage, where the change of topology is modeled by halting computations, repositioning of the finite element mesh to establish contact between liquid and substrate, change of the boundary conditions, remeshing, and interpolation of the existing solution on the new mesh.; Results demonstrate the importance of the air during the approaching stage in delaying contact between liquid and substrate and deforming the air-liquid interface. As the liquid comes increasingly close to the substrate, the air film breaks and contact with the substrate is established in a discontinuous fashion; the details of this process seem to be insignificant to the flow characteristics. After contact the liquid spreads on the substrate to a steady-state configuration; the time to steady-state and the leading edge of the coating are controlled by the behavior of the downstream contact line on the liquid. |
