Role of Surface Tension Gradients in Correcting Coating Defects in Corners

normally has an uneven surface. When surface tension can Following the application of a liquid coating to a curved subbe considered to be uniform, capillary forces tend to reduce strate, surface tension forces will act to redistribute the coating surface irregularities to produce a level film. This is the layer. The coating will thin at outside corners and thicken at dominant effect leading to relatively uniform, or level, paint inside corners as the free surface contracts to minimize the surface films, and for typical coating thicknesses is much more imenergy. If the coating is a multicomponent liquid with a volatile portant than gravity, for example. A linear theory involving component, the dynamics of the thinning process may be quite the use of the lubrication approximation, due to Orchard complex. Compositional changes in the bulk liquid during drying (1) , predicts the rate of capillary-induced leveling and has and convection of surfactant may cause surface tension gradient met with considerable practical success. or Marangoni effects. In addition there may be viscosity variations due to concentration changes and the liquid may exhibit shearThe beneficial effect of surface tension, leading to more thinning rheology. A numerical model has been developed, based uniform coating layers, is limited largely to solid surfaces on the lubrication approximations, for predicting the time-evoluor substrates whose curvature variation is small. Indeed, in tion of the coating layer thickness of a complex liquid on a curved regions where the substrate is highly curved, surface tension substrate. Substrate geometry is modeled as a time-independent can result in defects in the final coating: the coating tends overpressure distribution and the model includes such effects as to be thin at outside corners and to be thick or ‘‘puddled’’ evaporation, convection, and diffusion of solvent in the bulk liquid, at inside corners. Moreover, characteristic undulations can and convection and diffusion of a soluble surfactant. For a given be found in the final coating near these corners. Typical starting profile and substrate geometry, the temporal and spatial corner defects, sometimes known as ‘‘fat edges’’ and ‘‘picevolution of the free surface, bulk composition, surfactant concentration, surface tension, and layer-averaged viscosity are calcuture-framing’’ are illustrated schematically in Kornum and lated until the drying process is complete. We show that convection Raashou Nielsen (2) and are discussed further by Babel (3) . of surfactant away from outside corners may slow the thinning While the fundamental process leading to corner defects can in these regions. In addition, solvent evaporation may lead to be demonstrated for a nonevaporating Newtonian liquid, an Marangoni forces in the corner region, causing a ‘‘rebound’’ effect. industrially useful mathematical model must incorporate Surface tension forces will initially displace liquid from corner compositional changes during drying. Since the surface tenregions, but the thinning will produce surface tension gradients sion of many complex liquids depends on bulk composition, which act to pull liquid back to the corner region. If the evaporaspatial variation in composition for such liquids can lead to tion time scale is suitably matched to the time scale for flow insurface-tension-gradient or Marangoni effects. The resulting duced by surface tension gradients, corner defects in the final dry additional force on the liquid coating can modify the leveling coating layer can be substantially mitigated. q 1996 Academic Press, Inc.