The subject of this paper is a free boundary problem for a liquid layer that is dried by evaporation. Using a Stefan type problem, we model the diffusion driven drying a layer of a liquid paint consisting of resin and solvent. For the one-dimensional case, the movement of the free boundary is found in terms of a short time asymptotic analysis. When including a fluid flow and the levelling of the surface in a two-dimensional model, two small parameter cases are discussed. The first one concerns the levelling by surface tension under the assumption of a small aspect ratio, where the thin film equation appears in the free boundary condition. The second one concerns the effect of a small perturbation of the flat free boundary that shows different decay for long and short wavelength surface elevations.
|Journal||Nonlinear analysis : theory, methods & applications|
|Publication status||Published - 2001|
|Event||3rd World Congress of Nonlinear Analysis, WCNA 2000 - Catania, Sicily, Italy|
Duration: 19 Jul 2000 → 26 Jul 2000
Conference number: 3