Abstract
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.
Original language | English |
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Pages (from-to) | 1785-1796 |
Journal | Nonlinear analysis : theory, methods & applications |
Volume | 47 |
Issue number | 3 |
DOIs | |
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 |
Keywords
- METIS-200496