A free boundary problem for evaporating layers

B.W. van de Fliert

doi:10.1016/S0362-546X(01)00310-8

A free boundary problem for evaporating layers

B.W. van de Fliert

Research output: Contribution to journal › Article › Academic › peer-review

3 Citations (Scopus)

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
Pages (from-to)	1785-1796
Journal	Nonlinear analysis : theory, methods & applications
Volume	47
Issue number	3
DOIs	https://doi.org/10.1016/S0362-546X(01)00310-8
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

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10.1016/S0362-546X(01)00310-8

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title = "A free boundary problem for evaporating layers",

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.",

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T1 - A free boundary problem for evaporating layers

AU - van de Fliert, B.W.

N1 - Conference code: 3

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N2 - 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.

AB - 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.

KW - METIS-200496

U2 - 10.1016/S0362-546X(01)00310-8

DO - 10.1016/S0362-546X(01)00310-8

M3 - Article

VL - 47

SP - 1785

EP - 1796

JO - Nonlinear analysis : theory, methods & applications

JF - Nonlinear analysis : theory, methods & applications

SN - 0362-546X

IS - 3

T2 - 3rd World Congress of Nonlinear Analysis, WCNA 2000

Y2 - 19 July 2000 through 26 July 2000

ER -