The instability of liquid films with temperature-dependent properties flowing down a heated incline

We investigate the stability of free-surface flow on a heated incline. We develop a complete mathematical model for the flow which captures the Marangoni effect and also accounts for changes in the properties of the fluid with temperature. We apply a linear stability analysis to determine the stabil...

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Bibliographic Details
Published inAIMS mathematics Vol. 4; no. 6; pp. 1700 - 1720
Main Authors Pascal, Jean-Paul, D’Alessio, Serge, Rubaida Zafar, Syeda
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2019
Subjects
colloacation method
inclined flow
linear stability analysis
thermocapillary marangoni effect
variable fluid properties
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Summary:We investigate the stability of free-surface flow on a heated incline. We develop a complete mathematical model for the flow which captures the Marangoni effect and also accounts for changes in the properties of the fluid with temperature. We apply a linear stability analysis to determine the stability of the steady and uniform flow. The associated eigenvalue problem is solved numerically by means of a spectral collocation method. Comparisons with nonlinear simulations are also made and the agreement is good.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2019.6.1700