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

Jean-Paul Pascal; Serge D’Alessio; Syeda Rubaida Zafar; Jean-Paul Pascal; Serge D’Alessio; Syeda Rubaida Zafar

doi:10.3934/math.2019.6.1700

AIMS Mathematics

2019, Volume 4, Issue 6: 1700-1720. doi: 10.3934/math.2019.6.1700

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

1.
Department of Mathematics, Ryerson University, Toronto, Ontario, M5B 2K3, Canada
2.
Centre for Education in Mathematics and Computing, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

Received: 10 October 2018 Accepted: 07 January 2019 Published: 23 December 2019
MSC : 74E99

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.
- inclined flow,
- thermocapillary Marangoni effect,
- variable fluid properties,
- linear stability analysis,
- colloacation method
Citation: Jean-Paul Pascal, Serge D’Alessio, Syeda Rubaida Zafar. The instability of liquid films with temperature-dependent properties flowing down a heated incline[J]. AIMS Mathematics, 2019, 4(6): 1700-1720. doi: 10.3934/math.2019.6.1700

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Abstract

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.

References

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