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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

Special Issues: Applied and Industrial Mathematics in Canada and Worldwide

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.
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© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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