Abstract.
We study large scale surface deformations of a liquid film unstable due to the Marangoni effect caused by external heating on a smooth and solid substrate. The work is based on the thin film equation which can be derived from the basic hydrodynamic equations. To prevent rupture, a repelling disjoining pressure is included which accounts for the stabilization of a thin precursor film and so prevents the occurrence of completely dry regions. Linear stability analysis, nonlinear stationary solutions, as well as three-dimensional time dependent numerical solutions for horizontal and inclined substrates reveal a rich scenario of possible structures for several realistic fluid parameters.
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Bestehorn, M., Pototsky, A. & Thiele, U. 3D Large scale Marangoni convection in liquid films. Eur. Phys. J. B 33, 457–467 (2003). https://doi.org/10.1140/epjb/e2003-00186-3
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DOI: https://doi.org/10.1140/epjb/e2003-00186-3