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Study of the Stability of a Free Nonisothermal Liquid Film in a Gravity Field

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Abstract

Problem of a free liquid film vertically bounded by solid walls and being under the influence of gravity and thermocapillary forces in a thin-layer approximation is considered. A solution in which the film thickness is constant and temperature is a linear function of the longitudinal coordinate is investigated for stability analytically using the method of matched asymptotic expansions and numerically using the orthogonalization method for various values of acceleration of gravity. The results obtained analytically and numerically are in good agreement. It is shown that the solution is unstable, but the increment of perturbations is small even under terrestrial gravity.

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Authors and Affiliations

  1. Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    O. A. Burmistrova

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  1. O. A. Burmistrova
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Correspondence to O. A. Burmistrova.

Additional information

The author is grateful to V. V. Pukhnachev for stating the problem and his attention to this study.

This work was financially supported by the Russian Foundation for Basic Research (Grant No. 19-01-00096).

Original Russian Text © O.A. Burmistrova.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 61, No. 3, pp. 74–81, May–June, 2020.

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Burmistrova, O.A. Study of the Stability of a Free Nonisothermal Liquid Film in a Gravity Field. J Appl Mech Tech Phy 61, 377–383 (2020). https://doi.org/10.1134/S0021894420030086

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  • DOI: https://doi.org/10.1134/S0021894420030086

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