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Long-wavelength Marangoni Convection in a Thermally Modulated Field

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Abstract

This paper is concerned with the long-wave Marangoni instability in a horizontal liquid layer. The analysis has been carried out for the heat flux periodically oscillating at the deformable upper interface and at the rigid lower boundary. This type of instability is caused by the amplification of synchronous disturbances in response to the external forcing. Convection thresholds are determined, and the critical Marangoni number is expressed as a function of frequency. It is shown that the long-wavelength mode can give rise to the instability prior to the cellular mode within the definite range of parameters. The long-wavelength instability can have an influence on the space-qualified manufacturing, as well as the industrial process of thin films deposition on substrates.

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Authors and Affiliations

  1. Perm State University, 614990, Perm, Russia

    Boris L. Smorodin

  2. Department of Mathematics, Technion—Israel Institute of Technology, 32000, Haifa, Israel

    Alexander B. Mikishev & Alexander A. Nepomnyashchy

  3. Institute of Continuous Media Mechanics of Ural Branch of Russian Academy of Sciences, 614013, Perm, Russia

    Bela I. Myznikova

Authors
  1. Boris L. Smorodin
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  2. Alexander B. Mikishev
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  3. Alexander A. Nepomnyashchy
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  4. Bela I. Myznikova
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Correspondence to Alexander B. Mikishev.

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Smorodin, B.L., Mikishev, A.B., Nepomnyashchy, A.A. et al. Long-wavelength Marangoni Convection in a Thermally Modulated Field. Microgravity Sci. Technol. 21 (Suppl 1), 193–198 (2009). https://doi.org/10.1007/s12217-009-9128-6

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  • DOI: https://doi.org/10.1007/s12217-009-9128-6

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