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On dynamic excitation of Marangoni instability in a liquid layer with insoluble surfactant on the deformable surface

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Abstract

This paper is a continuation of our previous work presented at the IMA-6, see [1]. We continue to analyze the parametric excitation of Marangoni instability by a periodic flux modulation in a liquid layer with insoluble surfactant. Contrary to the previous investigation here the upper free surface of the layer is deformable. The linear stability analysis for the disturbances with arbitrary wave numbers is performed. Three response modes of the system to an external periodic stimulation were found – synchronous, subharmonic, and quasi-periodic ones. Results for different Galileo and inverse capillary parameters are presented. It is shown that contrary to the situation with nondeformable interface, at small values of Galileo and inverse capillary parameters a new subharmonic instability region appears in the range of long waves.

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References

  1. A.B. Mikishev, A.A. Nepomnyashchy, Eur. Phys. J. Special Topics 219, 81 (2013)

    Article  ADS  Google Scholar 

  2. G.Z. Gershuni, D.V. Lyubimov, Thermal Vibrational Convection (Wiley, Chichester, 1998)

  3. G. Ahlers, P.C. Hohenberg, M. Lücke, Phys. Rev. A. 32, 3493 (1985)

    Article  ADS  Google Scholar 

  4. B.L. Smorodin, A.B. Mikishev, A.A. Nepomnyashchy, B.I. Myznikova, Phys. Fluids 21, 062102 (2009)

    Article  ADS  Google Scholar 

  5. A.C. Or, R.E. Kelly, J. Fluid Mech. 456, 161 (2002)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  6. L.D. Landau, E.M. Lifshitz, Mechanics, Vol. 1 (Course of Theoretical Physics) (Pergamon, Oxford, 1976)

  7. A.B. Mikishev, A.A. Nepomnyashchy, J. Adhes. Sci. Technol. 25, 1411 (2011)

    Article  Google Scholar 

  8. H. Wong, C. Rumschitzki, C. Maldarelli, Phys. Fluids. 8, 3203 (1996)

    Article  ADS  MATH  Google Scholar 

  9. C.D. Eggleton, Y.P. Pawar, K.J. Stebe, J. Fluid Mech. 385, 79 (1999)

    Article  ADS  MATH  Google Scholar 

  10. G. Terrones, C.F. Chen, J. Fluid Mech. 255, 301 (1993)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  11. A.B. Mikishev, A.A. Nepomnyashchy, Microgravity Sci. Technol. 22, 415 (2010)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Sam Houston State University, Huntsville, TX, 77341, USA

    A.B. Mikishev

  2. Embry-Riddle Aeronautical University-Worldwide, Daytona Beach, FL, 33114, USA

    A.B. Mikishev

  3. Department of Mathematics, Technion – Israel Institute of Technology, Haifa, 32000, Israel

    A.A. Nepomnyashchy

  4. Minerva Center for Nonlinear Physics of Complex Systems, Technion – Israel Institute of Technology, Haifa, 32000, Israel

    A.A. Nepomnyashchy

Authors
  1. A.B. Mikishev
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  2. A.A. Nepomnyashchy
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Correspondence to A.B. Mikishev or A.A. Nepomnyashchy.

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Mikishev, A., Nepomnyashchy, A. On dynamic excitation of Marangoni instability in a liquid layer with insoluble surfactant on the deformable surface. Eur. Phys. J. Spec. Top. 224, 229–239 (2015). https://doi.org/10.1140/epjst/e2015-02355-5

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  • DOI: https://doi.org/10.1140/epjst/e2015-02355-5

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