Skip to main content
SpringerLink
Log in

Nonlinear deformations and nonlinear waves on charged and polarizable plane free surfaces

  • Published:
Surface Engineering and Applied Electrochemistry Aims and scope Submit manuscript

Abstract

The calculation procedure and the main results of the analytical and experimental investigations on the influence of an electric field on dielectric liquids with free surfaces in a weakly nonlinear approximation are presented. It is shown that both local and periodic nonlinear deformations and waves can be formed on the free surface. The behavior of free surfaces with the electric field intensity being varied has been studied.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Shikin, V.B., Phys.-Usp., 2011, vol. 54, no. 12, pp. 1203–1225.

    Article  Google Scholar 

  2. Zhakin, A.I., Phys.-Usp., 2013, vol. 56, no. 2, pp. 141–163.

    Article  Google Scholar 

  3. Reneker, D.H., Yarin, Al., Zussman, E., and Xu, H., Adv. Appl. Mech., 2007, vol. 41, pp. 43–197.

    Article  Google Scholar 

  4. Barrero, F. and Loscertales, I.G., Annu. Rev. Fluid Mech., 2007, vol. 39, pp. 89–106.

    Article  Google Scholar 

  5. Sretenskii, L.N., Teoriya volnovykh dvizhenii zhidkosti (Theory of Wave Motions of Fluids), Moscow: Nauka, 1977.

    Google Scholar 

  6. Grigor’ev, A.I., Shiryaeva, S.O., and Fedorov, M.S., Tech. Phys., 2010, vol. 55, no. 7, pp. 920–928.

    Article  Google Scholar 

  7. Zhakin, A.I., Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 1984, no. 3, pp. 94–102.

    Google Scholar 

  8. Zhakin, A.I., Magn. Gidrodin., 1983, no. 4, pp. 41–48.

    Google Scholar 

  9. Nonlinear Waves, Leibovich, S. and Seebass, A.R., Eds., Ithaca, NY: Cornell Univ. Press, 1974.

  10. Taylor, G.J., Proc. Roy Soc. London., 1969, vol. А313, pp. 453–475.

    Article  Google Scholar 

  11. Mora, J.F., Annu. Rev. Fluid Mech., 2007, vol. 39, pp. 217–243.

    Article  Google Scholar 

  12. Gamero-Castan, M., J. Fluid Mech., 2008, vol. 604, pp. 339–368.

    Google Scholar 

  13. Zhakin, A.I. and Belov, P.A., Surf. Eng. Appl. Electrochem., 2013, vol. 49, no. 2, pp. 141–147.

    Article  Google Scholar 

  14. Sugimoto, T., Asano, K., and Higashiyama, Y., J. Electrostat., 2001, vol. 53, pp. 25–38.

    Article  Google Scholar 

  15. Subbotin, A.V., JETP Lett., 2015, vol. 100, no. 10, pp. 657–661.

    Article  Google Scholar 

  16. Ramos, A. and Castellanos, A., Phys. Lett. A, 1994, vol. 184, pp. 268–272.

    Article  Google Scholar 

  17. Higuera, F.J., J. Fluid Mech., 2003, vol. 484, pp. 303–327.

    Article  MathSciNet  Google Scholar 

  18. Higuera, F.J., J. Fluid Mech., 2004, vol. 513, pp. 339–346.

    Article  Google Scholar 

  19. Bateman, H. and Erdélyi, A., Higher Transcendental Functions, Vol. 2, Chap. 10: Orthogonal Functions, Part 10.10: Legendre Polynomials, New York: McGraw-Hill, 1953.

    Google Scholar 

  20. Nikiforov, A.F. and Evarov, V.B., Spetsial’nye funktsii (Specific Functions), Moscow: Nauka, 1984.

    Google Scholar 

  21. Zhakin, A.I., Trudy V Vseross. nauchnoi konferentsii “Fiziko-khimicheskie i prikladnye problemy magnitnykh dispersnykh nanosistem,” 14–17 sentyabrya 2015 g. (Proc. 5th All-Russ. Sci. Conf. “Physical-Chemical and Applied Problems of Magnetic Dispersed Nanosystems,” September 14–17, 2015), Stavropol, 2015, pp. 86–93.

    Google Scholar 

  22. Lavrent’ev, M.A. and Shabat, B.V., Metody teorii funktsii kompleksnogo peremennogo (Methods of the Theory of Functions of Complex Variables), Moscow: Nauka, 1965.

    MATH  Google Scholar 

  23. Zhakin, A.I., Fiz. Nizkikh Temp., 1984, vol. 10, no. 3, pp. 237–248.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Southwest State University, Kursk, 305040, Russia

    A. I. Zhakin

Authors
  1. A. I. Zhakin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. I. Zhakin.

Additional information

Original Russian Text © A.I. Zhakin, 2017, published in Elektronnaya Obrabotka Materialov, 2017, No. 2, pp. 41–57.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhakin, A.I. Nonlinear deformations and nonlinear waves on charged and polarizable plane free surfaces. Surf. Engin. Appl.Electrochem. 53, 150–166 (2017). https://doi.org/10.3103/S1068375517020120

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1068375517020120

Keywords

Search

Navigation