Transient electrohydrodynamics of a liquid drop in AC electric fields

  • A. Esmaeeli
Regular Article


The transient behavior of a leaky dielectric liquid drop under a uniform AC electric field of small strength is investigated, using a closed form analytical solution. The drop settles to a quasi-steady state in a relaxation time that is set by the viscosities of the drop and the ambient fluid and the surface tension, and oscillates around a mean deformation with a frequency that is twice the electric field frequency. The mode of instantaneous deformation remains the same (oblate or prolate) or switches between oblate and prolate, depending on the relative importance of the time-periodic component of the deformation compared to that of the time-exponential. The structure of the flow field and its evolution is studied for representative fluid systems at a high and a low electric field frequency. The individual contribution of the net tangential and normal electric stresses, which are the driving forces of the problem, on the flow structure and drop deformation is characterized. On the basis of the mean (time-independent) and time-periodic components of the driving forces, the flow field is represented as the superposition of three different flow patterns. It is shown that the interplay of these flow patterns leads to formation and destruction of toroidal vortices, and that the residence time of these vortices correlates inversely with the field frequency.

Graphical abstract


Flowing Matter: Liquids and Complex Fluids 


  1. 1.
    Q. Wang, Z. Suo, X. Zhao, Nat. Commun. 3, 1157 (2012)ADSCrossRefGoogle Scholar
  2. 2.
    J.S. Eow, M. Ghadiri, Chem. Eng. J. 85, 357 (2002)CrossRefGoogle Scholar
  3. 3.
    H. Kim, D. Luo, D. Link, D.A. Weitz, M. Marquez, Z. Cheng, Appl. Phys. Lett. 91, 133106 (2007)ADSCrossRefGoogle Scholar
  4. 4.
    G. Taylor, Proc. R. Soc. A 291, 159 (1966)ADSCrossRefGoogle Scholar
  5. 5.
    C. Smith, J. Melcher, Phys. Fluids 10, 2315 (1967)ADSCrossRefGoogle Scholar
  6. 6.
    J.R. Melcher, G.I. Taylor, Annu. Rev. Fluid Mech. 1, 111 (1969)ADSCrossRefGoogle Scholar
  7. 7.
    D.A. Saville, Annu. Rev. Fluid Mech. 29, 27 (1997)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    S. Torza, R.G. Cox, S.G. Mason, Philos. Trans. R. Soc. A 269, 295 (1971)ADSCrossRefGoogle Scholar
  9. 9.
    O. Vizika, D. Saville, J. Fluid Mech. 239, 1 (1992)ADSCrossRefGoogle Scholar
  10. 10.
    J. Baygents, N. Rivette, H. Stone, J. Fluid Mech. 368, 359 (1998)ADSCrossRefGoogle Scholar
  11. 11.
    R. Allan, S. Mason, Proc. R. Soc. London A: Math. Phys. Eng. Sci. 267, 45 (1962)ADSCrossRefGoogle Scholar
  12. 12.
    C. Sozou, Proc. R. Soc. London A: Math. Phys. Eng. Sci. 331, 263 (1972)ADSCrossRefGoogle Scholar
  13. 13.
    R. Thaokar, Eur. Phys. J. E 35, 76 (2012)CrossRefGoogle Scholar
  14. 14.
    T. Ward, G. Homsy, Phys. Fluids 13, 3521 (2001)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    S. Lee, D. Im, I. Kang, Phys. Fluids 12, 1899 (2000)ADSCrossRefGoogle Scholar
  16. 16.
    T. Ward, G. Homsy, J. Fluid Mech. 547, 215 (2006)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    C. Christov, G. Homsy, Phys. Fluids 21, 083102 (2009)ADSCrossRefGoogle Scholar
  18. 18.
    N. Kaji, Y. Mori, Y. Tochitani, J. Heat Transfer 107, 788 (1985)CrossRefGoogle Scholar
  19. 19.
    A. Esmaeeli, M.A. Halim, Acta Mech. 229, 3943 (2018)CrossRefGoogle Scholar
  20. 20.
    G. Taylor, Proc. R. Soc. Lond. A 313, 453 (1969)ADSCrossRefGoogle Scholar
  21. 21.
    A. Castellanos, A. Gonzalez, IEEE Trans. Dielectr. Electr. Insul. 5, 334 (1998)CrossRefGoogle Scholar
  22. 22.
    J.Q. Feng, Proc. R. Soc. Lond. A 455, 2245 (1999)ADSCrossRefGoogle Scholar
  23. 23.
    M.N. Reddy, A. Esmaeeli, Int. J. Multiphase Flow 35, 1051 (2009)CrossRefGoogle Scholar
  24. 24.
    A. Esmaeeli, P. Sharifi, J. Electrost. 69, 504 (2011)CrossRefGoogle Scholar
  25. 25.
    T.B. Jones, Electromechanics of Particles (Cambridge University Press, New York, USA, 1995)Google Scholar
  26. 26.
    J. Sherwood, J. Fluid Mech. 188, 133 (1988)ADSCrossRefGoogle Scholar
  27. 27.
    T. Tsukada, T. Katayama, Y. Ito, M. Hozawa, J. Chem. Eng. Jpn. 26, 698 (1993)CrossRefGoogle Scholar
  28. 28.
    J.Q. Feng, T.C. Scott, J. Fluid Mech. 311, 289 (1996)ADSCrossRefGoogle Scholar
  29. 29.
    E. Lac, G.M. Homsy, J. Fluid Mech. 590, 239 (2007)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    O. Ajayi, Proc. R. Soc. Lond. A 364, 499 (1978)ADSCrossRefGoogle Scholar
  31. 31.
    J.W. Ha, S.M. Yang, J. Fluid Mech. 405, 131 (2000)ADSCrossRefGoogle Scholar
  32. 32.
    A. Esmaeeli, A. Behjatian, Phys. Rev. E 86, 036310 (2012)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Southern Illinois University at CarbondaleCarbondaleUSA

Personalised recommendations