2015 1(16)

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Kupershtokh A.L.1,2

1 Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk, Russia
2 Novosibirsk State University, Novosibirsk, Russia


Kupershtokh, A.L., (2015) Appearance of gas phase just before a breakdown of dielectric liquids because of heterogeneous nucleation under the action of strong electric fields, Modern Science: Researches, Ideas, Results, Technologies, Iss. #1(16), PP. 79 - 85.


Lattice Boltzmann Equation Method; phase transitions; dynamics of multiphase flows; computer simulations; binary mixtures; breakdown of dielectric liquids; electrostrictive instability; heterogeneous nucleation


In the earlier works, we proposed a new instability mechanism for dielectric liquid in strong electric fields: the anisotropic decay into a system of vapor channels in the liquid oriented along the field. Electrohydrodynamic flows with phase transitions are simulated using the lattice Boltzmann method (Lattice Boltzmann Equation, LBE). The critical values of electric field strength for a "pure" dielectric liquid obtained in LBE simulations are coincide well with the theoretical values obtained from the spinodal curve in the electric field. It was shown earlier that the critical field strength decrease significantly in the presence of gases dissolved in a dielectric liquid. However, these values are still noticeably higher than the ones observed in practice. In the present work, we propose a simple model of heterogeneous nucleation that can be used in LBE simulations. Influence of the heterogeneity centers together with dissolved gas leads to the further significant decrease of the critical electric field values down to 10–20 MV/cm that close to the experimental values observed in breakdowns of dielectric liquids.


  1. Frenkel, J. (1946). "Kinetic Theory of Liquids", Oxford Univ. Press, 485 p.

  2. Скрипов В.П. Метастабильная жидкость. М.: Наука, 1972. 312 с.

  3. Zel’dovich, Ya.B. and Todes, O.M. (1940). "The kinetics of formation of two-phase systems near the critical poin", J. Exp. Theor. Phys., Vol. 10, No. 12, pp. 1441-1445.

  4. Parmar, D.S. and Jalaluddin, A.K. (1973). "Determination of the limit of absolute thermodynamic stability of liquid using external electric fields as perturbation", Phys. Lett., Vol. 42A, No. 7, pp. 497-498.

  5. Ландау Л.Д., Лифшиц Е.М. Электродинамика сплошных сред. - М.: Гос. изд-во. физ.-мат. литературы. 1959. - 532 с.

  6. Kupershtokh A.L., Medvedev D.A. Anisotropic instability of a dielectric liquid in a strong uniform electric field: Decay into a twophase system of vapor filaments in a liquid // Phys. Rev.E. 2006. Vol. 74, N 2. P. 021505.

  7. Карпов Д.И., Куперштох А.Л. Анизотропный спинодальный распад полярного диэлектрика в сильном электрическом поле: метод молекулярной динамики // Письма в ЖТФ. 2009. Т. 35. Вып. 10. С. 87-94.

  8. Shahporonov, M.I. (1963). Methods of study of thermal movement of molecules and structure of liquids, Moskow University Press, USSR, 281 p.

  9. An W., Baumung K., Bluhm H. Underwater streamer propagation analyzed from detailed measurements of pressure release // J. Appl. Phys. 2007. Vol. 101, N 5. P. 053302.

  10. Kupershtokh, A.L. (2012). "Three-dimensional LBE simulations on hybrid GPU-clusters of the decay of a binary mixture of liquid dielectrics with a solute gas to a system of gas-vapor channels", Numerical Methods and Programming, Vol. 13, pp. 384-390.

  11. Kupershtokh, A.L. (2014). "Three-dimensional LBE simulations of a decay of liquid dielectrics with a solute gas into the system of gas-vapor channels under the action of strong electric fields", Computers and Mathematics with Applications, Vol. 67, No. 2, pp. 340-349.

  12. Chen S., Doolen G.D. Lattice Boltzmann method for fluid flow // Annu. Rev. Fluid Mech. - 1998. V. 30. P. 329-364.

  13. Aidun C.K., Clausen J.R. Lattice-Boltzmann Method for Complex Flows // Annu. Rev. Fluid Mech. 2010. V. 42. P. 439-472.

  14. Shan X., Chen H. Lattice Boltzmann model for simulating flows with multiple phases and components // Phys. Rev.E. 1993. V. 47, N 3. P. 1815-1819.

  15. Kupershtokh, A.L. (2005). "Simulation of flows with liquid-vapor interfaces by the lattice Boltzmann method", Vestnik NGU (Quart.J. of Novosibirsk State Univ.), Series: Math., Mech. and Informatics, Vol. 5, No. 3, pp. 29-42.

  16. Kupershtokh A.L., Medvedev D.A., Karpov D.I. On equations of state in a lattice Boltzmann method // Computers and Mathematics with Applications, 2009. Vol. 58, N 5. P. 965-974.

  17. Kupershtokh, A.L. (2012). "Three-dimensional simulations of two-phase liquid-vapor systems on GPU using the lattice Boltzmann method", Numerical Methods and Programming, Vol. 13, pp. 130-138.

  18. Kupershtokh, A.L., Medvedev, D.A. and Gribanov, I.I. (2014). "Modeling of thermal flows in a medium with phase transitions using the lattice Boltzmann method", Numerical Methods and Programming, Vol. 15, pp. 317-328.

  19. Chen, L., Kang, Q., Mu, Y., He, Y.-L. and Tao W.-Q. (2014). "A critical review of the pseudopotential multiphase lattice Boltzmann model: Methods and applications", Int.J. Heat Mass Transfer, Vol. 76, pp. 210-236.

  20. Kupershtokh, A.L. (2004). "Incorporating a body force term into the lattice Boltzmann equation", Vestnik NGU (Quart.J. of Novosibirsk State Univ.), Series: Math., Mech. and Informatics, Vol. 4, No. 2, pp. 75-96.

  21. Kupershtokh A.L. Criterion of numerical instability of liquid state in LBE simulations // Computers and Mathematics with Applications, 2010. V. 59, N 7. P. 2236-2245.

  22. Qian Y.H., Chen S. Finite size effect in lattice-BGK models // International Journal of Modern Physics C. 1997. Vol. 8, N 4. P. 763-771.

  23. Bunkin, N.F. and Bunkin, F.V. (1992). "Bubstones stable microscopic gas bubbles in very dilute electrolytic solution", Sov. Phys.J. Exp. Theor. Phys., Vol. 74, No. 2, pp. 271-276.

  24. Bunkin, N.F., Vinogradova, O.I., Kuklin, A.I., Lobeev, A.V. and Movchan, T.G. (1995). "Presence of submicroscopic air bubbles in water. Small-angle neutron scattering experiment", J. Exp. Theor. Phys. Lett., Vol. 62, No. 8, pp. 685-688.



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