Skip to main content
Log in

Wave Regimes of Electroconvection under Cathode Injection and Heating from Above

  • STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

Two-dimensional wave electroconvective flows and transient processes in a low conducting nonisothermal liquid filling a parallel-plate horizontal capacitor, which emerge due to the action of a steady electric field and the charge injected from the cathode, are simulated numerically. The dependences of the wave flow characteristics (stream function amplitude, oscillation frequency at a fixed point of the convective cell, and phase velocity of the wave) on the heating intensity and the electric field strength are obtained. The bifurcation diagrams and the stable wave solution map are constructed. The behavior of trajectories on the world line plot and the evolution of spatial harmonics are analyzed for the process of transition from the standing wave regime to the traveling wave regime.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.

Similar content being viewed by others

REFERENCES

  1. G. A. Ostroumov, Interaction of Electric and Electrohydrodynamic Fields (Nauka, Moscow, 1979) [in Russian].

    Google Scholar 

  2. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).

    Article  ADS  Google Scholar 

  3. Pattern Formation in Liquid Crystals, Ed. by A. Buka and L. Kramer (Springer, New York, 1995).

    Google Scholar 

  4. M. J. Gross and J. E. Porter, Nature (London, U.K.) 212, 1343 (1966).

    Article  ADS  Google Scholar 

  5. M. K. Bologa, F. P. Grosu, and I. A. Kozhukhar’, Electroconvection and Heat Transfer (Shtiintsa, Kishinev, 1977) [in Russian].

  6. Yu. K. Stishkov and A. A. Ostapenko, Electrohydrodynamic Flows in Liquid Dielectrics (Leningr. Univ., Leningrad, 1989) [in Russian].

    Google Scholar 

  7. F. Pontiga and A. Castellanos, Phys. Fluids 6, 1684 (1994).

    Article  ADS  Google Scholar 

  8. A. N. Mordvinov and B. L. Smorodin, J. Exp. Theor. Phys. 114, 870 (2012).

    Article  ADS  Google Scholar 

  9. J. C. Lacroix, P. Atten, and E. J. Hopfinger, J. Fluid Mech. 69, 539 (1975).

    Article  ADS  Google Scholar 

  10. A. N. Vereshchaga and E. L. Tarunin, in Numerical and Experimental Modeling of Hydrodynamic Phenomena in Zero Gravity, Collection of Articles (UrO Akad. Nauk SSSR, Sverdlovsk, 1988), p. 93 [in Russian].

    Google Scholar 

  11. A. N. Vereshchaga, in Hydrodynamics and Heat and Mass Transfer Processes, Collection of Articles (UrO AN SSSR, Sverdlovsk, 1989), p. 42 [in Russian].

    Google Scholar 

  12. Ph. Traore, A. T. Perez, D. Koulova, and H. J. Romat, J. Fluid Mech. 658, 279 (2010).

    Article  ADS  Google Scholar 

  13. J. Wu and P. Traore, Numer. Heat Transfer A 68, 471 (2015).

    Article  ADS  Google Scholar 

  14. T. F. Li, K. Luo, and H. L. Yi, Phys. Fluids 31, 064106 (2019).

    Article  ADS  Google Scholar 

  15. R. D. Selvakumar, J. Wu, J. Huang, and P. Traoré, Int. J. Heat Fluid Flow 89, 108787 (2021).

    Article  Google Scholar 

  16. V. A. Il’in and V. N. Aleksandrova, J. Exp. Theor. Phys. 130, 293 (2020).

    Article  ADS  Google Scholar 

  17. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Nauka, Moscow, 1986; Pergamon, New York, 1987).

  18. B. L. Smorodin and A. V. Taraut, Fluid Dyn. 45, 1 (2010).

    Article  ADS  MathSciNet  Google Scholar 

  19. E. L. Tarunin, Computational Experiment in Free Convection Problems (Irkut. Gos. Univ., Irkutsk, 1990) [in Russian].

    Google Scholar 

  20. F. H. Busse, in Hydrodynamic Instabilities and the Transition to Turbulence, Vol. 45 of Topics in Applied Physics, Ed. by H. L. Swinney and J. P. Gollub (Springer, Berlin, 1981).

  21. J. Niemela, G. Ahlers, and D. Cannel, Phys. Rev. Lett. 64, 1365 (1990).

    Article  ADS  Google Scholar 

  22. K. D. Eaton, D. R. Ohlsen, S. Y. Yamamoto, C. M. Surko, W. Barten, M. Lücke, M. Kamps, and P. Kolodner, Phys. Rev. A 43, 7105 (1991).

    Article  ADS  Google Scholar 

  23. W. Barten, M. Lücke, M. Kamps, and R. Schmitz, Phys. Rev. E 51, 5636 (1995).

    Article  ADS  Google Scholar 

  24. B. L. Winkler and P. Kolodner, J. Fluid Mech. 240, 31 (1992).

    Article  ADS  Google Scholar 

  25. P. Kolodner, C. M. Surko, and H. Williams, Phys. D (Amsterdam, Neth.) 37, 319 (1989).

  26. M. Liu and J. R. de Bruyn, Can. J. Phys. 70, 689 (1992).

    Article  ADS  Google Scholar 

  27. B. L. Smorodin and A. V. Taraut, J. Exp. Theor. Phys. 118, 154 (2014).

    Article  ADS  Google Scholar 

  28. V. A. Il’in and B. L. Smorodin, J. Appl. Mech. Tech. Phys. 49, 362 (2008).

    Article  ADS  Google Scholar 

  29. E. B. Barry, H. N. Yoshikawa, M. T. Fogaing, C. Kang, and I. Mutabazi, Micrograv. Sci. Technol. 33, 162021 (2021).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to B. L. Smorodin.

Ethics declarations

The authors declare that they have no conflicts of interest.

Additional information

Translated by N. Wadhwa

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Smorodin, B.L. Wave Regimes of Electroconvection under Cathode Injection and Heating from Above. J. Exp. Theor. Phys. 134, 112–122 (2022). https://doi.org/10.1134/S1063776121120153

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776121120153

Navigation