Skip to main content
SpringerLink
Log in

Numerical Estimates of the Influence of Ion Diffusion on Injection-Type Electroconvection in the Plane Layer of a Low-Conductivity Fluid

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

The influence of diffusion on isothermal electroconvective flow of a low- conductivity fluid under unipolar injection in the constant electric field in a plane-parallel electrode system is studied. The dependences of the space charge density and flow fields on the diffusion intensity are obtained. The diffusion coefficient of injected ions is numerically estimated for TO + I2. The results obtained are based on comparison of the numerical experiment with the available experimental data.

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

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

REFERENCES

  1. Tarunin, E.L. and Yamshinina, Yu.A., Calculation of electrohydrodynamic flow in highly inhomogeneous electric fields, Magn. Gidrodin., 1990, no. 2, pp. 142–144.

  2. Tarunin, E.L. and Yamshinina, Y.A., Bifurcation of stationary solutions of the system of equations of electrohydrodynamics for unipolar injection, Fluid Dyn., 1994, vol. 29, no. 3, pp. 319–324.https://doi.org/10.1007/BF02230763

    Article  ADS  MathSciNet  Google Scholar 

  3. Zhakin, A.I. and Tarapov, I.E., Instability and flow of a weakly conducting fluid in the presence of oxidation-reduction reactions at electrodes and recombination, Fluid Dyn., 1981, vol. 16, no. 4, pp. 505–510.https://doi.org/10.1007/BF01094591

    Article  ADS  Google Scholar 

  4. Ilyin, V.A., Mordvinov, A.N., and Petrov, D.A., Electroconvection of a low-conducting liquid during unipolar charge injection in a constant electric field, Zh. Eksp. Teor. Fiz., 2015, vol. 147, no. 1, pp. 181–188.

    Google Scholar 

  5. Il’in, V.A. and Chigorina, T.I., Stationary regimes of electric convection of a low-conductivity fluid in the case of unipolar charge injection in a constant electric field, Fluid Dyn., 2021, vol. 56, no. 5, pp. 601–611. https://doi.org/10.1134/S0015462821050049

    Article  ADS  MathSciNet  Google Scholar 

  6. Il’in, V.A., Electroconvection of a low-conductivity liquid in a constant electric field, Zh. Tekh. Fiz., 2013, vol. 83, no. 1, pp. 64–73.

    Google Scholar 

  7. Smorodin, B.L. and Taraut, A.V., Parametric convection of a low-conducting liquid in an alternating electric field, Fluid Dyn., 2010, vol. 45, no. 12, pp. 1–9. https://doi.org/10.1134/S0015462810010011

    Article  ADS  MathSciNet  Google Scholar 

  8. Il’in, V.A., Electroconvection of a low-conducting liquid in a horizontal capacitor under. unipolar charge injection, Zh. Tech. Fiz., 2017, vol. 87, no. 1, pp. 5–9.

    Google Scholar 

  9. Mordvinov, A.N. and Smorodin, B.L., Electroconvection under injection from cathode and heating from above, J. Exp. Theor. Phys., 2012, vol. 114, no. 5, pp. 870–877.

    Article  ADS  Google Scholar 

  10. Il’in, V.A. and Aleksandrova, V.N., Wave regimes of electroconvection in a low-conducting liquid under unipolar charge injection in a constant electric field, Zh. Eksp. Teor. Fiz., 2020, vol. 157, no. 2, pp. 349–356.

    Google Scholar 

  11. Parez, A.T. and Castellanos, A., Role of charge diffusion in finite amplitude electro-convection, Phys. Rev. A., 1989, vol. 40, no. 10, pp. 5844-5855.

    Article  ADS  Google Scholar 

  12. Smorodin, B.L. and Taraut, A.V., Influence of the electric field modulation on propagation of charge in a polar low-conducting liquid, Zh. Prikl. Mekh. Tekh. Fiz., 2008, vol. 49, no. 1, pp. 3–12.

    Google Scholar 

  13. Stishkov Yu.K. and Chirkov, V.A., Formation of electrohydrodynamic flows in highly inhomogeneous electric fields under two charge formation mechanisms, Zh. Tech. Fiz., 2012, vol. 82, no. 1, pp. 3–13.

    Google Scholar 

  14. Taraut, A.V. and Smorodin, B.L., Electroconvection in the presence of autonomous unipolar injection and residual conductivity, Zh. Eksp. Teor. Fiz., 2012, vol. 142, no. 2, pp. 403–412.

    Google Scholar 

  15. Sitnikov, A.A. and Stishkov, Y.K., Three-ion model of EHD flows in the “wire-over-plane” electrode system, Fluid Dyn., 2017, vol. 52, no. 2, pp. 171–177. https://doi.org/10.1134/S0015462817020016

    Article  ADS  MathSciNet  Google Scholar 

  16. Pankratieva, I.L. and Polyanskii, V.A., Simulation of electrohydrodynamic flows in low-conducting liquids, Zh. Prikl. Mekh. Tekh. Fiz., 1995, vol. 36, no. 4, pp. 36–44.

    Google Scholar 

  17. Zhang, M., Martinelli, F., Wu, J., Schmid, P.J., and Quadrio, M., Modal and non-modal stability analysis of electrohydrodynamic flow with and without cross-flow, J. Fluid. Mech., 2015, vol. 770, pp. 319–349.

    Article  ADS  MathSciNet  Google Scholar 

  18. Ostroumov, G.A., Vzaimodeistvie elektricheskikh i gidrodinamicheskikh polei. Fizicheskie osnovy elektrogidrodinamiki (Interaction of Electric and Hydrodynamic Fields. Physical Fundamentals of Electrohydrodynamics), Moscow: Nauka, 1979.

  19. Ostroumov, G.A., and Petrichenko, N.A., Insulating liquids as ionic conductors of electricity, EOM, 1974, no. 1, pp. 40–44.

  20. Rychkov, Yu.M., Contact phenomena in liquid low-conducting media, Inzh.-Fiz. Zh., 1997, no. 6, pp. 1007–1013.

  21. Stishkov, Yu.K., Observation of isothermal convection in the electric field of a flat capacitor, EOM, 1972, no. 1, pp. 61–62.

  22. Tarunin, E.L., Vychislitel’nyi eksperiment v zadachakh svobodnoi konvektsii (Computational Experiment in Problems of Natural Convection), Izd-vo Irkutsk. Univ., Irkutsk, 1990.

  23. Lacroix, J.C., Atten, P., and Hopfinger, E.J., Electro-convection in a dielectric liquid layer subjected to unipolar injection, J. Fluid Mech., 1975, vol. 69, pp. 539–563.

    Article  ADS  Google Scholar 

  24. Ermolaev, I.A. and Zhbanov, A.I., Investigation of the electroconvective flow of a weakly conducting liquid with unipolar injection conductivity by the finite element method, JEPT, 2002, vol. 75, no. 5, pp. 1125–1129.

    Google Scholar 

  25. Vainberg, M.M. and Trenogin, V.A., Teoriya vetvleniya reshenii nelineihykh uravnenii (Theory of Branching of the Solutions of Nonlinear Equations), Moscow: Nauka, 1969.

  26. Fedonenko, A.I. and Zhakin, A.I., Experimental studies of electroconvective motion in transformer oil, Magn. Gidrodin., 1982, no. 3, pp. 74–78.

  27. Ermolaev, I.A. and Zhbanov, A.I., Numerical investigation of unipolar injection in the presence of electroconvective motion in a plane layer of transformer oil, Fluid Dyn., 2003, vol. 38, no. 6, pp. 827–831.

    Article  ADS  Google Scholar 

Download references

Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

Author information

Authors and Affiliations

  1. Chernyshevskii Saratov Research State University, Saratov, Russia

    I. A. Ermolaev

Authors
  1. I. A. Ermolaev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. A. Ermolaev.

Ethics declarations

The authors of this work declare that they have no conflicts of interest.

Additional information

Translated by E.A. Pushkar

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ermolaev, I.A. Numerical Estimates of the Influence of Ion Diffusion on Injection-Type Electroconvection in the Plane Layer of a Low-Conductivity Fluid. Fluid Dyn 58, 980–987 (2023). https://doi.org/10.1134/S0015462823601596

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0015462823601596

Keywords:

Search

Navigation