Model of Electrothermal Convection of a Poorly Conducting Liquid in a Horizontal Capacitor

  • V. A. Il’inEmail author
  • N. N. Kartavykh


A five-mode model is used to analyze the electroconvection of a weakly conducting liquid in an alternating electric field of a horizontal capacitor with hard boundaries in the case of instantaneous charge relaxation. The nonlinear regimes of electroconvection are investigated. A pattern diagram is constructed. The quasi-periodic and synchronous oscillation regimes of convection are revealed. It is discovered that, depending on the external field frequency, the transition to chaos occurs either by quasi-periodicity or alternation.


electroconvection weakly conducting liquid transition to chaos 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ostroumov, G.A., Vzaimodeistvie elektricheskikh i gidrodinamicheskikh polei. Fizicheskie osnovy elektrogidrodinamiki (Interaction of Electric and Hydrodynamic Fields. Physical Principles of Electrohydrodynamics), Moscow: Nauka, 1979.Google Scholar
  2. 2.
    Bologa, M.K., Grosu, F.P., and Kozhukhar’, I.A., Elektrokonvertsiya i teploobmen (Electrical Conversion and Heat Transfer), Chisinau: Stiintsa, 1977.Google Scholar
  3. 3.
    Stishkov, Yu.K. and Ostapenko, A.A., Elektrogidrodinamicheskie techeniya v zhidkikh dielektrikakh (Electrohydrodynamic Fluxes un Liquid Dielectrics), Leningrad: Leningr. Gos. Univ., 1989.Google Scholar
  4. 4.
    Traore, Ph., Perez, A.T., Koulova, D., and Romat, H., J. Fluid Mech., 2010, vol. 658, pp. 279–293.CrossRefGoogle Scholar
  5. 5.
    Siddheshwar, P.G. and Radhakrishna, D., Commun. Nonlinear Sci. Numer. Simul., 2012, vol. 17, no. 7, pp. 2883–2895.MathSciNetCrossRefGoogle Scholar
  6. 6.
    Zhakin, A.I., Phys.-Usp., 2012, vol. 55, no. 5, pp. 465–488.CrossRefGoogle Scholar
  7. 7.
    Fogaing, M.T., Yoshikawa, H.N., Crumeyrolle, O., and Mutabazi, I., Eur. Phys. J. E: Soft Matter Biol. Phys., 2014, vol. 37, no. 4. doi 10.1140/epje/i2014-14035-0Google Scholar
  8. 8.
    Il’in, V.A., Tech. Phys., 2013, vol. 58, no. 1, pp. 60–69.CrossRefGoogle Scholar
  9. 9.
    Kartavykh, N.N., Smorodin, B.L., and Il’in, V.A., J. Exp. Theor. Phys., 2015, vol. 121, no. 1, pp. 155–165.CrossRefGoogle Scholar
  10. 10.
    Zhakin, A.I. and Kuzko, A.E., Fluid Dyn., 2013, vol. 48, no. 3, pp. 310–320.MathSciNetCrossRefGoogle Scholar
  11. 11.
    Skanavi, G.I., Fizika dielektrikov: oblast’ slabykh polei (Physics of Dielectrics: Range of Weak Fields), Moscow: Gos. Izd. Tekh.-Teor. Lit., 1949.Google Scholar
  12. 12.
    Vargaftik, N.B., Spravochnik po teplofizicheskim svoistvam gazov i zhidkostei (Handbook of Thermophysical Properties of Gases and Liquids), Moscow: Nauka, 1972.Google Scholar
  13. 13.
    Gershuni, G.Z. and Zhukhovitskii, E.M., Konvektivnaya ustoichivost’ neszhimaemoi zhidkosti (Convective Stability of an Incompressible Liquid), Moscow: Nauka, 1972.Google Scholar
  14. 14.
    Smorodin, B.L. and Velarde, M.G., J Electrostat., 2000, vol. 48, nos. 3–4, pp. 261–277.CrossRefGoogle Scholar
  15. 15.
    Bergé, P., Pomeau, Y., and Vidal, C., L’Ordre dans le Chaos: Vers une Approche Déterministe de la Turbulence, Paris: Hermann, 1988.zbMATHGoogle Scholar
  16. 16.
    Finucane, R.G. and Kelly, R.E., Int. J. Heat Mass Transf., 1976, vol. 19, pp. 71–83.CrossRefGoogle Scholar
  17. 17.
    Ahlers, G., Hohenberg, P.C., and Lücke, M., Phys. Rev. A, 1985, vol. 32, pp. 3493–3534.CrossRefGoogle Scholar

Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Perm State UniversityPermRussia

Personalised recommendations