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Periodic and Chaotic Oscillations in a Low Conducting Liquid in an Alternating Electric Field

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Abstract

We study the oscillatory and chaotic evolution of electroconvective flows of a nonisothermal low conducting liquid in the AC electric field of a horizontal capacitor. An analysis is carried out of liquids in which the temperature dependence of the electrical conductivity generates the volume charge. The periodic and chaotic regimes of liquid flow are investigated in the case of a finite relaxation time. It is found that all periodic oscillatory electroconvective regimes are synchronous with the external electric field, and can be divided into three classes with different time shift properties. Bifurcation maps and diagrams of electroconvective regimes are obtained, and the hysteretic transitions between oscillatory electroconvective regimes with different periodicity are studied. We also analyse the scenarios of transition to chaotic oscillations. Depending on the external field frequency, the transition from periodic to chaotic oscillations can occur via quasiperiodicity, a subharmonic cascade, or intermittence.

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References

  • Ahlers, G., Hohenberg, P.C., Lücke, M.: Thermal convection under external modulation of the driving force. I. The Lorenz model. Phys. Rev. A. 32, 3493–3518 (1985)

    Google Scholar 

  • Berge, P., Pomeau, Y., Vidal, C.: Order within chaos: towards a deterministic approach to turbulence. Wiley, New York (1987)

    MATH  Google Scholar 

  • Coddington, E.A., Levinson, N.: Theory of Ordinary Differential Equations. McGraw-Hill, New York (1955)

    MATH  Google Scholar 

  • Demekhin, E.A., Polyanskikh, S.V.: Instability of slender liquid jet in AC electric field of arbitrary frequency. Microgravity Science and Technology. 22(3), 369–375 (2010)

    Article  Google Scholar 

  • Finucane, R.G., Kelly, R.E.: Onset of instability in a fluid layer heated sinusoidally from below. Int. J. Heat Mass Transf. 19, 71–85 (1976)

    Article  Google Scholar 

  • Gross, M.J., Porter, J.E.: Electrically induced convection in dielectric liquids. Nature. 212(5068), 1343–1345 (1966)

    Article  Google Scholar 

  • Il’in, V.A.: Electroconvection of a poorly conducting fluid in a steady electric field. Technical Physics. 58(1), 60–69 (2013)

    Article  Google Scholar 

  • Il’in, V.A., Smorodin, B.L.: Periodic and chaotic regimes of liquid dielectric convection in a horizontal capacitor. Tech. Phys. Lett. 31(5), 432–434 (2005)

    Article  Google Scholar 

  • Il’in, V.A., Smorodin, B.L.: Nonlinear regimes of electroconvection in a low-conducting liquid. Tech. Phys. Lett. 33(4), 355–357 (2007)

    Article  Google Scholar 

  • Kashina, A., Alabuzhev, A.: The dynamics of oblate drop between heterogeneous plates under alternating electric field. Microgravity science and technology. 30(1–2), 11–17 (2018)

    Article  Google Scholar 

  • Landau, L.D., Lifshits, E.M.: Fluid mechanics. Pergamon Press, New York (1987a)

    MATH  Google Scholar 

  • Landau, L.D., Lifshits, E.M.: Course of theoretical physics, Vol. 1: Mechanics. Oxford, Butterworth–Heinemann (1987b)

  • Laroze, D., Siddheshwar, P.G., Pleiner, H.: Chaotic convection in a ferrofluid. Commun. Nonlinear Sci. Numer. Simulat. 18, 2436–2447 (2013)

    Article  MathSciNet  Google Scholar 

  • Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141 (1963)

    Article  MathSciNet  Google Scholar 

  • Mutabazi, I., Yoshikawa, H.N., Fogaing, M.T., Travnikov, V., Crumeyrolle, O., Futterer, B.: Thermo-electro-hydrodynamic convection under microgravity: a review. Fluid Dynamics Research. 48(6), 061413 (2016)

    Article  MathSciNet  Google Scholar 

  • Sadilov, E.S.: Influence of the electric field on parametric instability of two-layer system. Microgravity Science and Technology. 30(4), 361–367 (2018)

    Article  Google Scholar 

  • Siddheshwar, P.G., Radhakrishna, D.: Linear and nonlinear electroconvection under AC electric field. Commun. Nonlinear Sci. Numer. Simulat. 17, 2883–2895 (2012)

    Article  MathSciNet  Google Scholar 

  • Smorodin, B.L., Taraut, A.V.: Dynamics of electroconvective wave flows in a modulated electric field. J. Exp. Theor. Phys. 118(1), 158–165 (2014)

    Article  Google Scholar 

  • Smorodin, B.L., Velarde, M.G.: On the parametric excitation of electrothermal instability in a dielectric liquid layer using an alternating electric field. J. Electrost. 50, 205–226 (2001)

    Article  Google Scholar 

  • Zhakin, A.I.: Electrohydrodynamics. Phys.–Usp. 55(5), 465–488 (2012)

    Article  Google Scholar 

  • Zhdanov, S.A., Kosvintsev, S.R., Makarikhin, I.Y.: Influence of an electric field on the stability of thermogravitational flow in a vertical capacitor. J. Exp. Theor. Phys. 90(2), 352–359 (2000)

    Article  Google Scholar 

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  1. Perm State University, Perm, 614990, Russia

    B. L. Smorodin & N. N. Kartavykh

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  1. B. L. Smorodin
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  2. N. N. Kartavykh
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Correspondence to B. L. Smorodin.

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Smorodin, B.L., Kartavykh, N.N. Periodic and Chaotic Oscillations in a Low Conducting Liquid in an Alternating Electric Field. Microgravity Sci. Technol. 32, 423–434 (2020). https://doi.org/10.1007/s12217-020-09779-y

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  • DOI: https://doi.org/10.1007/s12217-020-09779-y

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