Abstract
A study is made of linear and nonlinear waves in liquid dielectrics in strong external electric fields. In the case of linear waves, it is assumed that the liquid has bipolar conduction, and allowance is made for recombination of oppositely charged ions. It is shown that two types of wave exist — acoustic and drift. Study of nonlinear waves shows that a solution can exist with stable nonexponential dispersal of a unipolar charged layer in an electric field. The stability of this solution is investigated. The conditions under which nonlinear drift waves can exist are found.
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Literature cited
G. A. Ostroumov, Interaction of Electric and Hydrodynamic Fields [in Russian], Nauka, Moscow (1979), p. 319.
M. K., Bologa, F. P. Grosu, and I. A. Kozhukhar', Electroconvection and Heat Transfer [in Russian], Shtiintsa, Kishinev (1977), p. 320.
J. R. Melcher, “Electrohydrodynamics,” Magn. Gidrodin., No. 2, 3 (1974).
G. I. Skanavi, Physics of Dielectrics (the Region of Weak Fields) [in Russian], Gostekhizdat, Moscow-Leningrad (1949), p. 500.
A. Nikuradze, Liquid Dielectrics [in Russian], ONTI IKT P SSSR, Moscow-Leningrad (1936), p. 236.
J. R. Melcher and G. I. Taylor, “Electrohydrodynamics — A review of the role of interfacial shear stresses,” Ann. Review of Fluid Mechanics, Vol. 1, Palo Acta (1969).
E. S. Yantovskii and M. S. Anfel'baum, “On the pumping action of a thin high-voltage electrode in a weakly conducting dielectric liquid,” Zh. Tekh. Fiz.,50, 1511 (1980).
Yu. K. Stishkov, “Observation of isothermal convection in the electric field of a planar capacitor,” Elektron. Obrab. Mater., No. 1, 61 (1972).
N. A. Petrichenko, “The pressure accompanying electrohydrodynamic flows in dielectric liquids,” Electron. Obrab. Mater., No. 5, 43 (1979).
N. A. Petrichenko, “The change in the pressure in a dielectric liquid at the tip of a point electrode in the presence of an electric field,” Elektron. Obrab. Mater., No. 6, 35 (1976).
Yu. A. Kopylov, “Electrical conductivity of high-resistivity organic liquids in the case of activated contact processes,” in: Organic Semiconducting Liquids. Proc. Dnepropetrovsk Agricultural Institute, Vol. 27 (1974), pp. 6–35.
I. Adamchevskii, Electrical Conductivity of Liquid Dielectrics [in Russian], Énergiya, Leningrad (1972), p. 296.
L. S. Kazatskaya, L. F. Obernikhina, V. R. Pokryshev, and I. M. Solodovnichenko, “High-voltage polarization of methane with chlorine substitution,” Elektron. Obrab. Mater., No. 3, 53 (1979).
L. S. Kazatskaya, V. R. Pokryshev, and L. F. Obernikhina, “Investigation of relaxation processes in liquid organic semiconductors,” Elektron. Obrab. Mater., No. 4, 56 (1980).
V. G. Levich, Physicochemical Hydrodynamics [in Russian], Izv. AN SSSR, Moscow (1952), p. 538.
I. E. Tarapov, “Fundamental problems of the hydrodynamics of magnetizable and polarizable media,” Author's Abstract of Doctoral Dissertation [in Russian], Dnepropetrovsk (1979), p. 39.
C. Kittel, Introduction to Solid State Physics, Wiley, New York (1966).
L. D. Landau and E. M. Lifshitz, Continuum Mechanics [in Russian], Gostekhizdat, Moscow (1954), p. 795.
V. V. Gogosov and V. A. Polyanskii, “Waves in electrohydrodynamics,” in: Seventh Riga Symposium on Magnetohydrodynamics, Vol. 1 [in Russian], Riga (1972), pp. 227–228.
G. B. Whitham, Linear and Nonlinear Waves, Wiley-Interscience, New York (1974).
N. J. Felici, “Direct current conduction in liquid dielectrics (Pt I),” Direct Current,2, 90 (1971).
T. J. Gallagher, Simple Dielectric Liquids, Mobility, Conduction and Breakdown, Clarendon Press, Oxford (1975), p. 154.
A. B. Vatazhin, “Smoothing of discontinuities of electric charge in electrohydrodynamics by diffusion processes,” Izv. Akad. Nauk SSSR, Mekh. Zhidk, Gaza, No. 1, 59 (1975).
V. A. Buchin, A. B. Vatazhin, and M. B. Pudov, “Electric charging of bodies by the removal from them of charged particles by a hydrodynamic flow,” Izv. Akad. Nauk SSSR, Mekh, Zhidk. Gaza, No. 5, 94 (1977).
T. R. Hewish, “The effects of induced motion on low-stress mobility measurements in liquid dielectrics subjected to charge injection,” Proc. Sixth Int. Conf. Conduct. and Breakdown Dielectr. Liq. Mont.-Saint-Aignan, 24–28 July, Dreux (1978), pp. 341–344.
A. I. Zhakin and I. E. Tarapov, “Instability and flow of a low-conductivity liquid in the presence of oxidation-reduction reactions on the electrodes and recombination,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4, 20 (1981).
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 98–106, January–February, 1983.
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Zhakin, A.I. Linear and nonlinear waves in liquid dielectrics. Fluid Dyn 18, 78–85 (1983). https://doi.org/10.1007/BF01090513
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DOI: https://doi.org/10.1007/BF01090513