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Critical conditions for instability of a highly charged oblate spheroidal drop

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Abstract

The spectrum of capillary oscillations of a charged oblate spheroidal drop is calculated in neglect of the interaction between modes by means of a perturbation expansion in the small deviation of the equilibrium shape of the drop from spherical. The critical conditions for instability of its nth mode with respect to the self-charge are calculated in the form of an analytical function describing how the dimensionless Rayleigh parameter characterizing the stability of the drop depends on the value of the spheroidal deformation.

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References

  1. A. G. Baily, Sci. Prog. Oxf. 61, 555 (1974).

    Google Scholar 

  2. V. I. Kozhenkov and N. A. Fuks, Usp. Khim. 45, 2274 (1976).

    Google Scholar 

  3. A. I. Grigor’ev and S. O. Shiryaeva, Izv. Ross. Akad. Nauk. Mekh. Zhidk. Gazov, No. 3, pp. 3–20 (1994).

  4. O. A. Basaran and L. E. Scriven, Phys. Fluids A 1, 795 (1989).

    ADS  MathSciNet  Google Scholar 

  5. A. I. Grigor’ev, A. A. Forstov, and S. O. Shiryaeva, in Proceedings of the Ninth International Conference on Atmospheric Electricity, St. Petersburg, Russia (1992), pp. 450–453.

  6. D. N. A. Jones, J. Meteorology 16, 504 (1959).

    Google Scholar 

  7. E. L. Ausman and M. Brook, J. Geophys. Res. 72, 6131 (1967).

    ADS  Google Scholar 

  8. H. R. Pruppacher and R. L. Piter, J. Atmos. Sci. 28, 86 (1971).

    Article  ADS  Google Scholar 

  9. I. D. Grigor’eva and S. O. Shiryaeva, Zh. Tekh. Fiz. 64(9), 202 (1994) [Tech. Phys. 39, 973 (1994)].

    Google Scholar 

  10. A. I. Grigor’ev, I. D. Grigor’eva, and S. O. Shiryaeva, J. Sci. Exploration 5, 163 (1991).

    Google Scholar 

  11. E. H. Trinh, Rev. Sci. Instrum. 56, 2059 (1985).

    Article  ADS  Google Scholar 

  12. S. O. Shiryaeva and A. I. Grigor’ev, Zh. Tekh. Fiz. 65(2), 1 (1995) [Tech. Phys. 40, 122 (1995)].

    Google Scholar 

  13. S. O. Shiryaeva and A. I. Grigor’ev, Zh. Tekh. Fiz. 66(9), 12 (1996) [Tech. Phys. 41, 865 (1996)].

    Google Scholar 

  14. L. D. Landau and E. M. Lifshitz, Fluid Mechanics [2nd ed., Pergamon Press, Oxford (1986); 3rd ed., Nauka, Moscow (1986), 733 pp.].

    Google Scholar 

  15. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media [2nd ed. with L. P. Pitaevskii, Pergamon Press, Oxford (1984); Nauka, Moscow (1982), 620 pp.].

    Google Scholar 

  16. R. E. Rosentsweig, Ferrohydrodynamics [Cambridge Univ. Press, New York (1985); Mir, Moscow (1989), 357 pp.].

    Google Scholar 

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Authors and Affiliations

  1. Yaroslavl State University, 150000, Yaroslavl, Russia

    A. I. Grigor’ev & S. O. Shiryaeva

Authors
  1. A. I. Grigor’ev
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  2. S. O. Shiryaeva
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Zh. Tekh. Fiz. 69, 10–14 (July 1999)

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Grigor’ev, A.I., Shiryaeva, S.O. Critical conditions for instability of a highly charged oblate spheroidal drop. Tech. Phys. 44, 745–749 (1999). https://doi.org/10.1134/1.1259340

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  • DOI: https://doi.org/10.1134/1.1259340

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