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Instability of the flat surface of a magnetic fluid in a cylindrical cavity in the presence of a vertical magnetic field

  • Gases and Fluids
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Abstract

The problem of a magnetic liquid which completely fills a vertical cylindrical cavity in an undeformable horizontal layer of a magnet having the same magnetic properties as the liquid is considered. The entire system is immersed in a uniform vertical magnetic field. in a linear formulation of the problem an approximate solution in the form of series is obtained for the evolution of an initial small deviation of the free surface of the liquid from its flat equilibrium shape. An experiment is performed which shows that the initially flat free surface takes on a stable domed shape as the field strength is increased (from zero) and that a further increase in the field in a certain restricted range leads to the formation of an annular corrugation. The structures observed, which are the result of the nonlinear stage in the development of the initial perturbation, are qualitatively similar to the first two modes of the solution obtained.

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References

  1. M. D. Cowley and R. E. Rosensweig, J. Fluid Mech. 30, 671 (1967).

    ADS  Google Scholar 

  2. R. E. Rosensweig, Ferrohydrodynamics, Cambridge University Press [Cambridge-New York (1985); Mir, Moscow (1989)].

    Google Scholar 

  3. B. M. Berkovsky, V. F. Medvedev, and M. S. Krakov, Magnetic Fluids: Engineering Applications, Oxford University Press, Oxford-New York (1993).

    Google Scholar 

  4. É. Ya. Blum, M. M. Maiorov, and A. O. Tsebers, Magnetic Fluids [in Russian], Zinatne, Riga (1989).

    Google Scholar 

  5. L. D. Landau and E. M. Lifshitz, Fluid Mechanics, 2nd ed., Pergamon Press, Oxford (1987).

    Google Scholar 

  6. A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics, Pergamon Press, Oxford (1964).

    Google Scholar 

  7. Tables of Zeros of Bessel Functions. Library of Mathematical Tables, No. 44 [in Russian], VTs Akad. Nauk SSSR, Moscow (1967).

  8. A. A. Blaker, Handbook for Scientific Photography [W. H. Freeman, San Francisco (1977); Mir, Moscow (1980)].

    Google Scholar 

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, 119899, Moscow, Russia

    V. M. Korovin & A. A. Kubasov

Authors
  1. V. M. Korovin
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  2. A. A. Kubasov
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Zh. Tekh. Fiz. 68, 23–30 (January 1998)

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Korovin, V.M., Kubasov, A.A. Instability of the flat surface of a magnetic fluid in a cylindrical cavity in the presence of a vertical magnetic field. Tech. Phys. 43, 19–26 (1998). https://doi.org/10.1134/1.1258929

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  • DOI: https://doi.org/10.1134/1.1258929

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