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On the Hill Equation Describing Oscillations of a Ferrofluid Free Surface in a Vertical Magnetic Field

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Abstract

We consider an isothermal ferrofluid layer which is nearly inviscid and semi-infinite. It is subjected to a magnetic field that consists of two parts. The first one is a vertical constant component. The second part is oscillating with time in a vertical plane. The linearized Laplace law describing the deformation of the free surface reduces to the study of a Hill equation, thus generalizing the Mathieu equation studied for a purely oscillating magnetic field. Using a classical method, we derive the marginal oscillating conditions and compare them with experimental situations.

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Authors and Affiliations

  1. MRC, Fac. Sciences Appl., Univ. Libre de Bruxelles, CP 165/62, Av. F.D. Roosevelt 50, Brussels, 1050, Belgium

    Marcel Hennenberg

  2. Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bontchev St., Bl. 4, Sofia, 1113, Bulgaria

    Slavtcho Slavtchev & Galin Valchev

Authors
  1. Marcel Hennenberg
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  2. Slavtcho Slavtchev
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  3. Galin Valchev
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Correspondence to Slavtcho Slavtchev.

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Hennenberg, M., Slavtchev, S. & Valchev, G. On the Hill Equation Describing Oscillations of a Ferrofluid Free Surface in a Vertical Magnetic Field. Microgravity Sci. Technol. 22, 455–460 (2010). https://doi.org/10.1007/s12217-010-9221-x

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  • DOI: https://doi.org/10.1007/s12217-010-9221-x

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