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On the surface stability of liquid conductors in electromagnetic shaping

Published online by Cambridge University Press:  26 April 2006

Thomas P. Felici
Thomas P. Felici
Affiliation:
LEMTA (CNRS URA875), Nancy, France
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Abstract

In a process involving electromagnetic shaping, a high-frequency electromagnetic field is used to deform a liquid conductor into a required shape. This is particularly relevant to processes such as levitation melting. In this paper the stability of such configurations are investigated. The second variation of an appropriate energy functional is derived whose minimum states correspond to stable configurations, thus providing a stability criterion. As an example, this is applied to the shaping of a levitated cylinder of circular cross-section and to an almost spherical axisymmetric shape. In both cases we find that these shapes are unstable. We then consider enclosing the entire shaping device in a metal shield, thus preventing the escape of the magnetic field. It is then shown that in general the shield has a stabilizing effect, whose exact nature depends on the topology of the liquid shape and on the field structure on its surface. This differing behaviour is discussed for two-dimensional spherical and toroidal shapes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 302 , 10 November 1995 , pp. 1 - 28
Copyright
© 1995 Cambridge University Press

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References

Bang-Yen Chen 1984 Total Mean Curvature and Submanifolds of Finite Type. World Scientific.
Brancher, J. P. 1980 Sur l'hydrodynamique des ferrofluides. Thesis, Institute National Polytechnique Lorraine, Nancy, France.
Brancher, J. P., Etay, J. & Sero Guillaume, O. 1983 Formage d'une lame métallique liquide: calcul et expériences. J. Méc. Theor. Appl. 2, 976–989.Google Scholar
Brancher, J. P. & Sero Guillaume, O. 1983 Sur l’équilibre des liquides magnétiques: applications à la magnétostatique.. J. Méc. Theor. Appl. 2, 265–283.Google Scholar
Descloux, J. 1991 Stability of the solutions of the bidimensional magnetic shaping problem in absence of surface tension. Eur. J. Mech. B/Fluids 10, 513–526.Google Scholar
Etay, J. 1980 Formage et guidage des métaux liquides sous l'action de champs magnétiques alternatifs. Rep. De DEA de Mécanique des Fluides. Inst. Nat. Polytechnique, Grenoble.
Etay, Gagnoud, A. & Garnier, M. 1986 Le problème de frontière libre en lévitation èlectromagnétique. J. Méc. Theor. Appl. 5, 911–934.Google Scholar
Felici, T. P. 1991 The inverse problem in the theory of electromagnetic shaping PhD thesis, Cambridge University.
Felici, T. P. & Brancher, J. P. 1991a Inverse electromagnetic shaping problem. Prog. Astronat. Aeronat. 148, 158–180.Google Scholar
Felici, T. P. & Brancher, J. P. 1991b Inverse shaping problem. Eur. J. Mech. B/Fluids 10, 501–934512.Google Scholar
Garnier, M. & Etay, J. 1982 Sur le contrôle électromagnétique des surfaces métalliques liquides et ses applications. J. Méc. Theor. Appl. 1, 911–925.Google Scholar
Henrot, A., Pierre, M. & Brancher, J. P. 1989 Un probleme inverse en formage des metaux liquides. Math. Modelling Numer. Anal. 23, 155.Google Scholar
Mestel, J. 1982 Magnetic levitation of liquid metals. J. Fluid Mech. 117, 27–43.Google Scholar
Muck, O. 1923 German patent 422004, Oct. 30
Okress, E. C., Wroughton, D. M., Comenetz, C., Brace, P. N. & Kelly, J. C. K. 1952 Electromagnetic levitation of solid and liquid metals.. J. Appl. Phys. 23545.Google Scholar
Polonis, B. M. & Parr, J. G. 1954 Phase transformations in titanium rich alloys of iron and titanium. Trans AIME 200, 1148.Google Scholar
Sero Guillaume, O. 1983 Sur l’équilibre des ferrofluides et des métaux liquids. Thesis, Institute National Polytechnique Lorraine, Nancy, France.
Shercliff. J. A. 1981 Magnetic shaping of molten metal columns. Proc. R. Soc. Lond. A 375, 455–473.Google Scholar
Sneyd, A. D. & Moffatt, H. K. 1982 The fluid dynamics of the leviatationn malting process. J. Fluid Mech. 117, 45–70.Google Scholar