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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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