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Stability of inviscid conducting liquid columns subjected to a.c. axial magnetic fields

Published online by Cambridge University Press:  26 April 2006

Antonio Castellanos  and
Heliodoro GonzÁalez
Antonio Castellanos
Affiliation:
Departmento Electónica y Electromagnetismo, Universidad de Sevilla, Spain
Heliodoro GonzÁalez
Affiliation:
Departmento Electónica y Electromagnetismo, Universidad de Sevilla, Spain Departmento Física Aplicada, Universidad de Sevilla, Spain
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Abstract

The natural frequencies and stability criterion for cylinderical inviscid conducting liquid bridges and jets subjected to axial alternating magnetic fields in the absence of gravity are obtained. For typical conducting materials a frequency greater than 100 Hz is enough for a quasi-steady approximation to be valid. On the other hand, for frequencies greater than 105 Hz an inviscid model may not be justified owing to competition between viscous and magnetic forces in the vicinity of the free surface. The stability is governed by two independent parameters. One is the magnetic Bond number, which measures the relative influence of magnetic and capillary forces, and the other is the relative penetration length, which is given by the ratio of the penetration length of the magnetic field to the radius. The magnetic Bond number is proportional to the squared amplitude of the magnetic field and inversely proportional to the surface tension. The relative penetration length is inversely proportional to square root of the product of the frequency of the applied field and the electrical conductivity of the liquid. It is shown in this work that stability is enhanced by either increasing the magnetic Bond number or decreasing the relative penetration length.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 265 , 25 April 1994 , pp. 245 - 263
Copyright
© 1994 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. 1972 Handbook of Mathematical Functions. Dover.
Baumgartl, J. 1992 Numericsche und experimentelle untersuchungen zur wirkung magnetischer felder in krystallzuchtungsanordunungen. Thesis, Technical Faculty, Erlangen University, Germany.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Garnier, M. & Moreau, R. 1983 Effect of finite conductivity on the inviscid stability of an interface submitted to a high-frequency magnetic field. J. Fluid Mech. 127, 365–377.Google Scholar
González, H., McCluskey, F. M. J., Castellanos, A. & Barrero, A. 1989 Stabilization of dielectric liqid bridges by electric fields in the absence of gravity. J. Fluid Mech. 206, 545–561.Google Scholar
Hurle, D. T. J., Müller, G. & Nitsche, R. 1987 Crystal growth from the melt. In Fluid Sciences and Materials Science in Space (ed. H. U. Walter). Springer.
Keller, W. & Mühlbauer, A. 1981 Floating-Zone Silicon. Marcel Dekker.
Martínez, I. & Cröll, A. 1992 Liquid bridges and floating zones. ESA-SP 333, 135–142.Google Scholar
Nicolás, J. A. 1992 Magnetohydrodynamic stability of cylindrical liquid bridges under a uniform axial magnetic field. Phys. Fluids A 4, 2573–2577.Google Scholar
Rayleigh, Lord 1945 The Theory of Sound, vol. 2. Dover.
Riahi, D. N. & Walker, J. S. 1989 Float zone shape and stability with the electromagnetic body force due to a radio-frequency induction coil. J. Cryst. Growth 94, 635–642.Google Scholar
Sanz, A. 1985 The influence of an outer bath in the dynamics of axisymmetric liquid bridges. J. Fluid Mech. 156, 101–140.Google Scholar