Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-17T22:53:50.844Z Has data issue: false hasContentIssue false
  • English
  • Français

Fluid motions induced by a periodic magnetic field in and about a liquid drop

Published online by Cambridge University Press:  29 March 2006

C. Sozou
C. Sozou
Affiliation:
Department of Applied Mathematics and Computing Science, The University, Sheffield, England
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we consider the flow field induced by a periodic magnetic field in and about a conducting liquid drop immersed in an incompressible insulating fluid. It is assumed that at infinity the magnetic field varies with time t as cos ωt, where ω is a constant. This magnetic field is associated with a periodic electric field which produces a net electric stress, dependent on the spatial variables, normal to the drop surface. This stress sets up a flow field, in and about the liquid drop, that creates an appropriate viscous stress so that there is stress balance at the drop surface. The flow field is periodic with angular frequency 2ω. For small drop deformations the drop shape at any instant is a spheroid. It is shown that for large ω the amplitude of the velocity field for a conducting drop is approximately independent of ω and for a non-conducting drop it is proportional to ω. The larger velocity amplitude for a non-conducting drop is probably due to the fact that in this case there is no dissipation of electromagnetic energy. The electric stress over the drop surface increases with ω and it is suggested that the drop will burst at large ω unless the amplitude of the applied magnetic field is suitably decreased.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 62 , Issue 4 , 27 February 1974 , pp. 697 - 704
Copyright
© 1974 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allan, R. S. & Mason, S. G. 1962 Proc. Roy. Soc. A, 267, 45.
Brazier-Smith, P. R. 1971 J. Fluid Mech. 50, 417.
Brazier-Smith, P. R., Jennings, S. G. & Latham, J. 1971 Proc. Roy. Soc. A, 325, 363.
Garton, C. G. & Krasucki, Z. 1964 Proc. Roy. Soc. A, 280, 211.
Sneyd, A. 1971 J. Fluid Mech. 49, 817.
Sozou, C. 1972a J. Fluid Mech. 56, 305.
Sozou, C. 1972b Proc. Roy. Soc. A, 331, 263.
Sozou, C. 1973 Proc. Roy. Soc. A, 334, 343.
Taylor, G. I. 1964 Proc. Roy. Soc. A, 280, 383.
Taylor, G. I. 1966 Proc. Roy. Soc. A, 291, 159.
Torza, R., Cox, R. G. & Mason, S. G. 1971 Phil. Trans. Roy. Soc. A, 269, 295.