Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-19T09:03:33.298Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalized energy methods in electrohydrodynamic stability theory

Published online by Cambridge University Press:  20 April 2006

B. J. S. Deo  and
A. T. Richardson
B. J. S. Deo
Affiliation:
Department of Engineering Mathematics, University of Bristol. U.K. Present address: Gearhart Geodata Services Ltd., Aberdeen, Scotland.
A. T. Richardson
Affiliation:
Department of Engineering Mathematics, University of Bristol. U.K.
Get access Rights & Permissions [Opens in a new window]

Abstract

A generalized energy stability analysis necessarily incorporating charge-diffusion effects is applied to an electrohydrodynamic equilibrium comprising a dielectric liquid confined between two planar electrodes and subjected to an injection of unipolar charge. Generalized energy, kinetic-charge and mixed-type functionals are considered. Using the physical constraint that the sign of space-charge density can never change, it is possible to bound the nonlinear terms in the functional evolution equations. Sufficient conditions to guarantee global monotonic stability in the mean are then derived. In the case of a strong injection of charge the mixed-type functional provides theoretical values of the stability parameter close to the experimental values. Sufficient conditional stability bounds are also obtained for the leading-order diffusion-free equilibrium.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 137 , December 1983 , pp. 131 - 151
Copyright
© 1983 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

Atten, P. 1975 Electrohydrodynamic stability of liquids subjected to unipolar injection. In Proc. Intl Conf. on Conduction and Breakdown in Dielectric Liquids, Delft, p. 119.
Atten, P. 1976 Rôle de la diffusion dans le problème de la stabilité hydrodynamique d'un liquide diélectrique soumis à une injection unipolaire forte C.R. Acad. Sci. Paris 283B, 29.Google Scholar
Atten, P. & Lacroix, J. C. 1974 Stabilité hydrodynamique non-linéaire d'un liquide isolant soumis à une injection unipolaire forte C.R. Acad. Sci. Paris 278B, 385.Google Scholar
Atten, P. & Lacroix, J. C. 1978 Electrohydrodynamic stability of liquids subjected to unipolar injection: nonlinear phenomena. J. Electrostat. 5, 439.Google Scholar
Atten, P. & Lacroix, J. C. 1979 Nonlinear hydrodynamic stability of liquids subjected to unipolar injection J. Méc. 18, 469.Google Scholar
Atten, P. & Moreau, R. 1972 Stabilité électrohydrodynamique des liquides isolants soumis à une injection unipolaire J. Méc. 11, 471.Google Scholar
Deo, B. J. S. 1983 Generalised energy stability analyses of electrohydrodynamic equilibria. Ph.D. thesis, University of Bristol.
Deo, B. J. S. & Richardson, A. T. 1983 Submitted to Q. J. Mech. Appl. Maths.
Joseph, D. D. 1976 Stability of Fluid Motions I and II. Springer.
Lacroix, J. C., Atten, P. & Hopfinger, E. J. 1975 Electroconvection in a dielectric liquid layer subjected to unipolar injection J. Fluid Mech. 69, 539.Google Scholar
Richardson, A. T. 1980 The linear instability of a dielectric liquid contained in a cylindrical annulus and subjected to unipolar charge injection Q. J. Mech. Appl. Maths 33, 277.Google Scholar