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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.
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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

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References

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