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The elongated shape of a dielectric drop deformed by a strong electric field

Published online by Cambridge University Press:  29 November 2010

DOV RHODES  and
EHUD YARIV
DOV RHODES
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, Haifa 32000, Israel
EHUD YARIV*
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, Haifa 32000, Israel
*
†Email address for correspondence: udi@technion.ac.il
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Abstract

A dielectric drop is suspended within a dielectric liquid and is exposed to a uniform electric field. Due to polarization forces, the drop deforms from its initial spherical shape, becoming prolate in the field direction. At strong electric fields, the drop elongates significantly, becoming long and slender. For moderate ratios of the permittivities of the drop and surrounding liquid, the drop ends remain rounded. The slender limit was originally analysed by Sherwood (J. Phys. A, vol. 24, 1991, p. 4047) using a singularity representation of the electric field. Here, we revisit it using matched asymptotic expansions. The electric field within the drop is continued into a comparable solution in the ‘inner’ region, at the drop cross-sectional scale, which is itself matched into the singularity representation in the ‘outer’ region, at the drop longitudinal scale. The expansion parameter of the problem is the elongated drop slenderness. In contrast to familiar slender-body analysis, this parameter is not provided by the problem formulation, and must be found throughout the course of the solution. The drop aspect-ratio scaling, with the 6/7-power of the electric field, is identical to that found by Sherwood (J. Phys. A, vol. 24, 1991, p. 4047). The predicted drop shape is compared with the boundary-integral solutions of Sherwood (J. Fluid Mech., vol. 188, 1988, p. 133). While the agreement is better than that found by Sherwood (J. Phys. A, vol. 24, 1991, p. 4047), the weak logarithmic decay of the error terms still hinders an accurate calculation. We obtain the leading-order correction to the drop shape, improving the asymptotic approximation.

JFM classification

Drops and Bubbles: Electrohydrodynamic effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 664 , 10 December 2010 , pp. 286 - 296
Copyright
Copyright © Cambridge University Press 2010

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References

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