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Resonant oscillations of inviscid charged drops

Published online by Cambridge University Press:  20 April 2006

John A. Tsamopoulos  and
Robert A. Brown
John A. Tsamopoulos
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Robert A. Brown
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
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Abstract

Moderate-amplitude axisymmetric oscillations of charged inviscid drops held together by surface tension are calculated by a multiple-timescale expansion. The corrections to the drop shape and velocity caused by mode coupling at second order in amplitude are predicted for two-, three- and four-lobed motions of drops with net charge up to the Rayleigh limit Qc ≡ 4π½. Resonant oscillations between four- and six-lobed motions occur for total charge values near $Q_{\rm r}\equiv (\frac{32}{3}\pi)^{\frac{1}{2}}$ and are analysed. Both frequency and amplitude modulation of the oscillation are predicted for drop motions starting from general initial deformations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 147 , October 1984 , pp. 373 - 395
Copyright
© 1984 Cambridge University Press

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