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A general analysis for the electrohydrodynamic instability of stratified immiscible fluids

Published online by Cambridge University Press:  29 June 2011

J. ZHANG ,
J. D. ZAHN  and
H. LIN
J. ZHANG
Affiliation:
Department of Mechanical & Aerospace Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, USA
J. D. ZAHN
Affiliation:
Department of Biomedical Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, USA
H. LIN*
Affiliation:
Department of Mechanical & Aerospace Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, USA
*
†Email address for correspondence: [email protected]
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Abstract

A general solution approach for the electrohydrodynamic instability of stratified immiscible fluids is presented. The problems of two and three fluid layers subject to normal electric fields are analysed. Analytical solutions are obtained by employing the transfer relations (Melcher 1981 Continuum Electromechanics. MIT Press) relating the disturbance stresses to the flow variables at the interface(s). This approach provides a convenient alternative to the direct solution of the linearized problem. The results assume a general format. Both new dispersion relations and those from various previous works are shown to be special cases when proper simplifications are considered. As a specific example, the instability behaviour of a three-layer channel flow is investigated in detail using this framework. This work provides a unifying method to treat a generic class of instability problems.

JFM classification

Drops and Bubbles: Electrohydrodynamic effects Instability: Instability Micro-/Nano-fluid dynamics: Microfluidics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 681 , 25 August 2011 , pp. 293 - 310
Copyright
Copyright © Cambridge University Press 2011

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References

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