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Interfacial instability in electrified plane Couette flow

Published online by Cambridge University Press:  06 January 2011

STEFAN MÄHLMANN  and
DEMETRIOS T. PAPAGEORGIOU
STEFAN MÄHLMANN*
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA
DEMETRIOS T. PAPAGEORGIOU
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA Department of Mathematics and Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

The dynamics of a plane interface separating two sheared, density and viscosity matched fluids in the vertical gap between parallel plate electrodes are studied computationally. A Couette profile is imposed onto the fluids by moving the rigid plates at equal speeds in opposite directions. In addition, a vertical electric field is applied to the shear flow by impressing a constant voltage difference on the electrodes. The stability of the initially flat interface is a very subtle balance between surface tension, inertia, viscosity and electric field effects. Under unstable conditions, the potential difference in the fluid results in an electrostatic pressure that amplifies disturbance waves on the two-fluid interface at characteristic wave lengths. Various mechanisms determining the growth rate of the most unstable mode are addressed in a systematic parameter study. The applied methodology involves a combination of numerical simulation and analytical work. Linear stability theory is employed to identify unstable parametric conditions of the perturbed Couette flow. Particular attention is given to the effect of the applied electric field on the instability of the perturbed two-fluid interface. The normal mode analyses are followed up by numerical simulations. The applied method relies on solving the governing equations for the fluid mechanics and the electrostatics in a one-fluid approximation by using a finite-volume technique combined with explicit tracking of the evolving interface. The numerical results confirm those of linear theory and, furthermore, reveal a rich array of dynamical behaviour. The elementary fluid instabilities are finger-like structures of interpenetrating fluids. For weakly unstable situations a single fingering instability emerges on the interface. Increasing the growth rates causes the finger to form a drop-like tip region connected by a long thinning fluids neck. Even more striking fluid motion occurs at higher values of the electric field parameter for which multiple fluid branches develop on the interface. For a pair of perfect dielectrics the vertical electric field was found to enhance interfacial motion irrespective of the permittivity ratio, while in leaky dielectrics the electric field can either stabilize or destabilize the interface, depending on the conductivity and permittivity ratio between the fluids.

JFM classification

Instability: Instability Interfacial Flows (free surface): Interfacial Flows (free surface) MHD and Electrohydrodynamics: MHD and Electrohydrodynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 666 , 10 January 2011 , pp. 155 - 188
Copyright
Copyright © Cambridge University Press 2011

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