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Linear stability of a two-fluid interface for electrohydrodynamic mixing in a channel

Published online by Cambridge University Press:  04 July 2007

F. LI ,
O. OZEN ,
N. AUBRY ,
D. T. PAPAGEORGIOU  and
P. G. PETROPOULOS
F. LI
Affiliation:
Department of Mechanical Engineering, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA
O. OZEN
Affiliation:
Department of Mechanical Engineering, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA
N. AUBRY
Affiliation:
Department of Mechanical Engineering, Carnegie Mellon University, Pittsburg, PA 15213, USA
D. T. PAPAGEORGIOU
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA
P. G. PETROPOULOS
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA
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Abstract

We study the electrohydrodynamic stability of the interface between two superposed viscous fluids in a channel subjected to a normal electric field. The two fluids can have different densities, viscosities, permittivities and conductivities. The interface allows surface charges, and there exists an electrical tangential shear stress at the interface owing to the finite conductivities of the two fluids. The long-wave linear stability analysis is performed within the generic Orr–Sommerfeld framework for both perfect and leaky dielectrics. In the framework of the long-wave linear stability analysis, the wave speed is expressed in terms of the ratio of viscosities, densities, permittivities and conductivities of the two fluids. For perfect dielectrics, the electric field always has a destabilizing effect, whereas for leaky dielectrics, the electric field can have either a destabilizing or a stabilizing effect depending on the ratios of permittivities and conductivities of the two fluids. In addition, the linear stability analysis for all wavenumbers is carried out numerically using the Chebyshev spectral method, and the various types of neutral stability curves (NSC) obtained are discussed.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 583 , 25 July 2007 , pp. 347 - 377
Copyright
Copyright © Cambridge University Press 2007

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