Table of Contents
ISRN Applied Mathematics
Volume 2011 (2011), Article ID 498718, 35 pages
http://dx.doi.org/10.5402/2011/498718
Review Article

Electrohydrodynamic Instability of Two Thin Viscous Leaky Dielectric Fluid Films in a Porous Medium

1Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis (Roxy), Cairo 11757, Egypt
2Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraidah 51452, Saudi Arabia

Received 23 March 2011; Accepted 4 May 2011

Academic Editor: R. Cardoso

Copyright © 2011 M. F. El-Sayed et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The effect of an applied electric field on the stability of the interface between two thin viscous leaky dielectric fluid films in porous medium is analyzed in the long-wave limit. A systematic asymptotic expansion is employed to derive coupled nonlinear evolution equations of the interface and interfacial free charge distribution. The linearized stability of these equations is determined and the effects of various parameters are examined in detail. For perfect-perfect dielectrics, the various parameters affect only for small wavenumber values. For dielectrics, the various parameters affect only for small wavenumber values. For effect for small wavenumbers, and a stabilizing effect afterwards, and for high wavenumber values for the other physical parameters, new regions of stability or instability appear. For leaky-leaky dielectrics, the conductivity of upper fluid has a destabilizing effect for small or high wavenumbers, while it has a dual role on the stability of the system in a wavenumber range between them. The effects of all other physical parameters behave in the same manner as in the case of perfect-leaky dielectrics, except that in the later case, the stability or instability regions occur more faster than the corresponding case of leaky-leaky dielectrics.