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Nonlinear Electrohydrodynamic Stability of Two Superposed Walters B′ Viscoelastic Fluids in Relative Motion Through Porous Medium

Published online by Cambridge University Press:  23 May 2013

M. F. El-Sayed ,
N. T. Eldabe ,
M. H. Haroun  and
D. M. Mostafa
M. F. El-Sayed*
Affiliation:
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt
N. T. Eldabe
Affiliation:
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt
M. H. Haroun
Affiliation:
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt
D. M. Mostafa
Affiliation:
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt
*
*mfahmye@yahoo.com
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Abstract

A nonlinear stability of two superposed semi-infinite Walters B′ viscoelastic dielectric fluids streaming through porous media in the presence of vertical electric fields in absence of surface charges at their interface is investigated in three dimensions. The method of multiple scales is used to obtain a Ginzburg-Landau equation with complex coefficients describing the behavior of the system. The stability of the system is discussed both analytically and numerically in linear and nonlinear cases, and the corresponding stability conditions are obtained. It is found, in the linear case, that the surface tension and medium permeability have stabilizing effects, and the fluid velocities, electric fields and kinematic viscoelastici-ties have destabilizing effects, while the porosity of porous medium and kinematic viscosities have dual role on the stability. In the nonlinear case, it is found that the fluid velocities, kinematic viscosities, kinematic viscoelasticities, surface tension and porosity of porous medium have stabilizing effects; while the electric fields and medium permeability have destabilizing effects.

Keywords

Nonlinear instabilityNon-Newtonian fluidsFlows through porous mediumMultiple time scales methodElectrohydrodynamics
Type
Research Article
Information
Journal of Mechanics , Volume 29 , Issue 4 , December 2013 , pp. 569 - 582
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013 

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