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In this work, the effect of transverse horizontal electric field on thestability of three layers of immiscible liquids is illustrated. The fluids aresubjected to a uniform horizontal electric field. Analytical and numericalsimulations of this system of linear evolution equations are performed. Thesolutions of the linearized equations of motion and the boundary conditionslead to deriving two simultaneous Mathieu equations of damping terms havingcomplex coefficients. The effects of the streaming velocity, the permeabilityof the porous medium, and the electrical properties of the flow on theinstability are investigated. In the case of uniform velocity, it is found thatelectric field has a stabilizing influence on the stability criteria. When theperiodicity of the velocity is considered, the method of multiple scales isapplied to obtain stability solution for the considered system. It is foundthat the phenomenon of the dual role is found for increasing the permeability parameter.In addition it is found that the velocity of the middle layer has adestabilizing effect whereas the dielectric constant ratio has an opposite influenceto the stability of the fluid layers.

KEYWORDS

Stability Analysis, Fluid Layers, Horizontal Field, Porous Media, Mathieu Equations

Cite this paper

Alkharashi, S. 2015 Electrohydrodynamics Instability of Three Periodic Streaming Fluids through Porous Media. Open Access Library Journal, 2, 1-12. doi: 10.4236-oalib.1101315.





Autor: Sameh A. Alkharashi1,2

Fuente: http://www.scirp.org/



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