TITLE:
Electrohydrodynamics Instability of Three Periodic Streaming Fluids through Porous Media
AUTHORS:
Sameh A. Alkharashi
KEYWORDS:
Stability Analysis, Fluid Layers, Horizontal Field, Porous Media, Mathieu Equations
JOURNAL NAME:
Open Access Library Journal,
Vol.2 No.2,
February
13,
2015
ABSTRACT: In this work, the effect of transverse horizontal electric field on the
stability of three layers of immiscible liquids is illustrated. The fluids are
subjected to a uniform horizontal electric field. Analytical and numerical
simulations of this system of linear evolution equations are performed. The
solutions of the linearized equations of motion and the boundary conditions
lead to deriving two simultaneous Mathieu equations of damping terms having
complex coefficients. The effects of the streaming velocity, the permeability
of the porous medium, and the electrical properties of the flow on the
instability are investigated. In the case of uniform velocity, it is found that
electric field has a stabilizing influence on the stability criteria. When the
periodicity of the velocity is considered, the method of multiple scales is
applied to obtain stability solution for the considered system. It is found
that 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 a
destabilizing effect whereas the dielectric constant ratio has an opposite influence
to the stability of the fluid layers.