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.
Cite this paper
Alkharashi, S. A. (2015). Electrohydrodynamics Instability of Three Periodic Streaming Fluids through Porous Media. Open Access Library Journal, 2, e1315. doi: http://dx.doi.org/10.4236/oalib.1101315.
Funada, T. and Joseph, D.D. (2001) Viscous Potential Flow Analysis of Kelvin-Helmholtz Instability in
a Channel. Journal of Fluid Mechanics, 445, 263-283. http://dx.doi.org/10.1017/S0022112001005572
Zakaria,
K., Sirwah, M.A. and Alkharashi, S. (2009) Instability through Porous Media of Three Layers Superposed Conducting
Fluids. European Journal of Mechanics-B/Fluids, 28, 259-270. http://dx.doi.org/10.1016/j.euromechflu.2008.08.002
Sadiq, I., Usha, R. and Joo, S.W. (2010) Instabilities in a Liquid Film
Flow over an Inclined Heated Porous Substrate. Chemical Engineering Science, 65, 4443-4459. http://dx.doi.org/10.1016/j.ces.2010.04.005
Prieling, D. and Steiner, H. (2013) Analysis of the Wall Mass Transfer on Spinning Disks Using an
Integral Boundary Layer Method. Chemical Engineering Science, 101, 109-119. http://dx.doi.org/10.1016/j.ces.2013.06.034
Li, F., Ozen, O. and Aubry, N. (2007) Linear Stability of a Two-Fluid Interface
for Electrohydrodynamic Mixing in a Channel.Journal of Fluid Mechanics, 583, 347-377. http://dx.doi.org/10.1017/S0022112007006222
Tseluiko, D. and Blyth, M.G. (2008) Electrified Viscous Thin Film Flow over Topography. Journal of Fluid Mechanics, 597, 449-475. http://dx.doi.org/10.1017/S002211200700986X
Espn,
L., Corbett, A. and Kumar, S. (2013) Electrohydrodynamic Instabilities in Thin Viscoelastic Films? AC
and DC Fields.Journal of Non-Newtonian Fluid Mechanics, 196, 102-111. http://dx.doi.org/10.1016/j.jnnfm.2012.12.013
Roberts, S.A. and Kumar,
S. (2009) AC Electrohydrodynamic Instabilities in Thin Liquid Films.Journal of Fluid Mechanics, 631, 255-279. http://dx.doi.org/10.1017/S0022112009006843