Nonlinear Kelvin-Helmholtz instability of Rivlin-Ericksen viscoelastic electrified fluid-particle mixtures saturating porous media
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt
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Revised: 8 February 2012
Accepted: 22 February 2012
Published online: 13 March 2012
The nonlinear electrohydrodynamic Kelvin-Helmholtz instability of two superposed semi-infinite Rivlin-Ericksen viscoelastic dielectric fluids streaming through porous media in the presence of suspended particles is investigated in three dimensions. The method of multiple scales is used to derive a nonlinear Schrödinger equation with complex coefficients. The linear and nonlinear stability conditions are obtained and discussed both analytically and numerically. The limiting cases of linear results recovered the previous studies. For the nonlinear two-dimensional case, we found that the system is always unstable and this instability decreases by increasing the medium permeability, the surface tension, and the porosity of the porous medium; while it increases by increasing fluid velocities, viscosities, viscoelasticities, electric field, and number densities of particles. Also, in the nonlinear three-dimensional case, we found that the medium permeability and the porosity of the porous medium have stabilizing effects, and the fluid velocities, viscoelasticities, surface tension, and electric field have destabilizing effects; while the number densities of particles and viscosities have no effect on the stability of the system. In the latter case, the dimension has different effects depending on increasing various parameters individually.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2012