Nonlinear stability of viscoelastic fluids streaming through porous medium under the influence of vertical electric fields producing surface charges

A nonlinear stability analysis of two superposed semi-infinite viscoelastic electrified fluids streaming through porous media in the presence of vertical electric fields admitting 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 linear and nonlinear stability analysis, in both twoand three-dimensional disturbances, are discussed both analytically and numerically . We found that the surface tension, porosity of porous medium, and kinematic viscosities have stabilizing effects in the linear analysis, and nonlinearity tends to weaken their stabilizing effects. Also, the medium permeability has a stabilizing effect in the linear analysis and a destabilizing effect in the nonlinear case. The fluid velocities are found to have destabilizing effect in the linear case, while they have dual role on the stability in the nonlinear case. It is found also that nonlinearity does not affect the linear behaviors of both electric fields and kinematic viscoelasticities, and that the system in absence of fluid velocities (or porous medium) is more unstable than in their present, while the system is less unstable in absence of electric fields. Comparison between the stability behaviors of all physical parameters in twoand three-dimensional disturbances have been done, and show interesting features. MSC: 76E17 • 76S05 • 76W05