Nonlinear electrohydrodynamic instability through two jets of an Oldroydian viscoelastic fluids with a porous medium under the influence of electric field

In the light of the viscous potential theory, a nonlinear instability of the surface waves propagating through two jets of viscoelastic fluids is scrutinized. The flow is jetting through porous media under the action of a uniform axial electric field. The Oldroyd B model is employed to characterize the rheological behavior of the viscoelastic fluid. A weakly nonlinear theory of wave propagation is deemed. A general dispersion relation and neutral curves are addressed and plotted for the different parameters. The Routh-Hurwitz criterion is utilized to determine the stability criteria. Several special cases are reported. It found that, in absence of porous media, the stability happens for large relaxation time and small retardation time. In addition, small retardation time leads to increase the elasticity of the fluid. Therefore, the stability is determined due to the elasticity of the fluid. However, in the presence of porous medium, the elasticity of the fluid decreases with the increase of relaxation time. Thus, the elasticity has a destabilizing effects. Furthermore, fluid viscosity has showed dual role of the stability diagram. Also, the case of Maxwell fluid is illustrated graphically. It is observed that Maxwell model is less stabilizing than Oldroyd model. The method of multiple time scale with the Taylor’s expansion is employed to conduct the well-known Ginzburg-Landau equation, which governs the nonlinear stability of the system. New several regions of stability and instability are identified due to the nonlinear effects.