Nonlinear instability of finitely conducting cylindrical flows through porous media

A weakly nonlinear stability of two-layers flows between two concentric circular cylinders in porous media, is investigated. The two fluids are subjected to a uniform-axial electric field. The boundary value-problem of the considered system is analytically treated using a perturbation procedure based on the multiple scales-technique. The results of the first order determine the dispersion relation and the higher orders result in a Ginzburg–Landau equation, describing the behavior of the system. The topological features of stability picture are depicted. The effects of the electric field, Darcy's coefficients, streaming and conductivity on the stability are identified. The nonlinear theory predicted more accurately the instability, where new instability regions, appearing due to the nonlinear effects.