Nonlinear interfacial stability for magnetic fluids in porous media

The weakly nonlinear stability is employed to analyze the interfacial phenomenon of two magnetic fluids in porous media. The effect of an oblique magnetic field to the separation face of two fluids is taken into account. The solutions of equations of motion under nonlinear boundary conditions lead to deriving a nonlinear equation in terms of the interfacial displacement. This equation is accomplished by utilizing the cubic nonlinearity. The method of multiple scale expansion is employed in order to obtain a dispersion relation for the first-order problem and nonlinear Ginzburg–Landau equation, for the higher-order problem, describing the behaviour of the system in a nonlinear approach. Regions of stability and instability are identified for the magnetic field intensity versus the wave number. It is found that the oblique magnetic filed has a stabilizing influence under some certain conditions for the directions of the magnetic fields. The resistance coefficient has a destabilizing influence in the linear description. Further, in the nonlinear scope, the increase of the resistance parameters plays both stabilizing and destabilizing role in the stability criteria.