Non-linear study of electrohydrodynamic Rayleigh–Taylor instability in a composite fluid–porous layer

The non-linear electrohydrodynamic RTI in presence of electric field bounded above by porous layer and below by a rigid surface, have been studied based on electrohydrodynamic approximations in the effect similar to the Stokes and lubrication approximations. The non-linear problem is studied numerically in the present paper using the Adams–Bashforth predictor and Adams–Moulton corrector numerical techniques. In the conclusion, the non-linear problem discussed here is quite different from that of Babchin et al. (1983) [10] considering the plane Couette flow. The present problem is greatly influenced by the slip velocity at the interface between porous layer and thin film. It is not amenable to analytical treatment as that of Babchin et al. [10]. Therefore, numerical solutions have to be found. Fourth-order accurate central differences are used for spatial discretization using predictor and corrector numerical technique.

► If there is a surface tension between the two fluids, stable wave exists, depending on the wave numbers.
► The stabilizing effect comes only from the surface tension between the two fluids.
► The fluids are inviscid and incompressible.