Nonlinear interfacial instability of two electrified miscible fluids

In a previews paper [1], a simplified formulation was presented to deal with the intcrfacial linear stability problem with mass and heat transfer, considering the presence of a periodic electric field. The present paper treats the same problem with a nonlinear approach. This approach is achieved by considering the multiple time scale method. The analysis reveals the existence of both resonant and non - resonant cases. Three types of nonlinear Schődinger equations are derived . The necessary and sufficient stability of conditions in obtained and the results are confirmed numerically. Graphs are drawn to illustrate the stability regions.