Nonlinear Marangoni instability in dielectric superposed fluids

Summary The nonlinear Marangoni instability of two dielectric superposed fluids is investigated. The system is stressed by a normal electric field such that it allows for the presence of surface charges at the interface. The method of multiple scale perturbations is used in order to obtain uniformly valid expansions. Two nonlinear Schrödinger equations describing the perturbed system are obtained. One of these equations is used to describe analytically and numerically the necessary conditions for stability and instability near the marginal state, while the other equation is used to obtain the nonlinear electrohydrodynamic cutoff wavenumber separating stable and unstable disturbances for the system.