Nonlinear electrohydrodynamic Kelvin-Helmholtz instability with mass and heat transfer. Effect of a perpendicular electric field

The nonlinear electrohydrodynamic Kelvin-Helmholtz instability of two superposed dielectric fluids with interfacial transfer of mass and heat is presented for two layers of finite thickness. The fluids are subjected to a normal electric field. The method of multiple scale perturbations is used to obtain a dispersion relation for the first-order and a Ginzburg-Landau equation, for the higher-orders, describing the behaviour of the perturbed system. The stability criterion is expressible in terms of various competing parameters representing the equilibrium heat flux, latent heat of evaporation, gravity, surface tension, densities of the fluids, dielectric constants of the fluids, thickness of the layers and thermal properties of the fluids. The stability of this perturbed system is discussed both analytically and numerically near the marginal state and the stability diagrams are obtained.