Three dimensional nonlinear instability analysis of electroconvective finite dielectric fluids

The nonlinear electrohydrodynamic Rayleigh-Taylor instability analysis for the interface between two finite fluid layers with interfacial transfer of heat and mass is studied for two and three dimensions cases. Multiple scales perturbation method is applied to get general linear dispersion relation and a nonlinear Ginzburg-Landau equation, representing the behaviour of the system. The stability of the system is analyzed theoretically and graphically. In linear case, the stability criterion is independent of heat and mass transfer coefficient, and both the dimensions and fluid depths have destabilizing effects, while both the electric field and the surface tension have stabilizing influences. In the nonlinear case, in the two-dimensional disturbances, for small electric field values E0, stability holds for only small wavenumbers range which decreases by increasing E0, while for high values of E0, stability exists also at high wavenumbers range which increases by increasing E0. The surface tension T and the fluid depths d1 and d2 have destabilizing effects, while the heat and mass transfere coefficient � has a dual role on the stability of the system, i.e stabilizing as well as destabilizing. In the three - dimensional disturbances, we found that the stability regions decreases under the effects of all the previous physical parameters.