Electrohydrodynamic Rayleigh-Taylor instability in leaky dielectric fluids

In this paper, an analysis is presented of the influence of electric field on the Rayleigh-Taylor instability (RTI) of two leaky dielectric fluids. A numerical model is developed based on the coupled solution of the governing equations of the electric field (i.e., Poisson equation) and the fluid flow (i.e., Navier-Stokes equation), where the leaky dielectric model is employed to take into account the free charges in the fluids. These equations are formulated within the framework of phase field and solved simultaneously. The numerical model, after validated with existing data, is applied to study the effect of the electric field on interfacial morphology associated with the RTI. Different from the perfect dielectric model, the free charges originating from the conductivity in a leaky dielectric fluid plays an important role in the evolution of the RTI under the influence of an applied field. Various interfacial morphologies have been observed in the electrohydrodynamic RTI, suggesting that the electric field has a significant influence on the RTI. An electric field (horizontal or vertical) may suppress or aggravate the instability depending on the system parameters the permittivity ratio and the conductivity ratio of the two leaky dielectric fluids.