A numerical phase field model is developed to investigate the Rayleigh-Taylor instability (RTI) subject to a horizontal electric field. The model entails the simultaneous solution of the electric field equation and the Navier-Stokes equation for fluid flow coupled with the phase field model for the evolution of the fluid-fluid interface deformation and morphology. The in-house Fortran code was developed to enable the computing. Results show that, for pure dielectric fluids, the presence of the horizontal electric field induces polarization charges and produces a Korteweg-Helmholtz force which acts to suppress the RTI. For poorly conducting liquids, for which a leaky dielectric description is more appropriate. In this model, both polarization and free charges present. The effect of the free charge in this case depends on the specific values of λε and λσ. For the fluids of λε >1, it aggravates RTI if λσ<λε, and suppresses that when λσ>λε.

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