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In this work, the electrohydrodynamic (EHD) instability induced by a unipolarcharge injection is extended from a single-phase dielectric liquid to atwo-phase system that consists of a liquid-air interface. A volume of fluid(VOF) model based two-phase solver was developed with simplified Maxwellequations implemented in the open-source platform OpenFOAM\textsuperscript. Thenumerically obtained critical value for the linear stability matches well withthe theoretical values. To highlight the effect of the slip boundary atinterface, the deformation of the interface is ignored. A bifurcation diagramwith hysteresis loop linking the linear and finite amplitude criteria, which isUf = 0.059, was obtained in this situation. It is concluded that the lack ofviscous effect at interface leads to a significant increase in the flowintensity, which is the reason for the smaller instability threshold intwo-phase system. The presence of interface also changes the flow structure andmakes the flow vortices shift closer to the interface.

Numerical analysis of electrohydrodynamic (EHD) instability in dielectric liquid-gas flows subjected to unipolar injection