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

In this work, the electrohydrodynamic instability induced by a unipolar charge injection is extended from a single-phase dielectric liquid to a two-phase system that consists of a liquid-air interface. A volume-of-fluid model-based two-phase solver was developed with simplified Maxwell equations implemented in the open-source platform OpenFOAM. The numerically obtained critical value for the linear stability matches well with the theoretical values. To highlight the effect of the slip boundary at interface, the deformation of the interface is ignored. A bifurcation diagram with hysteresis loop linking the linear and finite-amplitude criteria, which is U_{f}=0.059, was obtained in this situation. It is concluded that the lack of viscous effect at interface leads to a significant increase in the flow intensity, which is the reason for the smaller instability threshold in two-phase system. The presence of interface also changes the flow structure and results in a shear distribution of electric force, which may play an important role in the interface deformation.