Electrohydrodynamics (EHD) is known as a means to control liquid atomization at submicrometric scales by adjusting the external electric field that drives the deformation of the interface between fluids. While “liquid-air” systems have been extensively investigated, the EHD phenomenon in “liquid-liquid” systems is much less studied. In contrast to the liquid-air systems, (planar) liquid-liquid interfaces commonly exhibit a smaller surface tension and thus, their deformation requires an electric field of lower intensity. Furthermore, the characteristic length scales associated with the EHD phenomena (i.e. distance between electrodes against jet diameter) in liquid-liquid systems are much smaller, which in turn avoids the wide disparity of characteristic scales that undermines classic liquid-air EHD. The present work is devoted to the application of the recently developed computational approach for solving EHD problems focusing on liquid-liquid systems. The proposed method is based on the enriched finite element method (EFEM) formulated in [1, 2]. This method benefits from the realistic (physically consistent) modeling of the jump in the Maxwell stress across the material interface (due to different electric properties) as well as the pressure discontinuity (due to surface tension). Consequently, reasonably accurate solutions to the EHD phenomena can be obtained already on coarse meshes. Present work studies systems characterized by the ratio between the jet diameter and element size d j /h ≈ 5. While for traditional computational approaches (i.e., discontinuities smoothed over a few cells/elements) coarse meshes (d j /h ≈ 5) led to an unacceptable solution [3]. The results obtained in the present work show that the developed method can be extended to further challenging problems associated with microfluidics-driven processes (e.g, EHD-inkjet printing, inkjet-printing, digital microfluidics.)