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Drop deformations and flow fields were determined in this study by solving the Navier-Stokes and Laplace's equations governing the flow field and electric field, correspondingly. The Level Set method was used to study the free interface deformations of a single drop suspended in another viscous fluid and the coalescence between a drop and an interface. The first part of the study focused on the effect of the electric field strength and the two fluids physical properties (conductivity -, permittivity- and viscosity ratio) on the droplet shape. The second part of the study was aimed at the numerical study of the partial coalescence phenomenon and its validation on the ground of experimental data from the literature. The electric field effect on the partial coalescence phenomenon was also examined. In presence of critical electric field strength the coalescence proceeded as a single-stage process. [ABSTRACT FROM AUTHOR]