Numerical simulation of electrically deformed droplets less conductive than ambient fluid

In this paper, the 3-D deformation of an initially uncharged and spherical droplet suspended in another immiscible fluid under dc uniform electric field is numerically investigated. Both the droplet and the ambient fluids are considered as incompressible Newtonian fluids. In all the cases both fluids are slightly conductive (``leakyʹʹ dielectrics) with the ambient phase more conductive than the droplet. Three regimes were observed for droplet deformation: (1) oblate deformation (which can be predicted from the small perturbation theory), (2) oscillatory oblate-prolate deformation and (3) breakup of the droplet. It was found that an increased electric field causes the prolate deformation to be decreased in the oscillation regime. Further increase of the electric field leads to breakup, which creates a toroidal shape. It was shown that the threshold electric field strength depends on the viscosity ratio of both fluids. The critical electric capillary number beyond which the droplet eventually breaks up in a symmetric manner has been determined.