Field induced coalescence of two free water drops in a viscous dielectric fluid

The basic process of coalescence of droplets in a flowing water-in-oil emulsion under the action of an electric field is considered. The coalescence probability depends on the ratio of time of close proximity of droplets and time of decrease of spacing down to drops contact. For two free drops aligned with the field, the dynamical problem consists in the deformation of the drops, their motion and the thinning of the oil film between the drops. For very small droplets, assuming a negligible interface deformation, a very small initial spacing and a high value of viscosity ratio leads to an order of magnitude estimate of the time required for the drops to achieve contact. Numerical simulations confirm that this time is roughly inversely proportional to the maximum initial electrostatic pressure p_e0 at the facing interfaces and point up an influence of the electric Bond number defined as the ratio of electric and capillary forces.