Electrically induced coalescence of two facing anchored water drops in oil

We investigate the deformation and coalescence of two closely spaced drops of conducting liquid suspended in an insulating fluid under the action of an electric field. The equations governing droplets deformation are derived in the case of drops subjected to a potential difference. The critical conditions for existence of a stationary solution are determined for drops anchored on capillary tubes in the asymptotic case of very close drops. In particular, electrocoalescence is predicted to occur when the interfaces distortions are such that the initial drops spacing has decreased by nearly 50%. A numerical simulation gives the critical conditions for any spacing between the drops. Results compare favourably with the asymptotic approach in the common range of application.