Critical conditions for electrically induced coalescence of two very close water droplets 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. After a recap of previous work on two identical drops, an approximate treatment in the asymptotic case of very close drops leads to the determination of critical conditions for existence of a stationary solution. In particular, it is shown that instability and, therefore, electrocoalescence occurs when the surfaces distortions are such that the initial separation has decreased by about 45 %. The analysis is then extended to the case of drops of unequal size.