Electrocoalescence Criterion for Two Close Anchored Water Drops and Estimate for Pairs of Drops in a Field

An investigation is presented of 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, the equation governing the droplets deformation is derived in the asymptotic case of very close drops subjected to a potential difference. The critical conditions for the existence of a stationary solution are determined for a pair of droplets anchored on coaxial rings and on capillary tubes. In particular, electrocoalescence is predicted to occur when the interfaces distortions are such that the initial drops spacing has decreased by nearly 50%. The case of drops subjected to a uniform field is also considered, and an approximate expression for the critical field is proposed based on a semiempirical relation estimating the potential difference between two close spheres as a function of the applied field, of the spheres radius, and of their spacing.