Numerical study of coalescence and non-coalescence of two conducting drops in a non-conducting medium under electric field

Abstract

A numerical study, employing boundary element method (BEM), on the interaction of two perfectly conducting drops in a perfectly dielectric medium (PCPD), under electric field, is presented here. A scaling analysis is carried out to show that electric stress is balanced by the hydrodynamic stress while the capillary stress becomes subdominant as the drops approach each other under electric field. Parameters such as initial separation distance and electrocapillary number are numerically studied using BEM to see their effects on deformation of drops, characterized by their cone angle β at contact, in pre-contact phase. In the post-contact phase, the drops are bridged using Bird et al. (2009)’s analytical model, which is solved numerically. Thereafter BEM is employed to realize coalescence and non-coalescence as exhibited by the bridged drops, depending on critical cone angle. It is also shown numerically, that electrostatics play no part for PCPD system once the charges at the tips of the drop poles are neutralized on bridging thus validating Bird et al. (2009)’s assumption.