Drop-interface electrocoalescence mode transition under a direct current electric field

The electrocoalescence of a water drop at the water/oil interface in the presence of externally direct current electric fields was numerically analyzed with the finite element method by solving the Navier-Stokes and charge conservation equations. The proprietary software Comsol Multiphysics was used for this purpose, and the interface motion was captured by the Level-Set method. Good agreement was obtained between numerical and experimental results in the literature. The effects of the electric field strength, droplet size, oil phase permittivity, surface tension, bulk viscosity, water phase conductivity, and drop-interface distance were systematically assessed. Three coalescence modes were obtained: complete coalescence, including typical complete coalescence and complete coalescence with upheaval; partial coalescence, including typical partial coalescence and jet-like partial coalescence; and non-coalescence, including typical non-coalescence and breakup of bouncing-off droplet non-coalescence. The pressure gradients between the drop and the bridge rather than the sign of the pressure determined the coalescence. There is a critical non-dimensional drop-interface distance of electrocoalescence modes that has negligible dependence on the non-dimensional water phase conductivity. The ratio of the Weber Number (describing electric field effects) and the Ohnesorge Number (describing physical properties) was found to well describe the coalescence process. The outcome of this work is potentially useful for optimizing the design of compact and efficient oil-water separators.