Coalescence dynamic response of an aqueous droplet at an oil-water interface under a steady electric field

Abstract The electrocoalescence of an aqueous droplet at the oil-water 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 numerical description of droplet-interface coalescence transition from the viewpoint of flow field evolution and bridge dynamics was systematically examined, analyzed, and discussed. In the early droplet-interface merging process of CC (complete coalescence) modes, the droplet vortex pair was more strongly developed than the interface vortex pair, which gave rise to the enlargement of the droplet-interface liquid bridge and the fluid motion from the droplet to the interface. The interfacial velocity at the liquid bridge was much larger than at the other regions of the droplet surface in the upheaval CC mode. The upward velocity of the outflow-natured outer vortex pair was observed in the PC (partial coalescence) mode, leading to the formation of secondary droplets. In the jet-like PC mode, multiple outflow-natured vortex pairs simultaneously existed, forcing the droplet tail to break up into tiny satellite droplets. In the NC (non-coalescence) mode, the outflow-natured outer vortex pair was always directed upward, and with the breakup of bouncing-off droplets in the NC mode, an abnormal flow field with an irregular outflow-natured outer vortex pair was formed. Conductivity played little or no part in determining the CC-PC transition, but influenced the PC-NC transition. With the whole liquid bridge dynamics involving liquid bridge growth and decay dynamics taken into consideration, a good quartic polynomial function trend was obtained between the non-dimensional liquid bridge width W* and the non-dimensional time t*. In addition, the liquid decay dynamics and the coupling effect of the electric field and fluid physical properties (such as interfacial tension and viscosity) determine the partial coalescence process. The outcome of this work is potentially useful for optimizing the design of compact and efficient oil-water separators.