Multi-drop interaction in insulating oil under an application of an electric field.

An intriguing experimental observation in the electrocoalescence of water-in-oil emulsions is the occurrence of a very low critical electric field, beyond which the chaining of droplets and shorting of electrodes is observed, as compared with the experimental and theoretical predictions based on two equal-sized water droplets in oil. Motivated by these observations, a numerical, analytical, and experimental study on the interaction between multiple, unequal-sized, perfectly conducting droplets in a perfectly dielectric medium under an electric field is presented here. Experiments and numerical simulations indicate that the critical capillary number for two Unequal-sized droplets is less than that for two equal-sized droplets. The mechanism seems to be the greater cone angle at contact subtended by the smaller droplet on account of the strong electrohydrodynamic interaction with the bigger droplet. Our results indicate that multi-droplet interaction in a polydisperse emulsion can indeed lead to a critical capillary number much smaller than that for a two equal-sized droplet system.