Dynamics of non-coalescence in unequal sized, conducting multi-droplet system suspended in an insulating medium under an electric field

Abstract An intriguing experimental observation in electrocoalescence of water-in-oil emulsions is the occurrence of a very low critical electric field, beyond which 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. We show that the critical capillary number ($Ca_c$), based on the bigger droplet, in a two droplet system, reduces as the radius ratio of the smaller to bigger drop decreases. Secondly, in a system of three equally sized droplets, it is expected that the $Ca_c$ will be smaller than a two equal sized droplet system, since the electric field experienced by the central droplet is higher when surrounded by two droplets instead of one. Our results show that nonlinearity in the system due to both the asymmetric shape deformation and the electrostatic interaction between the multiple droplets, leads to significant reduction in $Ca_c$ for onset of non-coalescence in an unequal sized two droplet system or for equal and unequal sized three droplet systems, as compared with $Ca_c$ for two equal sized droplets. This is possibly one of the underlying mechanisms for observing much smaller $Ca_c$ in emulsions as compared with a system of two equal sized droplets, and could be responsible for a polydisperse water-in-oil emulsion being exceptionally susceptible to chaining under an electric field.