Electrohydrodynamics of conducting droplets suspended in a low-conducting liquid: The effect of the difference in mobilities of positive and negative ions

Accurate numerical and mathematical models are needed to develop technologies such as electrostatic phase separation of oil-water emulsions based on two-phase electrohydrodynamics. However, it is still unclear in which cases the ionic conductivity of the oil should be taken into account and what additional effects may appear. To address this issue, the present work studies numerically how accounting for the ion transport processes and the inequality of the ion mobilities affect the behavior of water droplets in oil. It is demonstrated that the difference in the mobilities of the positive and negative ions leads to the following effects: migration of a single droplet in an external electric field, non-symmetrical trajectories of approach of two equal droplets, non-symmetrical cone-dimple mode of electrocoalescence. These effects are explained and other conditions under which they can be observed are proposed.