Study on the transient response of water-in-oil droplet interface to electric field

The transient response of water-in-oil droplet interface to electric field, which is important to intensification of separation processes of emulsions, was theoretically and experimentally investigated in this paper. A mathematic model was developed to find out the dynamic mechanisms of the transient process. By discussing the interface velocity and the stresses on the interface, the effects of two mainly governed dimensionless numbers, electric capillary number (Ca) and Ohnesorge number (Oh), on the oscillation modes were explained in detail. A greater Ca or Oh leads to a transformation of oscillation modes from underdamping to overdamping. For the amplitude of the first overshoot (Am) which monotonically decreases with Oh, however, there exists a critical Ca at which Am reaches its peak value. Afterwards, with the help of high speed photography, the rising time of overdamping mode was investigated. Despite of very small discrepancy, good agreement between model predictions and experimental results of the scaling law of the dimensionless rising time was observed. The results indicate that the dimensionless rising time shows a linear relationship with Ca under semi-log coordination. This valuable scaling law could provide reference for the optimizing design of oil-water separation devices.