Deformation and Interaction of Droplet Pairs in a Microchannel under ac Electric Fields

The deformation and interaction of a droplet pair in an electric field determine the success of droplet coalescence. Electric intensity and initial droplet separation are crucial parameters in this process. In this work, a combined theoretical and numerical analysis is performed to study the electrohydrodynamics of confined droplet pairs in a rectangular microchannel under ac electric fields. We develop a theoretical model to predict the relationship between critical electric intensity and droplet separation. A geometrical model relating the initial droplet separation to the cone angle is also established to determine the critical separation for partial coalescence. These models are validated by comparisons with existing experimental observations. According to the initial separation and electric intensity, five regimes of droplet interactions are classified by direct numerical simulations, namely noncoalescence, coalescence, partial coalescence, ejection after coalescence, and ejection with partial coalescence. According to their controlling mechanisms, the five regimes are distinguished by three well-defined boundaries. The detailed dynamics of the partial coalescence phenomenon is resolved when the droplet separation exceeds the critical value. A dynamic liquid bridge between the droplets is sustained by the competition between surface tension and electric stress. The dynamics of ejected microjets at the exterior ends are also addressed to show their responses to the oscillating electric field. The full understanding of the droplet dynamics under electric fields can be used to predict the droplet fusion behaviors and thus to facilitate the design of droplet-based microfluidic devices.