Deformation and Approaching of Droplet Pair in a Microchannel under AC Electric Fields

Electric fields are widely used to induce the coalescence of water-in-oil emulsion droplets in droplet-based microfluidics. The dipole-dipole interaction amplifies the dielectrophorectic force experienced by two neighboring droplets to drive them toward each other. An ac electric field can act in a cumulative manner to merge the adjacent interfaces of the two droplets, even if the electric field is weak. Here we perform a combined numerical and theoretical analysis to explore the coupled flow and electric field of droplet pair in a rectangular microchannel under ac electric fields. Numerical simulations are carried out by solving of the conservation equations coupled with an improved volume-of-fluid/adaptive-mesh-refinement method and a charge-conservative leaky-dielectric model for two-phase electrohydrodynamic problems. To improve the fidelity and efficiency of the simulations, several adaptive mesh refinement criteria are used simultaneously, including gradient-based refinement along the interface, curvature-based refinement for interface with high curvature, and thickness-based refinement for thin region between confinement walls and interfaces. The evolutions of deformation parameter and droplet separation, as well as the distribution of the electric force are analyzed to reveal the responses of droplet pair to the ac field. A theoretical model with correlation parameter is established for the time needed for droplet coalescence in terms of initial droplet separation and ac field intensity. By taking account into the deformation and movement of the droplets, this model can predict more precisely the droplet manipulation for arbitrary electric field frequencies.