Electrohydrodynamic-induced partial coalescence between a droplet and a liquid–air interface

Abstract

When a droplet coalesces with a flat liquid–air interface, a secondary drop may be left behind resulting in only a partial coalescence rather than complete coalescence. In this paper, we employ an arbitrary Lagrangian–Eulerian method to demonstrate that applying an electric field favours the occurrence of partial coalescence. To understand this phenomenon, we systematically study the effect of an external electric field on the coalescence process between a droplet and a liquid–air interface. In an electric field, the induced electric stresses can overcome the downward flow of the droplet, thus lifting it upwards. As a result, the positive Laplace pressure in the neck region squeezes the droplet towards pinch-off. We observe that both the initial neck expansion and neck shrinkage are suppressed by the electric field. These effects become weaker as the Ohnesorge number $Oh$ increases. Based on the scaling analysis, we report a critical Ohnesorge number $O{h_c} = 14.39{\varGamma ^{3/2}} + 0.029$ to quantify the transition from partial coalescence to complete coalescence in the presence of an electric field, where $\varGamma $ represents the dimensionless electric Bond number. Finally, a relationship between the secondary droplet size and the two key dimensionless numbers of $Oh$ and $\varGamma $ has been developed, which could be useful for producing droplets of desired sizes in microfluidic applications.