Dynamics of two unequal-sized drops coalescence at a liquid–liquid interface

Abstract

The secondary droplets formed during the coalescence of two drops have an important role in many applications, including raindrop formation in clouds and emulsions coarsening. The process of secondary drop generation at the liquid–liquid interface is numerically investigated using a coupled level set and volume of fluid method during the coalescence of two drops of different parent drop size ratios. The coalescence dynamics has been found to depend on the five-dimensionless parameters, namely, the Ohnesorge numbers for liquid-1 and 2, the Bond number, the Atwood number, and the diameter ratio of the two drops. As a function of these non-dimensional parameters, different pinch-off regimes, namely, first-, second-, and no pinch-off, are studied. The result shows that the local neck curvatures at the onset of pinch-off play a key role in the appearance of various pinch-off regimes. The second-stage pinch-off occurs primarily within the Ohnesorge number range from 0.002 to 0.01, i.e., inertio-capillary regime range. Above this range, a direct transition from the first-stage pinch-off to no pinch-off occurs with the increasing Ohnesorge number. Within the inertio-capillary regime, the pinch-off mechanism in both the first and second-stage pinch-off regime is found to be almost independent of the Atwood number and the parent drop size ratio. Capillary waves produced at the contact region of two drops have also been observed to influence the pinch-off process. A large parent size ratio induces the higher curvature near the neck zone, resulting in stronger capillary waves. Strong viscous forces, however, dampen the propagation of capillary waves at a large Ohnesorge number. The critical Ohnesorge number is obtained for both the first and second-stage pinch-off regimes above which the strong viscous forces hinder a secondary drop pinch-off.