Bridge expansion after coalescence of two droplets in air: Inertial regime

When two liquid droplets approach at negligible velocity in air, their coalescence spontaneously occurs by jump-to-contact instability and a connecting bridge joining the two facing interfaces at the nanoscale is created. We report experimental investigations of the expansion of this initial bridge by means of high-speed imaging. By considering droplets of water, polydimethylsiloxane, or paraffin of a few hundred micrometers, we investigate regimes where inertia takes a major role. Depending on the Ohnesorge number (Oh), the dynamics of the bridge differs a lot. For Oh approximate to 1, the initial flow is rapidly attenuated and the connecting bridge between the two droplets adopts a smooth parabolic shape. The maximum interface curvature and the minimum liquid pressure remain at the bridge center. The expansion is thus caused by the capillary pressure that drives the fluid toward the center. At small Oh, in the inertial regime, the length of the initial bridge grows at constant speed and the bridge expansion can be described by the propagation of nondispersive capillary wave packets. The central part of the bridge takes a cylindrical shape connected to the droplets by a narrow region of very large curvature. At the resolved scale, the interface exhibits slope discontinuities. By considering dihedral potential flows that result in the presence of the slope discontinuities, we show that the apparent angle made by the interface controls the flow rate that enters the bridge and thus determines its radial expansion.

Automated summary

This study investigates the dynamics of the connecting bridge between two approaching liquid droplets in the regime where inertia plays a major role. The expansion of the bridge and its shape are found to vary significantly depending on the Ohnesorge number. At higher Oh values, the bridge expansion is driven by capillary pressure, resulting in a smooth parabolic shape, while at smaller Oh values, the bridge length grows at a constant speed with slope discontinuities at the interface.