Droplet coalescence in air: formation and expansion of the bridge

In numerous natural or man-made processes, from clouds formation to emulsions separation, coalescence drives the size growth of droplets. It is a complex phenomenon that involves several mechanisms at various scales and time. In this talk we will describe the main two mechanisms that control the two stages of droplet coalescence in air. The first one concerns the jump-to-contact instability which has been evidenced by Atomic Force Microscopy (AFM). This hydrodynamic instability due to van der Waals forces occurs at the nanoscale and is responsible for the bridge formation between two droplets when the two facing surfaces are separated by a distance of around 10 nm. Specific experiments by Frequency Modulation-AFM have been developed to measure this critical distance and point out that its value is fixed by the Hamaker constant and the surface tension of the liquid. 

The second mechanism concerns the expansion of the initial bridge and is determined by the Ohnesorge number (Oh). For usual liquids, Oh is small, and the length of the initial bridge grows at constant speed (inertial regime). The bridge is cylindrical and its longitudinal expansion can be described by the propagation of nondispersive capillary wave packets. At the resolved scale, the interface exhibits slope discontinuities. By considering dihedral potential flows associated with 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. For Oh ~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. In this case, the expansion is caused by the capillary pressure that drives the fluid toward the center.