The restitution coefficient of bouncing binary droplet collisions

Bouncing droplets abound in nature and industrial applications. Droplets can bounce in different impact scenarios, such as in binary droplet collisions and droplet impact on super-hydrophobic surfaces or liquid surfaces. In bouncing process, initially the impacting droplet spreads, reaching a maximum extent before retracting due to surface tension and leaving the surface accompanied by oscillation in shape. During this process, kinetic energy is transferred to surface energy and lost due to viscosity. Thus, the coefficient of restitution is less than unity and depends both on the magnitude of the initial viscous loss and that occurs during post-collision oscillation. Here, we study these physics using extensive experimental measurements of head-on, equal-size binary droplet collisions imaged using a high-speed camera. A semi-theoretical model as a function of Weber number (kinetic energy vs. surface energy) and Ohnesorge number (viscosity vs. surface tension) was developed, which agrees well with the measured coefficient of restitution. Data of impacts on super-hydrophobic surfaces reported in the literature is also compared.