Numerical investigations of head-on collisions of binary unequal-sized droplets on superhydrophobic walls

Droplet head-on impact is widely encountered in nature, industry, and agricultural applications. In our study, a two-dimensional axisymmetric model, using the volume-of-fluid method, is built to simulate unequally sized droplet head-on impact on a superhydrophobic surface. The collision regime, after droplet coalescence, is obtained with dimensionless parameters, as well as the contact time, maximum spreading diameter, restitution coefficient, and viscous dissipation. When the impact droplet is larger than the stationary droplet on the substrate, the merged droplet can easily jump up. At high Bond numbers (Bo) or high Ohnesorge numbers (Oh), the merged droplet cannot jump up due to significant gravitational effects or viscous effects, respectively. The energy for droplet jumping mainly comes from the released surface energy after the coalescence of father and mother droplets. The contact time of a droplet with the superhydrophobic substrate is proportional to the Weber number to the 0.5th power (We(0.5)), and the maximum spreading diameter of a merged droplet is proportional to We(0.2). With an increasing size ratio of the father droplet to the mother droplet, both the contact time and maximum spreading diameter increase. These findings will help gain insights into the dynamics of droplet head-on impact.