Probabilistic droplet bouncing

While droplet impingement has been extensively researched, the resultant bouncing probability is yet to be quantified. We derive a model capturing the probability of a drop to bounce on a liquid surface, obtaining a dependence on four ratios: inertia to capillarity (Weber number, We), inertia to viscosity (Reynolds number, Red), inertia-capillarity to viscosity (Laplace number, Laa), and drop radius to liquid layer depth. Our theory is backed by laboratory experiments, with maximal bouncing at We≈1, Red≳1, radius–depth ratios of ≈1/5, and Laa−1/4>0.01. As Laa−1/4 increases, the probability increases in a sigmoidal manner.