Probabilistic droplet bouncing

While drops impinging on surfaces, a biologically prevalent phenomenon, 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 three ratios: inertia to capillarity (Weber number, We), inertia-capillarity to viscosity (Laplace number, La), and drop radius to liquid layer depth. Our theory is backed by laboratory experiments, with maximal bouncing at We≈1, radius-depth ratios of ≈1/5, and La^-1/4>0.01. As La^-1/4 increases, the probability increases in a sigmoidal fashion.