Energetics of a bouncing drop: Coefficient of restitution, bubble entrapment, and escape

Drops bouncing on an ultra-smooth solid surface can either make contact with the surface or be supported on a thin cushion of gas. If the surface is superhydrophobic, either complete or partial rebound usually occurs. Recent experiments have shed light on the lubrication effect of the underlying gas layer at the onset of impact. Using axisymmetric direct numerical simulations, we shed light on the energetics of a drop bouncing from a solid surface. A complete energy budget of the drop and the surrounding gas during one complete bouncing cycle reveals a complex interplay between various energies that occur during impact. Using a parametric study, we calculate the coefficient of restitution as a function of Reynolds and Weber numbers, and the results are in good agreement with the reported experiments. Our simulations reveal that the Weber number, not the Reynolds number, has a stronger effect on energy losses as the former affects the shape of the drop during impact. At higher Weber and Reynolds numbers, a tiny gas bubble gets trapped inside the drop during impact. We show that a large amount of dissipation occurs during the bubble entrapment and escape process. Finally, analysis of the flow field in the underlying gas layer reveals that maximum dissipation occurs in this layer, and a simple scaling law is derived for dissipation that occurs during impact