Modeling the gentle bouncing of a drop with quasi-static thin film equations

We extend a thin film model used successfully to account for weak drop deformations in both Atomic Force Microscope and Surface Force Apparatus experiments to the case of a free buoyant drop approaching a solid horizontal surface. In order to limit the collision velocity, we assume that the drop is released sufficiently close to the surface to stay well below terminal velocity, unlike previous theoretical and experimental treatments. We describe how a new asymptotic boundary condition can account partially for the deformation of the drop, assuming hydrostatic pressure inside the drop throughout the collision. We compare briefly with experiment and with previous treatments of more energetic collisions, and describe the detailed dynamics of the thin film as the drop approaches the wall, bounces a few times and finally settles to macroscopic equilibrium. In particular, we track the detailed evolution of the film pressure profiles, film force and film thickness profiles over the course of the collision. In spite of complicated phenomena seen in the film profiles, a simple damped oscillator model of Legendre et al. shows qualitative agreement for the center of mass trajectory, the discrepancy being due to the drop behavior on the first rebound.