The coefficient of restitution for air bubbles colliding against solid walls in viscous liquids

The motion of air bubbles undergoing collisions with solid walls was studied experimentally. Using a high speed camera, the processes of approach, contact, and rebound were recorded for a wide range of fluid properties. The process is characterized considering a modified Stokes number, St∗=(CAMρdeqU0)/(9μ), which compares the inertia associated with the bubble (added mass) and viscous dissipation. We found that the dependence of the coefficient of restitution, ϵ=−Ureb/U0, with the impact Stokes number can be approximated by −log ϵ∼(Ca/St∗)1/2, where Ca is the capillary number; this behavior is very different from that found for the case of solid spheres. Most importantly, it shows that ϵ does not depend on the approach velocity. Considering a model for the process of contact and rebound of a deformable particle, this dependence is validated. Furthermore, by comparing the experimental trajectories and velocities of the bubble approach with model predictions, it was found that the film drainage is dominated by inertial effects; viscous effects, which would dominate for the case of approaching solid particles, are of secondary importance in this case.