A force balance model for the motion, impact, and bounce of bubbles

A force balance model has been developed to predict the terminal velocity of a sub-millimetric bubble as its rises in water under buoyancy. The dynamics of repeated collisions and rebounds of the bubble against a horizontal solid surface is modeled quantitatively by including forces due to buoyancy, added mass, drag, and hydrodynamic lubrication—the last arises from the drainage of water trapped in the thin film between the solid surface and the surface of the deformable bubble. The result is a self-contained, parameter-free model that is capable of giving quantitative agreement with measured trajectories and observed collisions and rebounds against a solid surface as well as the spatio-temporal evolution of the thin film during collision as measured by interferometry.