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

Abstract

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-temp..