Force Balance Model for Bubble Rise, Impact, and Bounce from Solid Surfaces

A force balance model for the rise and impact of air bubbles in a liquid against rigid horizontal surfaces that takes into account effects of buoyancy and hydrodynamic drag forces, bubble deformation, inertia of the fluid via an added mass force, and a film force between the bubble and the rigid surface is proposed. Numerical solution of the governing equations for the position and velocity of the center of mass of the bubbles is compared against experimental data taken with ultraclean water. The boundary condition at the air water interface is taken to be stress free, which is consistent for bubbles in clean water systems. Features that are compared include bubble terminal velocity, bubbles accelerating from rest to terminal speed, and bubbles impacting and bouncing off different solid surfaces for bubbles that have already or are yet to attain terminal speed. Excellent agreement between theory and experiments indicates that the forces included in the model constitute the main physical ingredients to describe the bouncing phenomenon.