The impact and bounce of air bubbles at a flat fluid interface

The rise and impact of bubbles at an initially flat but deformable liquid-air interface in ultraclean liquid systems are modelled by taking into account the buoyancy force, hydrodynamic drag, inertial added mass effect and drainage of the thin film between the bubble and the interface. The bubble-surface interaction is analyzed using lubrication theory that allows for both bubble and surface deformation under a balance of normal stresses and surface tension as well as the long-range nature of deformation along the interface. The quantitative result for collision and bounce is sensitive to the impact velocity of the rising bubble. This velocity is controlled by the combined effects of interfacial tension via the Young-Laplace equation and hydrodynamic stress on the surface, which determine the deformation of the bubble. The drag force that arises from the hydrodynamic stress in turn depends on the hydrodynamic boundary conditions on the bubble surface and its shape. These interrelated factors are accounted for in a consistent manner. The model can predict the rise velocity and shape of millimeter-size bubbles in ultra-clean water, in two silicone oils of different densities and viscosities and in ethanol without any adjustable parameters. The collision and bounce of such bubbles with a flat water/air, silicone oil/air and ethanol/air interface can then be predicted with excellent agreement when compared to experimental observations.