Surface Bubble Coalescence*

Bubble coalescence at a free surface occurs in our daily lives with drinks and on a global scale at the surface of the ocean. We present an experimental study of bubble coalescence at an air-water interface, and characterize the evolution of both the underwater neck and the surface bridge. We explore a wide range of Bond number, which compares gravity and capillary forces and is a dimensionless measure of the free surface's effect on bubble geometry. The nearly spherical $Bo \ll 1$ bubbles exhibit the same inertial-capillary growth of the classic underwater dynamics, with limited upper surface displacement. For $Bo > 1$, the bubbles are non-spherical - residing predominantly above the free surface - and while an inertial-capillary scaling for the underwater neck growth is still observed, the controlling length scale is defined by the curvature of the bubbles near their contact region. With it, an inertial-capillary scaling collapses the neck contours across all Bond number to a universal shape. Finally, we characterize the upper surface with a simple oscillatory model which balances capillary forces and the inertia of liquid trapped at the center of the liquid-film surface.