Mobile or Immobile? Rise Velocity of Air Bubbles in High-Purity Water

The velocity of bubbles rising in pure liquids is affected by the boundary conditions at the liquid-air interface, with bubbles rising the fastest when the bubble surface is fully mobile. The presence of even very small amounts of surface-active molecules causes tangential immobility at the liquid-air interface and subsequently results in slower bubble rise velocity. The existing literature on the rise velocities of air bubbles in high-purity water does not provide a conclusive picture on whether or not the water-air interface is immobile, with the most discrepancies reported for very small bubbles. This paper presents the first systematic study of bubble rise velocities in high-purity water for a sufficiently wide range of bubble sizes (bubble diameter between 48 mu m and 1.5 mm) and for the same experimental conditions, which will allow firm conclusions to be drawn on this issue. For bubbles of diameter 800 mu m or larger, the measured rise velocity is in a good agreement with the theoretical predictions for a completely mobile water-air interface, but the velocity starts to deviate from that of mobile bubbles as the size becomes smaller. The smaller the bubble, the closer the rise velocity corresponds to an immobile water-air interface, and for Re < 1, the bubble rise velocity agrees with the Stokes law. We use the rear stagnant cap model to explain why smaller bubbles are significantly more sensitive to any surface-active impurities than larger ones.