Stability of bubbles in a closed volume of liquid-gas solution

Abstract

The conditions are examined under which a single bubble and a number of bubbles are in equilibrium within a closed volume of liquid that is maintained at constant temperature and pressure. It is predicted that depending on the amount of gas present in the volume, there may be no equilibrium state for the bubble or bubbles, one equilibrium size, or two possible equilibrium sizes. In the latter case, it is also predicted that the equilibrium state corresponding to the larger bubble size is a stable equilibrium state. This is in contrast to the case of an unbounded volume of liquid where there is the possibility of only one equilibrium state for a bubble, and this state is unstable. The predicted stability for a bubble in a closed volume was examined experimentally, and agreement was found between the measurement and the prediction. A striking result is the reduction in the stable equilibrium size with the number of bubbles present. In particular, micron-sized bubbles can be shown to be in stable equilibrium under the constraint of a closed volume, and for reasonable conditions of liquid temperature and pressure.