Stability of a flat gas-liquid interface containing nonidentical spheres to gas transport: toward an explanation of particle stabilization of gas bubbles.

It is shown that a flat interface between a soluble gas and a liquid that contains an arbitrary number of partially wetting nonidentical spheres is linearly stable to slight perturbations caused by fluctuations in the gas volume. Stability is proved by showing that the rate of change of the volume of the gas with curvature of the interface is positive in the neighborhood of the equilibrium state of zero interface curvature. Physically, the volume fluctuations induce fluctuations in the curvature of the interface that would naturally lead to dissolution of gas into the liquid in the case of positive curvature and entry of gas into the bubble in the case of negative curvature, either of which restores equilibrium. This result may possibly explain the unusual long-term stability of gas bubbles covered by colloidal particles in the recent experiments of Du et al. (Du, Z.; Bilbao-Montoya, M. P.; Binks, B. P.; Dickinson, E.; Ettelaie, R.; Murray, B. S. Langmuir 2003, 19, 3106).