Linear stability of an expanding spherical liquid film

As a simple model of processes relevant to generation of foams, we consider the stability of an expanding spherical liquid film. Primary influences on stability considered are destabilizing effects of intermolecular attractive forces in the liquid, competing with stabilizing effects of surface tension and its gradients resulting from perturbations to surfactant distribution. Linear stability and growth rates are determined for a film, such as a soap bubble, that is expanding by an increase in the volume of the interior gas. A bubble with fixed total interfacial surfactant is found to become increasingly unstable with expansion by virtue of film thinning and surfactant dilution; the expansion flow exerts a stabilizing influence, but this effect is negligible in practical situations.