Capillary instability of a fast-draining film

Abstract

The linear stability of a liquid film is examined, when its thickness is time dependent, for the case of a head-on collision of two bubbles. An analytical expression for surface perturbations is given for long waves. For symmetric disturbances, the amplification factor remains less than unity if the wavelength is shorter than a critical value. For antisymmetric disturbances, the film is unstable.