Viscous Rayleigh-Taylor instability in aqueous foams

We consider the stability of a long soap film as it is accelerated broadside into a region of passive gas, in which the receding interface is unstable via the Rayleigh-Taylor mechanism. In particular, we examine how the growth rate of the unstable mode depends on the viscosity of the liquid and the surfactant distribution, showing that the maximal growth rate and the corresponding wavenumber both decrease as the solutal Marangoni number of the system increases. We examine the consequences of these results for the brittle fracture of aqueous foams, where Rayleigh-Taylor instabilities provide a mechanism for film rupture. For a range of Reynolds and solutal Marangoni numbers, a strong dependence of the instability on the film size is predicted.