Stability of draining plane-parallel films containing surfactants

The stability of partially mobile draining thin liquid films with respect to axisymmetric fluctuations was studied. The material properties of the interfaces (Gibbs elasticity, surface and bulk diffusions) were taken into account. When studying the long wave stability of films, the coupling between the drainage and perturbation flows was considered and the lubrication approximation was applied. Two types of wave modes were examined: radially-bounded and unbounded waves. The difference between the thickness of loss of stability, h(st), the transitional thickness, h(tr), at which the critical wave causing rupture becomes unstable, and the critical thickness, h(cr), when the film ruptures, is demonstrated. Both the linear and the non-linear theories give h(st) > h(tr) > h(cr). The numerical results show that the interfacial mobility does not significantly influence the thickness of the draining film rupture. The interfacial tension and the disjoining pressure are the major factors controlling the critical thickness. The available experimental data for critical thicknesses of foam and emulsion films show excellent agreement with the theoretical predictions. The important role of the electromagnetic retardation term in the van der Waals interaction is demonstrated. Other published theories of the film stability are discussed.