Stability of evaporating two-layered liquid film in the presence of surfactant - III. Non-linear stability analysis

摘要

In this study we perform non-linear stability analysis of a two-layered liquid film attached to a horizontal solid substrate. The film contains surfactant that is soluble in both liquid phases. The evaporation of solvent from the upper film is also taken into account. The him can exhibit both thermal and surfactant Marangoni instabilities coupled with the effect of the solvent mass loss. The effect due to the van der Waals disjoining pressure is also examined. One particular system is considered: tetrachlorethane-water film upon a PVC plate. We study numerically the influence of surfactant on the him rupture time and the critical film thickness. The role of different factors on the critical thickness and the rupture time is investigated: the intensity of evaporation, the ratio of the thickness of the two layers, the surfactant concentration, and the surfactant distribution coefficient. We demonstrate that the initial perturbations in the squeezing mode are more unstable than the perturbations in the bending mode. It is shown that the effect of surfactant on the film stability is well established. The comparison with the case of pure liquid phases shows that when the surfactant concentration is high enough (tangentially immobile film surfaces) the short and moderate waves are significantly suppressed. Optimal values of the film thicknesses ratio and of the surfactant distribution coefficient are obtained which correspond to maximal stability of the two-layered film against fluctuations. It is found that the results from the linear and non-linear stability analysis differ significantly for the case of pure liquid phases and the differences between them decrease with the increase of the surfactant concentration. (C) 1998 Elsevier Science Ltd. All rights reserved. [References: 22]