Stratification of a Foam Film Formed from a Nonionic Micellar Solution: Experiments and Modeling

Thin liquid films containing surfactant micelles or other nanocolloidal particles are considered to be the key structural elements of foams containing gas and liquid. We report here the experimental results and theoretical modeling for the phenomenon of the stratification (stepwise thinning) of a foam film formed from a nonionic micellar solution. The film stratification phenomenon was experimentally observed by reflected light microinterferometry. We observed that the stepwise layer-by-layer decrease of the film thickness is due to the appearance and growth of a dark spot of one layer less than the film thickness in the film. The dark spot expansion is driven by the diffusion of the dislocation (or vacancy) in the micellar lattice. The vacancies from the meniscus diffuse and condense into the dark spot, leading to its expansion inside the film. We experimentally observed the expansion of the dark spot at various film thicknesses (i.e., the number of micellar layers) and at different film sizes. We also measured the contact angle between the film and the meniscus; we used the data to estimate the structural film interaction energy barrier and the apparent diffusion coefficient. We used the two-dimensional diffusion model to model the dynamics of the dark spot expansion with consideration to the apparent diffusion coefficient and the film size. The model predictions are in good agreement with the experimental observations. On the basis of this model, we carried out a parametric study depicting the effects of the film thickness (or the number of micellar layers) and film area on the rate of the dark spot expansion. We also generalized the model previously proposed by Kralchevsky et al. [Langmuir 1990, 6, 1180-1189], incorporating the effects of the film size, film thickness, and apparent diffusion coefficient to predict the dark spot expansion rate.