Statistics of rupture in relation to the stability of thin liquid films with different size

Abstract

We study the stability and the thinning behavior of foam films in the presence of ionic surfactant. Using the method of capillary cell at low pressures (20–50 Pa), combined with interference microscopy, we measured the film thickness vs. time, the critical thickness of rupture, and the lifetime of films with different sizes. The film behavior is characterized by two separate stages: at first, there is a hydrodynamic thinning without rupture; afterwards, film rupture occurs as a stochastic process. The measured lifetimes in an ensemble of films are scattered in a certain range. We found that this statistical behavior is well described by a specific distribution, with cumulative probability 1 − exp(− βt 2/2). By means of theoretical considerations, this distribution is derived from the time dependent differential probability for film rupture. Fitting of experimental data for the statistics of the film lifetimes is performed. This permits one to find the average transient lifetime at the stochastic stage; thus, thinning and rupture are distinguished. The size dependence of the drainage time is shown to comply with theories which describe the behavior of films with irregular thickness. The time for thinning, and the inverse drainage rate coefficient, scale with the film radius as r f 4 / 5 . This work may be relevant to understanding the stability of fluid dispersions in dependence of the particle size.