Comparative validation of the analytical models for the Marangoni effect on foam film drainage

Abstract

The aim of this paper is to evaluate four of the well-known models for drainage of thin liquid films, containing non-ionic surfactants, by applying them to different types of draining foam films stabilized by either strong or weak non-ionic surfactants. The effect of non-ionic surfactants on the drainage of foam films under different conditions was studied. The following series of surfactants were employed: (1) methylisobutyl carbinol (MIBC), (2) Dowfroth 200, (3) pentaethyleneglycol monodecyl ether (C 10E 5), (4) pentaethyleneglycol monododecyl ether (C 12E 5), (5) hexaethyleneglycol monododecyl ether (C 12E 6), (6) octaethyleneglycol monododecyl ether (C 12E 8) and (7) tetraethyleneglycol monooctyl ether (C 8E 4). The experimental ‘thickness’ vs ‘time’ dependences were processed with four kinetic models: (1) the model developed by Scheludko on the basis of the Stefan–Reynolds lubrication theory (Scheludko model); (2) the model of Radoev, Dimitrov and Ivanov for foam films confined between partially mobile planar gas–liquid surfaces (RDI model); (3) the model of Ruckenstein and Sharma for foam films with surfaces wrinkled by capillary waves (RSh model); (4) the model of Manev–Tsekov–Radoev for foam films with surfaces corrugated by quasi-stationary inhomogeneities (MTR model). A systematic validation based on the statistical level of uncertainty of the model predictions, as compared to the experimental results was preformed. The test on the model kinetic equations confirmed their validations reported in the literature. In addition, cases in which none of the models is valid were identified as well. Ultimately, it was concluded that thin film drainage is a complex phenomenon, which should be studied further by different experimental techniques and modelling approaches.