An axisymmetric model for the analysis of dynamic surface tension

Abstract

A quantitative treatment of dynamic surface tension data has been carried out with different mathematical approaches taking into account a diffusion-controlled mechanism. The classical model has been modified in order to achieve a better description of the experimental conditions by considering a finite diffusion domain. The domain has been fixed keeping the restriction that the surfactant concentration in this region should remain constant after the adsorption at the air–water interface, in such a way that the number of surfactant unimers is 30 times the number adsorbed at the interface. The finite diffusion restriction has been used both in 1D and axisymmetric models, the latter one being the most accurate and needing a smaller diffusion domain since it considers surfactant adsorption at a sphere resembling the physical experiments. A distorted sphere geometry taking into account the Laplace–Young equation has also been studied.