Dynamic Surface Tension of Solutions of Surfactant Mixtures

Abstract

Abstract A quantitative theory of the dynamic surface tension for 2 multicomponent mixture of surfactants obeying the Langmuir adsorption isotherms with constant diffusion coefficients in the bulk and in the adsorbed layer is developed for diffusion-controlled and diffusion-convective-controlled adsorption models. The effect of the mutual diffusion in the adsorbed layer and the effect of the convective transfer are estimated in an analytical form for the short-time and long-time approximations. It is concluded that the dynamic surface tension can be described by the diffusion-convective-controlled model. It is shown that the equation F (γ( t )) = log[(γ o - γ( t ))/(γ( t ) - γ e )] = n log ( t / t rel ) is valid over a wide range of time for the multicomponent mixture of surfactants. Because the diffusion-controlled and diffusion-convective-controlled adsorption models are shown to be asymptotical correlation n equals one-half. Simple formulae are derived to calculate the parameters n and t rel and the dynamic surface tension over a wide range of time for adsorption isotherms of multicomponent mixtures obeying the Langmuir adsorption isotherms.