Dynamic Surface Tension of Aqueous Surfactant Solutions: 1. Diffusion-Convective Controlled Adsorption

Abstract

A quantitative theory of the dynamic surface tension with a constant diffusion coefficient is developed for diffusion-controlled and diffusion-convective-controlled adsorption. The effect of the convective transfer is estimated in an analytical form for the short-time and large-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 of F(γ,( t)) = log[(γ 0 - γ( t))/(γ( t) - γ e)] = n log( t/ t) is valid over a wide range of time. The phenomenological approach of Rosen and co-workers is shown to be asymptotical correlation n equals one-half. The simple formula is derived to calculate the parameters n, t, D (diffusion coefficient), and the dynamic surface tension over a wide range of time for adsorption isotherms of different types (linear, Langmuir, and Freundlich).