On the Theory of Dynamic Surface Tension of Ionic Surfactant Solutions, I: Diffusion-Convective Adsorption

Abstract

A quantitative theory for dynamic surface tension has been developed for the diffusion-controlled and diffusion-convective-controlled models without any “quasi-equilibrium” hypotheses. A rigorous model considers both the diffusion and the migration of surfactant and electrolytes in the electrical field that develops as the charged surfactant adsorbs at a planar interface. The surface concentration of surfactant is calculated by using the coupled Poisson and Nernst–Planck equations. An unknown electrical potential in the Nernst–Planck equation is found from the integral form of the charge-balance equation. It is shown that the proposed system of equations describes over a wide range of time the non-steady-state process in the bulk for both ionic surfactants and electrolytes. The relaxation equation ofF(γ(t)) = log[(γ0− γ(t))/(γ(t) − γe)] =nlog(t/trel) is suitable to describe the dynamic surface tension process over a wide range of times for diffusion-controlled and diffusion-convective-controlled adsorption. The simple formula is derived to calculate the parameters ofn,trel(the relaxation time), andDeff(the effective diffusion coefficients) from the experimental data represented in the form of the relaxation functionF(t) versus log(t). The analytical expressions are obtained to describe the dynamic surface tension for short and long times by using the diffusion-controlled and diffusion-convective-controlled adsorption obeying linear, rectangular, and arbitrary adsorption isotherms.