Diffusion-controlled adsorption kinetics at the air/solution interface

 To describe diffusion-controlled adsorption, the diffusion equation is solved under different initial and boundary conditions by means of a Laplace transformation. By solving this equation, it has been found that the solution, which Ward and Tordai used, is only applicable for x>0; therefore, it is incorrect if the derivation is made at x = 0. Ward and Tordai did not notice this and the first derivation was made at x = 0 in order to get the dynamic surface adsorption, Γ(t). In this paper, an accurate solution, which is applicable for x≥ 0, is given and the expression for Γ(t) is obtained. Furthermore the relationship between the dynamic surface tension and Γ(t) is derived. As an example, the dynamic surface tensions of an aqueous octyl-β-d-glucopyranosid solution were measured by means of the maximum bubble pressure method. By using the derived theory it has been proved that the controlling mechanism of the adsorption process of this surfactant at the long-time-adsorption limits changes as a function of the bulk concentration; only at dilute concentration is it controlled by diffusion.