Diffusion-controlled adsorption kinetics at the air/solution interface

To describe diffusion-controlled adsorption, the diffusion equation is solv ed under different initial and boundary conditions by means of a Laplace tr ansformation. By solving this equation, it has been found that the solution , which Ward and Tordai used, is only applicable for x > 0: therefore, it i s incorrect if the derivation is made at x = 0. Ward and Tordai did not not ice this and the first derivation was made at x = 0 in order to get the dyn amic surface adsorption, Gamma(t). In this paper, an accurate solution, whi ch is applicable for x greater than or equal to 0, is given and the express ion for Gamma(t) is obtained. Furthermore the relationship between the dyna mic surface tension and Gamma(t) is derived. As an example, the dynamic sur face tensions of an aqueous octyl-beta-D-glucopyranosid solution were measu red by means of the maximum bubble pressure method. By using the derived th eory it has been proved that the controlling mechanism of the adsorption pr ocess of this surfactant at the long-time-adsorption limits changes as a fu nction of the bulk concentration; only at dilute concentration is it contro lled by diffusion.