The graphs demonstrate how the concentration gradient towards the surface first increases and then decreases with time and leads finally again to a homogeneous surfactant distribution in the solution bulk. The theoretical model which describes the "diffusion controlled" adsorption process of surfactants at a solution surface was derived by Ward & Tordai in 1946 and results in a Volterra-type integral equation:
where D is the diffusion coefficient and co is the surfactant bulk concentration. The equation describes the change of Γ(t) with time t, however, its application to dynamic surface tension data g(t) is not simple. In the book mentioned above by Fainerman, Möbius and Miller a paragraphs is dedicated to the general physical idea of all adsorption kinetics models, and to particularities of various models.