Diffusion-controlled adsorption kinetics at air/solution surface studied by maximum bubble pressure method

In studying the diffusion-controlled adsorption kinetics of aqueous surfactant solutions at the air/solution surface by means of the maximal bubble pressure method, Fick's diffusion equation for a sphere should be used. In this paper the equation was solved by means of Laplace transformation under different initial and boundary conditions. The dynamic surface adsorption Gamma(t) for a surfactant solution, which was used to describe the diffusion-controlled adsorption kinetics at the solution surface, was derived. Different from the planar surface adsorption, the dynamic surface adsorption Gamma(t) for the short time consists of two terms: one is the same as Ward-Tordai equation and the other reflects the geometric effect caused by the spherical bubble surface. This effect should not be neglected for the very small radius of the capillary. The equilibrium surface tension gamma(eq) and the dynamic surface tension gamma(t) of aqueous C10E6[CH3(CH2)(9)(OCH2CH2)(6)OH] solution at temperature 25degreesC were measured by means of Wilhelmy plate method and maximal bubble pressure method respectively. As t --> 0, the theoretical analysis is in good agreement with experimental results and the dependence of gamma(t) on (roott + r(0)/rootpiD)(2) is linear.