A simplified method for predicting the dynamic surface tension of concentrated surfactant solutions

A simplified method for predicting the dynamic surface tension of concentrated surfactant solutions is proposed. It is implemented using the framework of the Henry's Law analytical solution to the Ward and Tordai equation for diffusion-controlled adsorption, with the necessary parameters being deduced from the measured equilibrium surface tension equation and a value for the surfactant monomer diffusivity. The method is tested by calculating the dynamic surface tension relaxations of aqueous C10E6 and C10E8 solutions over concentration ranges from well below to well above their critical micelle concentrations (cmc). Results are compared with measured relaxations over 0.001-50 s, and semiquantitative agreement is found, with the best results obtained for concentrations near the cmc. The predictive method may prove useful in such applications as the screening of candidate surfactants for inks used in inkjet printing.