Diffusion-controlled adsorption at the liquid-air interface: The long-time limit

The applicability of the Hansen and Joos long-time Limits for the dynamic surface tension of solutions is investigated by regressing diffusion coefficients from numerical solutions to the Ward and Tordai equation. The Hansen limit is found to correctly describe the dynamic surface tension evolutions at long times. However, both the surfactant concentration and the adsorption time affect the accuracy of the long-time limit. The study also indicates that, because the reduction in surface tension (at long times) may be smaller than can be measured by current tensiometry methods, the application of the Hansen limit to long-time data may not always be feasible. (C) 2001 Academic Press.