Modeling and measurement of the dynamic surface tension of surfactant solutions

Surfactant solutions are usually used under conditions accompanied by transient dynamic surfaces, and therefore the dynamic surface tension (DST) is important in many industrial processes. Theories regarding DST have been developed exclusively on the adsorption theory that molecules are transported from bulk solution to the interface. However, the adsorption theory is not closed and requires another relationship between the interfacial concentration of the adsorbing molecules and the bulk concentration of molecules near and at the surface, which at present is based on assumptions. In addition, DST obtained by the adsorption theory contains several parameters that must be determined beforehand, and it is not simple to use for practical purposes. Here, we propose a new model based on the concept that surfactant molecules rotate during the process reaching the equilibrium surface state, which is different from the conventional adsorption theory, and we obtained a simple expression of DST as a function of the surface age. In addition, an experiment was carried out to determine DST by measuring the period and weight of droplets falling from a capillary. The expression by the proposed model was compared with the results of this experiment and with those reported previously by several other authors, and good agreement was obtained. Furthermore, the characteristic time in the model was shown to be correlated with the concentrations of solutions regardless of the type of solutions examined.