Robust Method to Determine Critical Micelle Concentration via Spreading Oil Drops on Surfactant Solutions

The spreading of a liquid on another is often encountered in oil spills and coatings and is also of industrial relevance in pharmaceuticals and petrochemicals. In this study, the spreading of oil drops on aqueous solutions containing cationic, anionic, and nonionic surfactants over a wide range of surfactant concentrations is investigated. The spreading behavior quantified by measuring the time evolution of the projected area of the oil lens reveals the occurrence of a maximum, which is strongly dependent on the concentration of the surfactant in the aqueous solution. Our experiments show that this dependence is different at concentrations above and below the critical micelle concentration (CMC) of the surfactant and can be captured by two straight lines of different slopes. Interestingly, these two straight lines intersect at a concentration that coincides with the CMC of the surfactants in solution. We find that this behavior is universal as shown by performing experiments with different types of surfactants, their purity, and other system variables. Thus, we propose a method to unambiguously determine the CMC of surfactant solutions compared to the conventional techniques. The proposed method is simple, versatile, and applicable for the determination of CMC of both ionic and nonionic surfactants.