A reaction kinetics approach to model the spreading of oil drop on aqueous surfactant solutions

The spreading of oil drops on aqueous solutions containing surfactants of various concentrations varying across critical micellar concentration (CMC) is investigated. The fate of the dispensed oil drop was visualized using time-resolved video-microscopy. The projected area of the oil drop is found to increase initially due to the spreading processes, reaches a maximum, and finally decreases due to the dissolution of the oil drop into the bulk of the surfactant solution. The two competing effects of spreading and dissolution lead to a non-monotonic temporal evolution of the projected area, modeled using a reactions kinetic approach. In particular, we show that a series reaction of the form A→B→C is analogous to the spreading-dissolution process observed in our experiments. This analogy allows us to estimate the rate constants associated with the spreading and dissolution of the oil drop, which can be further used to quantify the CMC of the surfactants in solutions.