Dynamic interfacial adsorption in aqueous surfactant mixtures: Theoreticalstudy

A theoretical framework is developed to predict the dynamic surface tension as well as the dynamic surface concentration and composition at the air-so lution interface of aqueous solutions containing any number of nonionic sur factant components. We utilize an extension of the Ward and Tordai model fo r mixed surfactant systems to describe the diffusion of the surfactant mole cules in the bulk aqueous phase. We assume that surfactant adsorption at th e interface is diffusion controlled, that is, that the surfactant molecules adsorbed at the interface establish instantaneous equilibrium with those p resent in the aqueous phase adjacent to the interface. To determine this eq uilibrium condition, we utilize a recently developed molecular-thermodynami c theory for the equilibrium adsorption of mixed surfactant systems. This t heory has the significant advantage of requiring no surfactant mixture depe ndent parameters. Since the Fickian diffusion-based theory underlying the e xtended Ward and Tordai model does not contain any surfactant mixture depen dent parameters either, one can fully predict the dynamic interfacial prope rties of the mixed surfactant system without conducting any experiments on this system. Specifically, the only required inputs to the theoretical fram ework presented here are the molecular structures and the diffusion coeffic ients of each surfactant component comprising the mixture and a single equi librium surface tension measurement for solutions containing each of the in dividual surfactant components. In addition, we develop a simplified time s cale approach designed to allow "quick"insight into the relationship betwee n the molecular structure of the surfactants and their dynamic interfacial properties for both single surfactants and surfactant mixtures. We then uti lize the theory developed here, including the simplified time scale approac h, to analyze four illustrative examples involving hypothetical surfactant mixtures where the surfactant molecular parameters were selected to demonst rate a range of interesting dynamic interfacial behavior. In particular, we show how the theory can be used to aid in the design of practical products containing surfactant mixtures that exhibit interesting dynamic interfacia l properties.