Dynamic interfacial adsorption in aqueous surfactant mixtures: Theoretical study

A theoretical framework is developed to predict the dynamic surface tension as well as the dynamic surface concentration and composition at the air-solution interface of aqueous solutions containing any number of nonionic surfactant components. We utilize an extension of the Ward and Tordai model for mixed surfactant systems to describe the diffusion of the surfactant molecules in the bulk aqueous phase. We assume that surfactant adsorption at the interface is diffusion controlled, that is, that the surfactant molecules adsorbed at the interface establish instantaneous equilibrium with those present in the aqueous phase adjacent to the interface. To determine this equilibrium condition, we utilize a recently developed molecular-thermodynamic theory for the equilibrium adsorption of mixed surfactant systems. This theory has the significant advantage of requiring no surfactant mixture dependent parameters. Since the Fickian diffusion-based theory underlying the extended Ward and Tordai model does not contain any surfactant mixture dependent parameters either, one can fully predict the dynamic interfacial properties of the mixed surfactant system without conducting any experiments on this system. Specifically, the only required inputs to the theoretical framework presented here are the molecular structures and the diffusion coefficients of each surfactant component comprising the mixture and a single equilibrium surface tension measurement for solutions containing each of the individual surfactant components. In addition, we develop a simplified time scale approach designed to allow "quick"insight into the relationship between the molecular structure of the surfactants and their dynamic interfacial properties for both single surfactants and surfactant mixtures. We then utilize the theory developed here, including the simplified time scale approach, to analyze four illustrative examples involving hypothetical surfactant mixtures where the surfactant molecular parameters were selected to demonstrate 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 interfacial properties.