Generalized Theoretical Framework for the Dilatational Viscoelasticity of Multicomponent Surfactant Mixtures

A theoretical formalism is developed for the dilatational viscoelastic modulus (ε) at fluid interfaces stabilized by mixtures of n soluble, nonionic surfactants. The model generalizes the diffusion–adsorption treatment by explicitly considering the coupling between the diffusive fluxes of each component and the dependence of the surface tension (σ) on the complete composition of the interfacial monolayer (Γi). An analytical expression for the complex modulus ε is derived regarding the equilibrium surface concentrations, diffusion coefficients, and the partial derivatives that define the interfacial equation of state and adsorption isotherms. It is rigorously demonstrated that this general formalism converges to established limiting cases in the literature: the Lucassen–van den Tempel model for a single surfactant and the models developed for binary mixtures by Jiang et al. and Joos. The framework is applied to analyze experimental data of the literature for a ternary mixture of ethoxylated alcohols (C10EO5/C12EO5/C14EO8) by Fainerman et al. The analysis reveals that the predictive fidelity of the formalism is critically dependent on the suitability of the selected thermodynamic adsorption model, underscoring that an accurate description of the interfacial equation of state and adsorption isotherms is an indispensable prerequisite for the quantitative implementation of the dynamic theory.