Double-layer structure and interfacial tension at an ionic surfactant-laden interface

The interfacial concentration of surfactant is asymptotically small due to electrostatic repulsion, scaling as ε^2/3Γ_∞, where Γ_∞ is the maximum packing surface concentration. Moreover, the atypical double-layer structure consists of an inner layer of width O(ε^4/3h) within a Debye layer of width O(εh), outside of which is an electroneutral bulk solution of surfactant and counterions at uniform concentration c_∞. The surfactant and counterion concentrations in the inner layer scale as O(ε^2/3c_∞) and O(ε^-2/3c_∞) respectively, whereas both are O(c_∞) in the Debye layer. The interfacial tension is predicted to decrease from its clean value (i.e. in the absence of surfactant) as O(ε^2/3). This asymptotic prediction is in qualitative agreement with experimental data. Our elucidation of this unique double-layer structure could provide new approaches to analyze dynamic interfacial tension, dilatational surface rheology and emulsion stability.