A simple numerical solution of diffusional equations for dilatational rheology of complex surfactant mixtures in any geometry

Abstract

Dilatational rheology of a multi-component surfactant mixture at fluid-fluid interfaces is of importance for many real-life applications (biology, food products, crude oil production, etc.). However, although experimental data are easily measured, they cannot yet be analyzed in the framework of diffusional exchange between the surfactant solution and the interface when the number of the components exceeds two. Furthermore, although the single component analytical models exist for different interface geometries (flat, spherical, cylindrical), the binary mixture model is only available for a flat interface. To alleviate these limitations, a simple numerical scheme has been developed enabling the calculation of dilatational rheology with diffusional exchange for an n-component mixture in any geometry. The derived approach is limited to the case where relaxation is controlled by diffusion only and it relies on the matrix inversion of a set of first principle equations (mass conservation, diffusion and adsorption isotherm). Numerical solutions were validated against the exact analytical expression of both single component model and binary mixture dilatational rheology.