Numerical method for coupled interfacial surfactant transport on dynamic surface meshes of general topology

Abstract

We consider surfactant transport on moving and deforming fluid interfaces with main emphasize on the case of mixtures of several surfactants. Since the interface can be significantly covered by surfactants, the model incorporates cross-effects in terms of both cross-diffusion as well as non-idealities of the surfactant mixtures. This is accounted for by means of the interfacial Maxwell–Stefan equations with appropriate thermodynamic driving forces.Our numerical method for detailed computation of surfactant transport is based on the collocated Finite Area Method on meshes of general topology, including automatic mesh motion and remeshing methods to allow for strongly deforming interfaces. This allows for mass conservative solution of the interfacial transport equations, which are solved in a block-coupled manner to accurately describe the cross-effects. The diffusive fluxes, which are to be inserted into the system of surfactant balances, come from an iterative inversion of the Maxwell–Stefan equations. The cross-effects lead to heterogeneous diffusivities, which in turn can cause numerical instabilities at increasing heterogeneity. Therefore, we propose an enhanced discretization procedure which is easy to implement for the finite area diffusion operator, yielding numerical conservation, robustness and boundedness. While the method can be extended to soluble surfactants in a straightforward manner, we focus here on the insoluble case.