A conservative interface-interaction model with insoluble surfactant

In this paper we extend the conservative interface-interaction method of Hu et al. (2006) [34], adapted for weakly-compressible flows by Luo et al. (2015) [37], to include the effects of viscous, capillary, and Marangoni stresses consistently as momentum-exchange terms at the sharp interface. The interface-interaction method is coupled with insoluble surfactant transport which employs the underlying sharp-interface representation. Unlike previous methods, we thus achieve discrete global conservation in terms of interface interactions and a consistently sharp interface representation. The interface is reconstructed locally, and a sub-cell correction of the interface curvature improves the evaluation of capillary stresses and surfactant diffusion in particular for marginal mesh resolutions. For a range of numerical test cases we demonstrate accuracy and robustness of the method. In particular, we show that the method is at least as accurate as previous diffuse-interface models while exhibiting throughout the considered test cases improved computational efficiency. We believe that the method is attractive for high-resolution level-set interface-tracking simulations as it straightforwardly incorporates the effects of variable surface tension into the underlying conservative interface-interaction approach.