Numerical Modeling of Insoluble Surfactants in Two-Phase Flows and Its Application to Breaking Waves

Surfactants at fluid interfaces significantly impact fluid dynamics by altering the distribution of surface tension. This study models these effects by incorporating Marangoni forces into an incompressible two-phase Navier-Stokes solver. We employ a two-way coupled direct numerical simulation of the two phases, integrating an insoluble surfactant transport equation at the interface. Surface tension is represented using a linear Langmuir isotherm, which linearly relates to local interfacial surfactant concentration. Our framework confines surfactants to the liquid-gas interface, preventing numerical diffusion into the bulk liquid phases. The solver is validated for mass conservation and surface transport against both analytical and numerical solutions. We investigated the effect of surfactants on rising bubbles in quiescent air. The rise velocity of surfactant-laden bubbles decreased compared to clean bubbles, and the terminal bubble shapes were altered due to the formation of stagnation caps. Our observations are consistent with existing research. Furthermore, we examined surfactant effects on breaking waves, focusing on jet profiles and entrainment characteristics in comparison to clean water scenarios. This study can be further extended to analyze surfactant effects on various flow configurations, such as droplet deformation and breakup, as well as the behavior of falling liquid films.