Modelling of interfacial flows with surfactants: micelle formation and interfacial viscosity effects

Surfactant-laden multiphase flow is crucial in all kinds of applications because of the presence of surfactants which can be either as desirable additives or undesirable contaminants. Many types of physical behaviours can occur such as the reduction of the local value of surface tension, the generation of Marangoni stress, the endowment of the interface with shear and dilatational viscosities, micelle formation, the interaction with solid substrates and modification of contact line motion. Most of the numerical frameworks that are able to deal with surfactant-laden systems are based on many assumptions and consider, or prioritise, certain limiting situations, e.g., insoluble surfactant, concentrations below the critical micelle concentration, and the absence of interfacial viscous effects. There is therefore a need for a generalised model that can encompass all of the aforementioned effects. Here, we present the progress we have made in the development of such a model and provide several flow examples motivated by industrial and environmental applications.