Phase-field modelling of multi-phase flows with soluble surfactants

Project description

Phase-field modelling is emerging as a promising tool for the treatment of problems with interfaces. The classical description of interface problems requires the numerical solution of partial differential equations on moving domains in which the domain motions are also unknowns, thereby requiring a computational treatment that includes moving meshes. Phase-field modelling may be understood as a methodology to reformulate interface problems as equations posed on fixed domains.

This project will explore application of phase-field modelling on interfaces coated with surfactants in multi-phase systems. Surfactants are surface active agents that are known to affect the surface tension of interfaces and their presence can significantly alter the dynamics of flows. They are used in a range of processes and applications such as foam fabrication, emulsification or mixing. Of particular interest is the case when the surfactant is soluble in the bulk of the fluid, especially when the bulk concentration exceeds the critical micelle concentration, beyond which the molecules start forming multi-molecule aggregates called micelles. One of the aims of this project is to perform a formal asymptotic analysis in order to connect phase-field models to sharp interface models in the appropriate limit, and thereby discovering new model descriptions and computational approaches to multi-phase flows with soluble surfactants. Special cases might include study of thin films and/or film rupture.