Phase field modelling of surfactants in multi-phase flow
This work provides a theoretical and numerical framework for modeling surfactants in multi-phase flows with three or more fluids, addressing a gap in existing models for triple junctions.
The authors derived a thermodynamically consistent diffuse interface model for surfactants in multi-phase flow with three or more fluids, coupling Cahn-Hilliard, Navier-Stokes, and advection-diffusion equations. Numerical simulations support the theoretical findings, particularly regarding surfactant behavior at triple junctions.
A diffuse interface model for surfactants in multi-phase flow with three or more fluids is derived. A system of Cahn-Hilliard equations is coupled with a Navier-Stokes system and an advection-diffusion equation for the surfactant ensuring thermodynamic consistency. By an asymptotic analysis the model can be related to a moving boundary problem in the sharp interface limit, which is derived from first principles. Results from numerical simulations support the theoretical findings. The main novelties are centred around the conditions in the triple junctions where three fluids meet. Specifically the case of local chemical equilibrium with respect to the surfactant is considered, which allows for interfacial surfactant flow through the triple junctions.