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.
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Oliver R.A. Dunbar, Kei Fong Lam, Björn Stinner, Phase field modelling of surfactants in multi-phase flow. Interfaces Free Bound. 21 (2019), no. 4, pp. 495–547DOI 10.4171/IFB/429