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Interfaces and Free Boundaries

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Volume 21, Issue 4, 2019, pp. 495–547
DOI: 10.4171/IFB/429

Published online: 2019-12-18

Phase field modelling of surfactants in multi-phase flow

Oliver R.A. Dunbar[1], Kei Fong Lam[2] and Björn Stinner[3]

(1) California Institute of Technology, Pasadena, USA
(2) The Chinese University of Hong Kong, Hong Kong
(3) University of Warwick, Coventry, UK

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.

Keywords: Surfactant, diffuse interface, adsorption isotherm, triple junction, thermodynamic consistency

Dunbar Oliver, Lam Kei Fong, Stinner Björn: Phase field modelling of surfactants in multi-phase flow. Interfaces Free Bound. 21 (2019), 495-547. doi: 10.4171/IFB/429