Communications in Mathematical Sciences

Volume 12 (2014)

Number 8

Diffuse interface modelling of soluble surfactants in two-phase flow

Pages: 1475 – 1522



Harald Garcke (Fakultät für Mathematik, Universität Regensburg, Germany)

Kei Fong Lam (Mathematics Institute, University of Warwick, Coventry, United Kingdom)

Björn Stinner (Mathematics Institute and Centre for Scientific Computing, University of Warwick, Coventry, United Kingdom)


Phase field models for two-phase flow with a surfactant soluble in possibly both fluids are derived from balance equations and an energy inequality so that thermodynamic consistency is guaranteed. Via a formal asymptotic analysis, they are related to sharp interface models. Both cases of dynamic as well as instantaneous adsorption are covered. Flexibility with respect to the choice of bulk and surface free energies allows us to realise various isotherms and relations of state between surface tension and surfactant. Some numerical simulations display the effectiveness of the presented approach.


two-phase flow, surfactant, phase field model, adsorption isotherm

2010 Mathematics Subject Classification

35C20, 35Q35, 35R01, 35R35, 76D45, 76T99

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