Commun. Comput. Phys., 14 (2013), pp. 879-915.

On Diffuse Interface Modeling and Simulation of Surfactants in Two-Phase Fluid Flow

Stefan Engblom 1*, Minh Do-Quang 2, Gustav Amberg 2, Anna-Karin Tornberg 3

1 Division of Scientific Computing, Department of Information Technology, Uppsala University, SE-751 05 Uppsala, Sweden.
2 Linne Flow Centre, Department of Mechanics, School of Engineering Science, Royal Institute of Technology, S-100 44 Stockholm, Sweden.
3 Linne Flow Centre, Department of Numerical Analysis, School of Computer Science and Communication, Royal Institute of Technology, S-100 44 Stockholm, Sweden.

Received 12 July 2012; Accepted (in revised version) 28 December 2012
Available online 19 March 2013


An existing phase-field model of two immiscible fluids with a single soluble surfactant present is discussed in detail. We analyze the well-posedness of the model and provide strong evidence that it is mathematically ill-posed for a large set of physically relevant parameters. As a consequence, critical modifications to the model are suggested that substantially increase the domain of validity. Carefully designed numerical simulations offer informative demonstrations as to the sharpness of our theoretical results and the qualities of the physical model. A fully coupled hydrodynamic test-case demonstrates the potential to capture also non-trivial effects on the overall flow.

AMS subject classifications: 76T30, 65M60, 65Z05

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Key words: Phase-field model, Cahn-Hilliard equation, surface active agent, Ginzburg-Landau free energy, well-posedness.

*Corresponding author.
Email: (S. Engblom), (M. Do-Quang), (G. Amberg), (A.-K. Tornberg)

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