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

Published online by Cambridge University Press:  03 June 2015

Stefan Engblom ,
Minh Do-Quang ,
Gustav Amberg  and
Anna-Karin Tornberg
Stefan Engblom*
Affiliation:
Division of Scientific Computing, Department of Information Technology, Uppsala University, SE-751 05 Uppsala, Sweden
Minh Do-Quang*
Affiliation:
Linné Flow Centre, Department of Mechanics, School of Engineering Science, Royal Institute of Technology, S-100 44 Stockholm, Sweden
Gustav Amberg*
Affiliation:
Linné Flow Centre, Department of Mechanics, School of Engineering Science, Royal Institute of Technology, S-100 44 Stockholm, Sweden
Anna-Karin Tornberg*
Affiliation:
Linné Flow Centre, Department of Mechanics, School of Engineering Science, Royal Institute of Technology, S-100 44 Stockholm, Sweden
*
Corresponding author.Email:stefane@it.uu.se
Email:minh@mech.kth.se
Email:gustava@mech.kth.se
Email:annak@nada.kth.se
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Abstract

An existing phase-fieldmodel 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.

Keywords

76T3065M6065Z05Phase-field modelCahn-Hilliard equationsurface active agentGinzburg-Landau free energywell-posedness
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 4 , October 2013 , pp. 879 - 915
Copyright
Copyright © Global Science Press Limited 2013

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