A generalized continuous surface tension force formulation for phase-field models for multi-component immiscible fluid flows

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We present a new phase-field method for modeling surface tension effects on multi-component immiscible fluid flows. Interfaces between fluids having different properties are represented as transition regions of finite thickness across which the phase-field varies continuously. At each point in the transition region, we define a force density which is proportional to the curvature of the interface times a smoothed Dirac delta function. We consider a vector valued phase-field, the velocity, and pressure fields which are governed by multi-component advective Cahn-Hilliard and modified Navier-Stokes equations. The new formulation makes it possible to model any combination of interfaces without any additional decision criteria. It is general, therefore it can be applied to any number of fluid components. We give computational results for the four component fluid flows to illustrate the properties of the method. The capabilities of the method are computationally demonstrated with phase separations via a spinodal decomposition in a four-component mixture, pressure field distribution for three stationary drops, and the dynamics of two droplets inside another drop embedded in the ambient liquid.

Original languageEnglish
Pages (from-to)3105-3112
Number of pages8
JournalComputer Methods in Applied Mechanics and Engineering
Issue number37-40
Publication statusPublished - 2009 Aug 1

Bibliographical note

Funding Information:
This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MEST) (No. R01-2008-000-20855-0). The author thanks Professors Kyungkeun Kang and Jihoon Lee for valuable discussions on this topic. The author also thanks an anonymous referee for very valuable comments and suggestions on this paper.

Copyright 2009 Elsevier B.V., All rights reserved.


  • Continuum surface tension
  • Interfacial tension
  • Multi-component Cahn-Hilliard equation
  • Navier-Stokes equation
  • Nonlinear multigrid method
  • Phase-field model

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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