A continuous surface tension force formulation for diffuse-interface models

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218 Citations (Scopus)


We present a new surface tension force formulation for a diffuse-interface model, which is derived for incompressible, immiscible Navier-Stokes equations separated by free interfaces. The classical infinitely thin boundary of separation between the two immiscible fluids is replaced by a transition region of small but finite width, across which the composition of the one of two fluids changes continuously. Various versions of diffuse-interface methods have been used successfully for the numerical simulations of two phase fluid flows. These methods are robust, efficient, and capable of computing interface singularities such as merging and pinching off. But prior studies used modified surface tension force formulations, therefore it is not straightforward to calculate pressure field because pressure includes the gradient terms resulting from the modified surface tension term. The new formulation allows us to calculate the pressure field directly from the governing equations. Computational results showing the accuracy and effectiveness of the method are given for a drop deformation and Rayleigh capillary instability.

Original languageEnglish
Pages (from-to)784-804
Number of pages21
JournalJournal of Computational Physics
Issue number2
Publication statusPublished - 2005 Apr 10
Externally publishedYes

Bibliographical note

Funding Information:
The author thanks his advisor, John Lowengrub, for intellectual and financial support. This work was supported by the National Science Foundation, Division of Mathematical Sciences and the Department of Energy, Basic Energy Sciences Division. The author acknowledges the support of the Network and Academic Computing Services (NACS) at the University of California, Irvine.


  • Continuum surface tension
  • Diffuse-interface
  • Phase field

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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