A diffuse-interface model for axisymmetric immiscible two-phase flow

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44 Citations (Scopus)


A diffuse-interface model is considered for solving axisymmetric immiscible two-phase flow with surface tension. The Navier-Stokes (NS) equations are modified by the addition of a continuum forcing. The interface between the two fluids is considered as the half level set of a mass concentration c, which is governed by the Cahn-Hilliard (CH) equation - a fourth order, degenerate, nonlinear parabolic diffusion equation. In this work, we develop a nonlinear multigrid method to solve the CH equation with degenerate mobility and couple this to a projection method for the incompressible NS equations. The diffuse-interface method can deal with topological transitions such as breakup and coalescence smoothly without ad hoc 'cut and connect' or other artificial procedures. We present results for Rayleigh's capillary instability up to forming satellite drops. The results agree well with the linear stability theory.

Original languageEnglish
Pages (from-to)589-606
Number of pages18
JournalApplied Mathematics and Computation
Issue number2
Publication statusPublished - 2005 Jan 14
Externally publishedYes

Bibliographical note

Funding Information:
The author thanks his advisor, John Lowengrub, for intellectual and financial support. This work was supported by the Department of Energy (Office of Basic Sciences), The National Science Foundation and the Minnesota Supercomputer Institute.


  • Cahn-Hilliard equation
  • Coalescence
  • Nonlinear multigrid method
  • Pinch-off
  • Rayleigh instability
  • Satellite drops

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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