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

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

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
Volume160
Issue number2
DOIs
Publication statusPublished - 2005 Jan 14
Externally publishedYes

Fingerprint

Diffuse Interface
Cahn-Hilliard Equation
Two-phase Flow
Two phase flow
Navier Stokes equations
Breakup
Multigrid Method
Coalescence
Stability Theory
Incompressible Navier-Stokes Equations
Linear Stability
Projection Method
Surface Tension
Level Set
Rayleigh
Diffusion equation
Forcing
Parabolic Equation
Fourth Order
Surface tension

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

A diffuse-interface model for axisymmetric immiscible two-phase flow. / Kim, Junseok.

In: Applied Mathematics and Computation, Vol. 160, No. 2, 14.01.2005, p. 589-606.

Research output: Contribution to journalArticle

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