Phase field modeling and simulation of three-phase flows

Junseok Kim, John Lowengrub

Research output: Contribution to journalArticlepeer-review

152 Citations (Scopus)


We derive a thermodynamically consistent phase-field model for flows containing three (or more) liquid components. The model is based on a Navier-Stokes (NS) and Cahn-Hilliard system (CH) which accounts for surface tension among the different components and three-phase contact lines. We develop a stable conservative, second order accurate fully implicit discretization of the NS and three-phase (ternary) CH system. We use a nonlinear multigrid method to efficiently solve the discrete ternary CH system at the implicit time-level and then couple it to a multigrid/projection method that is used to solve the NS equation. We demonstrate convergence of our scheme numerically and perform numerical simulations to show the accuracy, flexibility, and robustness of this approach. In particular, we simulate a three-interface contact angle resulting from a spreading liquid lens on an interface, a buoyancy-driven compound drop, and the Rayleigh-Taylor instability of a flow with three partially miscible components.

Original languageEnglish
Pages (from-to)435-466
Number of pages32
JournalInterfaces and Free Boundaries
Issue number4
Publication statusPublished - 2005
Externally publishedYes


  • Arbitrary miscibility
  • Interfacial tension
  • Nonlinear multigrid
  • Ternary Cahn-Hilliard system
  • Ternary fluid flow

ASJC Scopus subject areas

  • Surfaces and Interfaces


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