Commun. Comput. Phys., 12 (2012), pp. 613-661.

Phase-Field Models for Multi-Component Fluid Flows

Junseok Kim 1*

1 Department of Mathematics, Korea University, Seoul 136-701, Republic of Korea.

Received 30 November 2010; Accepted (in revised version) 4 August 2011
Available online 1 March 2012


In this paper, we review the recent development of phase-field models and their numerical methods for multi-component fluid flows with interfacial phenomena. The models consist of a Navier-Stokes system coupled with a multi-component Cahn-Hilliard system through a phase-field dependent surface tension force, variable density and viscosity, and the advection term. The classical infinitely thin boundary of separation between two immiscible fluids is replaced by a transition region of a small but finite width, across which the composition of the mixture changes continuously. A constant level set of the phase-field is used to capture the interface between two immiscible fluids. Phase-field methods are capable of computing topological changes such as splitting and merging, and thus have been applied successfully to multi-component fluid flows involving large interface deformations. Practical applications are provided to illustrate the usefulness of using a phase-field method. Computational results of various experiments show the accuracy and effectiveness of phase-field models.

AMS subject classifications: 76D05, 76D45, 76T30, 82C26

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Key words: Navier-Stokes, Cahn-Hilliard, multi-component, surface tension, interface dynamics, interface capturing, phase-field model.

*Corresponding author.
Email: (J. S. Kim)

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