### Abstract

We present a new phase-field method for modeling surface tension effects on multi-component immiscible fluid flows. Interfaces between fluids having different properties are represented as transition regions of finite thickness across which the phase-field varies continuously. At each point in the transition region, we define a force density which is proportional to the curvature of the interface times a smoothed Dirac delta function. We consider a vector valued phase-field, the velocity, and pressure fields which are governed by multi-component advective Cahn-Hilliard and modified Navier-Stokes equations. The new formulation makes it possible to model any combination of interfaces without any additional decision criteria. It is general, therefore it can be applied to any number of fluid components. We give computational results for the four component fluid flows to illustrate the properties of the method. The capabilities of the method are computationally demonstrated with phase separations via a spinodal decomposition in a four-component mixture, pressure field distribution for three stationary drops, and the dynamics of two droplets inside another drop embedded in the ambient liquid.

Original language | English |
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Pages (from-to) | 3105-3112 |

Number of pages | 8 |

Journal | Computer Methods in Applied Mechanics and Engineering |

Volume | 198 |

Issue number | 37-40 |

DOIs | |

Publication status | Published - 2009 Aug 1 |

### Keywords

- Continuum surface tension
- Interfacial tension
- Multi-component Cahn-Hilliard equation
- Navier-Stokes equation
- Nonlinear multigrid method
- Phase-field model

### ASJC Scopus subject areas

- Computer Science Applications
- Computational Mechanics
- Mechanical Engineering
- Mechanics of Materials
- Physics and Astronomy(all)