A continuous surface tension force formulation for diffuse-interface models

Junseok Kim

doi:10.1016/j.jcp.2004.10.032

A continuous surface tension force formulation for diffuse-interface models

Junseok Kim^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

271 Citations (Scopus)

Abstract

We present a new surface tension force formulation for a diffuse-interface model, which is derived for incompressible, immiscible Navier-Stokes equations separated by free interfaces. The classical infinitely thin boundary of separation between the two immiscible fluids is replaced by a transition region of small but finite width, across which the composition of the one of two fluids changes continuously. Various versions of diffuse-interface methods have been used successfully for the numerical simulations of two phase fluid flows. These methods are robust, efficient, and capable of computing interface singularities such as merging and pinching off. But prior studies used modified surface tension force formulations, therefore it is not straightforward to calculate pressure field because pressure includes the gradient terms resulting from the modified surface tension term. The new formulation allows us to calculate the pressure field directly from the governing equations. Computational results showing the accuracy and effectiveness of the method are given for a drop deformation and Rayleigh capillary instability.

Original language	English
Pages (from-to)	784-804
Number of pages	21
Journal	Journal of Computational Physics
Volume	204
Issue number	2
DOIs	https://doi.org/10.1016/j.jcp.2004.10.032
Publication status	Published - 2005 Apr 10
Externally published	Yes

Bibliographical note

Funding Information:
The author thanks his advisor, John Lowengrub, for intellectual and financial support. This work was supported by the National Science Foundation, Division of Mathematical Sciences and the Department of Energy, Basic Energy Sciences Division. The author acknowledges the support of the Network and Academic Computing Services (NACS) at the University of California, Irvine.

Keywords

Continuum surface tension
Diffuse-interface
Phase field

ASJC Scopus subject areas

Numerical Analysis
Modelling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2004.10.032

Cite this

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title = "A continuous surface tension force formulation for diffuse-interface models",

abstract = "We present a new surface tension force formulation for a diffuse-interface model, which is derived for incompressible, immiscible Navier-Stokes equations separated by free interfaces. The classical infinitely thin boundary of separation between the two immiscible fluids is replaced by a transition region of small but finite width, across which the composition of the one of two fluids changes continuously. Various versions of diffuse-interface methods have been used successfully for the numerical simulations of two phase fluid flows. These methods are robust, efficient, and capable of computing interface singularities such as merging and pinching off. But prior studies used modified surface tension force formulations, therefore it is not straightforward to calculate pressure field because pressure includes the gradient terms resulting from the modified surface tension term. The new formulation allows us to calculate the pressure field directly from the governing equations. Computational results showing the accuracy and effectiveness of the method are given for a drop deformation and Rayleigh capillary instability.",

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note = "Funding Information: The author thanks his advisor, John Lowengrub, for intellectual and financial support. This work was supported by the National Science Foundation, Division of Mathematical Sciences and the Department of Energy, Basic Energy Sciences Division. The author acknowledges the support of the Network and Academic Computing Services (NACS) at the University of California, Irvine.",

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AU - Kim, Junseok

N1 - Funding Information: The author thanks his advisor, John Lowengrub, for intellectual and financial support. This work was supported by the National Science Foundation, Division of Mathematical Sciences and the Department of Energy, Basic Energy Sciences Division. The author acknowledges the support of the Network and Academic Computing Services (NACS) at the University of California, Irvine.

PY - 2005/4/10

Y1 - 2005/4/10

N2 - We present a new surface tension force formulation for a diffuse-interface model, which is derived for incompressible, immiscible Navier-Stokes equations separated by free interfaces. The classical infinitely thin boundary of separation between the two immiscible fluids is replaced by a transition region of small but finite width, across which the composition of the one of two fluids changes continuously. Various versions of diffuse-interface methods have been used successfully for the numerical simulations of two phase fluid flows. These methods are robust, efficient, and capable of computing interface singularities such as merging and pinching off. But prior studies used modified surface tension force formulations, therefore it is not straightforward to calculate pressure field because pressure includes the gradient terms resulting from the modified surface tension term. The new formulation allows us to calculate the pressure field directly from the governing equations. Computational results showing the accuracy and effectiveness of the method are given for a drop deformation and Rayleigh capillary instability.

AB - We present a new surface tension force formulation for a diffuse-interface model, which is derived for incompressible, immiscible Navier-Stokes equations separated by free interfaces. The classical infinitely thin boundary of separation between the two immiscible fluids is replaced by a transition region of small but finite width, across which the composition of the one of two fluids changes continuously. Various versions of diffuse-interface methods have been used successfully for the numerical simulations of two phase fluid flows. These methods are robust, efficient, and capable of computing interface singularities such as merging and pinching off. But prior studies used modified surface tension force formulations, therefore it is not straightforward to calculate pressure field because pressure includes the gradient terms resulting from the modified surface tension term. The new formulation allows us to calculate the pressure field directly from the governing equations. Computational results showing the accuracy and effectiveness of the method are given for a drop deformation and Rayleigh capillary instability.

KW - Continuum surface tension

KW - Diffuse-interface

KW - Phase field

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DO - 10.1016/j.jcp.2004.10.032

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SN - 0021-9991

VL - 204

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EP - 804

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 2

ER -

A continuous surface tension force formulation for diffuse-interface models

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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