A Phase-Field/Fluid Motion Model of Solidification: Investigation of Flow Effects During Directional Solidification and Dendritic Growth

Published

July 1, 1998

Author(s)

D M. Anderson, Geoffrey B. McFadden, William J. Boettinger, A A. Wheeler

Abstract

The phase-field model of solidification is extended to include the effects of fluid flow in the melt. The phase-field model is based on coupling the equations for heat flow in the liquid and solid phases with an auxiliary equation that describes the evolution of the phase-field variable, which is a non-conserved order parameter indicating the local phase, solid or liquid, at each point of the material. The solid-liquid interface is then represented by a diffuse transition layer in which the phase-field variable changes rapidly between its values in the bulk phases. The model is extended to include fluid flow by a further coupling to the Navier-Stokes equations. Preliminary studies have been performed for a model in which the solid phase is treated as a liquid of high viscosity compared to the liquid phase. The main coupling in the Navier-Stokes equations is then through an additional term in the stress tensor that depends on the gradients of the phase-field variable, representing the effects of capillary forces within the diffuse interface.

Proceedings Title

Proceedings of the NASA Microgravity Materials Science Conference, 1998

Conference Dates

July 14-16, 1998

Conference Location

Undefined

Conference Title

NASA Microgravity Materials Science Conference

Pub Type

Conferences

Keywords

fluid flow, Navier-Stokes equation, phase field, solidification, surface tension onisotropy

Citation

Anderson, D. , McFadden, G. , Boettinger, W. and Wheeler, A. (1998), A Phase-Field/Fluid Motion Model of Solidification: Investigation of Flow Effects During Directional Solidification and Dendritic Growth, Proceedings of the NASA Microgravity Materials Science Conference, 1998, Undefined (Accessed April 25, 2024)