A Phase-Field/Fluid Motion Model of Solidification: Investigation of Flow Effects During Directional Solidification and Dendritic Growth
D M. Anderson, Geoffrey B. McFadden, William J. Boettinger, A A. Wheeler
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 of the NASA Microgravity Materials Science Conference, 1998
, McFadden, G.
, Boettinger, W.
and Wheeler, A.
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
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