A Phase-Field/Fluid Motion Model of Solidification: Investigation of Flow Effects During Directional Solidification and Dendritic Growth
D M. Anderson, William J. Boettinger, Geoffrey B. McFadden, A A. Wheeler
The phase-field model of diffusion-controlled solidification has recently been 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 extended model includes fluid flow by a further coupling to the Navier-Stokes equations. In our work, the solid phase is treated as a fluid 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. This model is applied to solidification and crystal growth situations in order to investigate the effect of fluid motion in the melt on the growth characteristics.
Proceedings of the NASA Microgravity Materials Science Conference, 2000
, Boettinger, W.
, McFadden, G.
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, 2000, Undefined
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