Skip to main content Accessibility help
×
Home

Solid–mush interface conditions for mushy layers

  • Nicholas R. Gewecke (a1) and Tim P. Schulze (a2)

Abstract

A subtle issue in the study of mushy zones which form during the solidification of binary alloys is that there are two distinct types of solid–mush interfaces which may occur. One of these is a eutectic front and the other is a front which separates the mushy layer and, assuming complete solute rejection, a layer of pure solid. For semi-infinite-domain configurations that admit similarity solutions, such as those at a uniform initial temperature and concentration with an imposed cold temperature at the lower boundary, only one of the two types appears, and the type of front is determined by the various parameters of the system. In a finite domain, it is possible for each type of front to appear at different times. Specifically, the advance of the eutectic front is restricted by the isotherm associated with the eutectic temperature, and the other front type will appear over a longer time scale. Leading up to the time when the front changes type, the concentration being frozen into the solid decreases. This process writes a history of the system into the solid.

Copyright

Corresponding author

Email address for correspondence: ngewecke@math.udel.edu

References

Hide All
1. Anderson, D. M. 2003 A model for diffusion-controlled solidification of ternary alloys in mushy layers. J. Fluid Mech. 483, 165197.
2. Davis, S. H. 2001 Theory of Solidification. Cambridge University Press.
3. Emms, P. W. & Fowler, A. C. 1994 Compositional convection in the solidification of binary alloys. J. Fluid Mech. 262, 111139.
4. Fowler, A. C. 1985 The formation of freckles in binary alloys. IMA J. Appl. Math. 35, 159174.
5. Gewecke, N. R. & Schulze, T. P. 2011 The rapid advance and slow retreat of a mushy zone. J. Fluid Mech. 674, 227243.
6. Kerr, R. C., Woods, A. W., Worster, M. G. & Huppert, H. E. 1990 Solidification of an alloy cooled from above. Part 3. Compositional stratification within the solid. J. Fluid Mech. 218, 337354.
7. Langer, J. S. 1980 Instabilities and pattern formation in crystal growth. Rev. Mod. Phys. 52, 128.
8. Schulze, T. P. & Worster, M. G. 1999 Weak convection, liquid inclusions and the formation of chimneys in mushy layers. J. Fluid Mech. 388, 197215.
9. Schulze, T. P. & Worster, M. G. 2005 A time-dependent formulation of the mushy-zone free-boundary problem. J. Fluid Mech. 541, 193202.
10. Worster, M. G. 1986 Solidification of an alloy from a cooled boundary. J. Fluid Mech. 167, 481501.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed