Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-25T00:35:51.379Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of Finite Rate Phase Transformation Kinetics on The Steady-State Solidification Front Propagation Speed in Undercooled Pure Liquids

Published online by Cambridge University Press:  10 February 2011

J. A. Norris  and
D. R. Kassoy
J. A. Norris
Affiliation:
Dept. of Mechanical Engineering, Univ. of Colorado, Boulder, CO 80309–0427
D. R. Kassoy
Affiliation:
Dept. of Mechanical Engineering, Univ. of Colorado, Boulder, CO 80309–0427
Get access

Abstract

This novel approach to modeling the steady-state solidification of undercooled pure liquids is based upon first principles. Continuum equations are used to describe a volumetrically averaged, coexisting mixture of solid and liquid in the thin phase transformation zone between regions of pure liquid and pure solid. These equations are coupled with a dynamic equilibrium based rate law that describes temperature dependent phase transformation kinetics. The time scale associated with finite rate phase transformation is found to depend on a solidification activation energy, thermal energy, and the enthalpy of fusion. The model leads naturally to an eigenvalue problem for the solidification front propagation speed. In addition, the variation of the volumetrically averaged liquid fraction across the solidification zone is predicted.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 481: Symposium P – Science and Technology of Semiconductor Surface Preparation , 1997 , 59
Copyright
Copyright © Materials Research Society 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Willnecker, R., Herlach, D. M. and Feuerbacher, B., Physical Review Letters 62, pp. 2707–2710 (1989).Google Scholar
2. Carslaw, H. S. and Jaeger, J. C., Conduction of Heat in Solids, 2nd ed. (Oxford University Press, London, 1959), pp. 282–296.Google Scholar
3. Ozisik, M. N., Heat Conduction, (John Wiley and Sons, New York, 1980), pp. 397–431.Google Scholar
4. Kassoy, D. R. and Williams, F. A., The Physics of Fluids 11, pp. 1343–1351 (1968).Google Scholar
5. Jackson, K. A. and Chalmers, B., Canadian Journal of Physics 34, pp. 473–490 (1956).Google Scholar
6. Norris, J. A., PhD thesis, University of Colorado at Boulder, 1993.Google Scholar
7. Ashby, M. F. and Jones, D. R. H., Engineering Materials 2: An Introduction to Microstructures, Processing and Design, (Pergamon, Oxford, 1986), p. 13.Google Scholar