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Hydrodynamic interactions in directional solidification

Published online by Cambridge University Press:  26 April 2006

Stephen H. Davis
Stephen H. Davis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
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Abstract

A binary liquid undergoes unidirectional solidification. The one-dimensional steady state is susceptible to morphological instability that causes the solid/liquid interface to change from a planar state to a cellular pattern. This paper examines the effects on this transition of volume-change convection, buoyancy-driven convection or forced flows. It emphasizes how flows alter stability limits, create scale and pattern changes in morphology, and create, through coupling, new instabilities. Emphasis is placed on the physical mechanisms of the interactions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 212 , March 1990 , pp. 241 - 262
Copyright
© 1990 Cambridge University Press

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References

Alexander, J. I. D., Wollkind, D. J. & Sekerka, R. F., 1986 J. Cryst. Growth 79, 849.
Boettinger, W. J., Shechtman, D., Schaefer, R. J. & Biancaniello, F. S., 1984 Metall. Trans. 15A, 55.
Brattkus, K.: 1988 Directional solidification of dilute binary alloys. Ph.D. Dissertation, Northwestern University.
Brattkus, K. & Davis, S. H., 1988a Phys. Rev. B38, 11452.
Brattkus, K. & Davis, S. H., 1988b J. Cryst. Growth 87, 385.
Brattkus, K. & Davis, S. H., 1988c J. Cryst. Growth 89, 423.
Brown, R. A.: 1988 AIChE J. 34, 881.
Caroli, B., Caroli, C., Misbah, C. & Roulet, B., 1985a J. Phys. Paris 46, 401.
Caroli, B., Caroli, C., Misbah, C. & Roulet, B., 1985b J. Phys. Paris 46, 1657.
de Cheveigné, S., Guthmann, C., Kurowski, P., Vicente, E. & Biloni, H., 1988 J. Cryst. Growth 93, 616.
de Cheveigné, S., Guthmann, C. & Lebrun, M. M. 1985 J. Cryst. Growth 73, 242.
de Cheveigné, S., Guthmann, C. & Lebrun, M. M. 1986 J. Phys. Paris 47, 2095.
Coriell, S. R., Cordes, M. R., Boettinger, W. S. & Sekerka, R. F., 1980 J. Cryst. Growth 49, 13.
Coriell, S. R., McFadden, G. B., Boisvert, R. F. & Sekerka, R. F., 1984 J. Cryst. Growth 69, 514.
Coriell, S. R., McFadden, G. B. & Sekerka, R. F., 1985 Ann. Rev. Mater. Sci. 15, 119.
Coriell, S. R. & Sekerka, R. F., 1976 J. Cryst. Growth 34, 157.
Dantzig, J. A. & Chao, L. S., 1986 Proc. 10th US Natl Cong. Appl. Mech., Austin, p. 249. ASME.
Delves, R. T.: 1968 J. Cryst. Growth 3/4, 562.
Delves, R. T.: 1971 J. Cryst. Growth 8, 13.
Eshelman, M. A. & Trevedi, R., 1987 Acta Metall. 35, 2443.
Forth, S. A. & Wheeler, A. A., 1989 J. Fluid Mech. 202.
Heslot, F. & Libchaber, A., 1985 Physica Scr. T9, 126.
Huppert, H. E.: 1990 J. Fluid Mech. 212, 209.
Hurle, D. T. J., Jakeman, E. & Wheeler, A. A., 1982 J. Cryst. Growth 58, 163.
Hurle, D. T. J., Jakeman, E. & Wheeler, A. A., 1983 Phys. Fluids 26, 624.
Jenkins, D. R.: 1985 IMA J. Appl. Maths 35, 145.
Langer, J. S.: 1980 Rev. Mod. Phys. 52, 1.
McFadden, G. B., Boisvert, R. F. & Coriell, S. R., 1987 J. Cryst. Growth 84, 371.
McFadden, G. B., Coriell, S. R. & Alexander, J. I. D. 1988 Commun. Pure Appl. Maths 41, 683.
Merchant, G. J. & Davis, S. H., 1989a J. Cryst. Growth 96, 737.
Merchant, G. J. & Davis, S. H., 1989b Phys. Rev. Lett. 63, 573.
Merchant, G. J. & Davis, S. H., 1989c Directional solidification near minimum cx: two-dimensional isolas and multiple solutions. Phys. Rev. B (1 December issue).Google Scholar
Mullins, W. W. & Sekerka, R. F., 1964 J. Appl. Phys. 35, 444.
Novick-Cohen, A. & Sivashinsky, G. I. 1986 Physica 20D, 237.
Rasenat, S., Busse, F. H. & Rehberg, I., 1989 J. Fluid Mech. 199, 519.
Riley, D. S. & Davis, S. H., 1989a Applied Mathematics Tech. Rep. 8838. Northwestern University.
Riley, D. S. & Davis, S. H., 1989b Hydrodynamic stability of the melt during the solidification of a binary alloy with small segregation coefficient. Physica D (in press).Google Scholar
Riley, D. S. & Davis, S. H., 1990 Long-wave morphological instabilities in the directional solidification of a dilute binary mixture. SIAM J. Appl. Maths (Spring 1990, pending publication).Google Scholar
Rosenberger, F.: 1979 Fundamentals of Crystal Growth I. Springer.
Rutter, J. W. & Chalmers, B., 1953 Can. J. Phys. 31, 15.
Schaefer, R. J. & Coriell, S. R., 1982 In Materials Processing in the Reduced Gravity Environment of Space (ed. G. E. Rindone). p. 479. Mat. Res. Soc. Symp. Proc. North-Holland.
Sivashinsky, G. I.: 1983 Physica 8D, 243.
Sriranganathan, R., Wollkind, D. J. & Oulton, D. B., 1983 J. Cryst. Growth 62, 265.
Tiller, W. A., Jackson, K. A., Rutter, J. W. & Chalmers, B., 1953 Acta-Metall. 1, 428.
Trevedi, R., Sekhar, J. A. & Seetharaman, V., 1989 Met. Trans. 20A, 769.
Ungar, L. H., Bennett, M. J. & Brown, R. A., 1985 Phys. Rev. B31, 5923.
Ungar, L. H. & Brown, R. A., 1984a Phys. Rev. B29, 1367.
Ungar, L. H. & Brown, R. A., 1984b Phys. Rev. B30, 3993.
Wollkind, D. J. & Segel, L. A., 1970 Phil. Trans. R. Soc. Lond. A 268, 351.
Wollkind, D. J., Sriranganathan, R. & Oulton, D. B., 1984 Physica 12D, 215.
Young, G. W. & Davis, S. H., 1986 Phys. Rev. B34, 3388.
Young, G. W., Davis, S. H. & Brattkus, K., 1986 J. Cryst. Growth 83, 560.