Abstract
The patterns formed via the directional solidification of binary mixtures are paradigmatic of the type of structures which can arise in non-equilibrium dissipative systems. This paper will review the current status of our attempts to understand these patterns. We will focus in turn on phenomena in shallow cell systems, the highly non-equilibrium deep cell regime and the transition to dendritic growth.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Systems Far From Equilibrium, J.E. Wesfried, ed., Springer-Verlar, 1988.
For an introduction, see Langer, J.S., Rev. Mod. Phys. 52, 1 (1980).
Mullins, W.W. and Sekerka, R.F., J. Appl. Phys. 34, 323 (1964).
Levine, H., Rappel, W.J. and Riecke, H., ‘Resonant interactions and travelling solidification cells’, preprint.
Simon, A., Bechhoefer, J. and Libchaber, A., Phys. Rev. Lett. 61, 2574 (1988).
Kessler, D., Koplik, J. and Levine, H., Adv. Phys. 37, 255 (1988); Langer, J.S., Chance and Matter, J. Souletie, ed., ( North-Holland, 1987 ); Brener, E. and Melnikov, V.I., preprint.
Kessler, D. and Levine, H., ‘Linear stability of directional solidification cells’, preprint.
de Cheveigne, S., Guthmann, C. and Lebrun, M.M., J. de Physique 47, 2095 (1986).
See C. Guthmann, this volume.
Kessler, D. and Levine, H., Phys. Rev. A 39, 3041 (1989).
Misbah, C., Saito, Y. and Muller-Krumbhaar, H., preprint.
Wollkind, D.J., Oulton, D.B. and Sriranganthan, R., J. de Physique 45, 505 (9184) and references therein.
See Brown, R., et al in Supercomputer Research in Chemistry and Chemical Engineering, K. Jensen, ed., ( ACS, Washington, 1987 ).
Riecke, H. and Papp, H.G., Phys. Rev. A 33, 547 (1987).
See G. Faivre, this volume.
Rabaud, M., Mich all and, S. and Couder, Y., preprint.
Coullet, P., Gunratne, G. and Goldstein, R., preprint (1989).
Haug, P., preprint (1989).
Jones, G.A. and Proctor, M.R.E., Phys. Lett. A 121, 224 (1987).
Ben-Amar, M. and Moussallam, B., Phys. Rev. Lett. 60, 317 (1988).
Pelce, P. and Pumir, A., J. Cryst. Growth 73, 357 (1985).
Kessler, D., Koplik, J. and Levine, H., Phys. Rev. A 34, 4980 (1986).
Maashall, M., Ben-Amar, M. and Hakim, V. (preprint, 1989 ).
Dombre, T. and Hakim, V., Phys. Rev. A 36, 2811 (1987); Ben-Amar, M. and Moussallam, B., Phys. Rev. Lett. 60, 317 (1988).
Karma, A. and Pelce, P., preprint (1989).
Pieters, R. and Langer, J.S., Phys. Rev. Lett. 56, 1948 (1986); Kessler, D. and Levine, H., Europhys. Lett. 4, 215 (1987).
Kessler, D. and Levine, H., Phys. Rev. A 33, 2621, 2634 (1986); Bensimon, D., Phys. Rev. A 33, 1302 (1986).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Kluwer Academic Publishers
About this chapter
Cite this chapter
Levine, H. (1990). Directional Solidification: Theoretical Methods and Current Understanding. In: Walgraef, D., Ghoniem, N.M. (eds) Patterns, Defects and Materials Instabilities. NATO ASI Series, vol 183. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0593-1_11
Download citation
DOI: https://doi.org/10.1007/978-94-009-0593-1_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6755-3
Online ISBN: 978-94-009-0593-1
eBook Packages: Springer Book Archive