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On long-wave morphological instabilities in directional solidification

Published online by Cambridge University Press:  26 September 2008

A. C. Skeldon ,
G. B. McFadden ,
M. D. Impey ,
D. S. Riley ,
K. A. Cliffe ,
A. A. Wheeler  and
S. H. Davis
A. C. Skeldon
Affiliation:
Department of Theoretical Mechanics, University of Nottingham, University Park, Nottingham NG7 2RD, UK
G. B. McFadden
Affiliation:
National Institute of Science and Technology, Gaithersburg, Maryland 20899, USA
M. D. Impey
Affiliation:
Inter a Information Technologies Ltd, Chiltern House, 45 Station Road, Henley-on-Thames, Oxon RG9 1 AT, UK
D. S. Riley
Affiliation:
Department of Theoretical Mechanics, University of Nottingham, University Park, Nottingham NG7 2RD, UK
K. A. Cliffe
Affiliation:
AEA Technology, B424.4Harwell Laboratory, Didcot, Oxon OXII ORA, UK
A. A. Wheeler
Affiliation:
Faculty of Mathematical Studies, University of Southampton, Southampton S09 5NH, UK
S. H. Davis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA
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Abstract

A binary liquid that undergoes directional solidification is susceptible to morphological instabilities which cause the solid/liquid interface to change from a planar to a cellular state. This paper presents a numerical study of a class of long-wave equations that describe the evolution of interface morphology. We find new bifurcation points, new solution branches, and the existence of inverted hexagonal nodes and cells.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 6 , Issue 6 , December 1995 , pp. 639 - 652
Copyright
Copyright © Cambridge University Press 1995

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