Journal article
Instability in the self-similar motion of a planar solidification front
- Abstract:
- Understanding the solidification process of a binary alloy is important if one is to control the microstructure obtained during the casting of metals. While much work has been done on the steady state solidification problem, despite their relevance to metallurgical applications, there is less known about non-steady solidification problems and their stability. In the paper we shall consider the non-steady solidification problem in which the planar solidification front moves in a self-similar manner, in both infinite and semi-infinite planar one-dimensional geometries. For each geometry exact solutions are known for the resulting Stefan problem. We direct our attention to the stability of each solution, demonstrating that while the concentration and thermal solutions remain stable, the interface corresponding to the solidification front can develop instabilities. For each geometry, we find that there are always unstable perturbations, although we observe qualitative differences in the form of the unstable perturbations for each case. These results generalize and extend several existing studies in the literature, and throw light on the instability inherent in the non-steady solidification process.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 363.8KB, Terms of use)
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- Publisher copy:
- 10.1093/imamat/hxx037
Authors
- Publisher:
- Oxford University Press
- Journal:
- IMA Journal of Applied Mathematics More from this journal
- Volume:
- 83
- Issue:
- 1
- Pages:
- 106–130
- Publication date:
- 2018-01-25
- Acceptance date:
- 2017-11-02
- DOI:
- EISSN:
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1464-3634
- ISSN:
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0272-4960
- Keywords:
- Pubs id:
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pubs:807742
- UUID:
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uuid:52aa4c0c-2eeb-493e-abad-561427f77ac3
- Local pid:
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pubs:807742
- Source identifiers:
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807742
- Deposit date:
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2017-12-03
Terms of use
- Copyright holder:
- Brosa Planella et al
- Copyright date:
- 2018
- Notes:
- © The Author(s) 2017. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. This is the accepted manuscript version of the article. The final version is available online from Oxford University Press at: https://doi.org/10.1093/imamat/hxx037
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