Instability in the self-similar motion of a planar solidification front
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...
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| Format: | Journal article |
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Oxford University Press
2018
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| _version_ | 1797068680111063040 |
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| author | Brosa Planella, F Please, C Van Gorder, R |
| author_facet | Brosa Planella, F Please, C Van Gorder, R |
| author_sort | Brosa Planella, F |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T22:13:39Z |
| format | Journal article |
| id | oxford-uuid:52aa4c0c-2eeb-493e-abad-561427f77ac3 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T22:13:39Z |
| publishDate | 2018 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | oxford-uuid:52aa4c0c-2eeb-493e-abad-561427f77ac32022-03-26T16:26:58ZInstability in the self-similar motion of a planar solidification frontJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:52aa4c0c-2eeb-493e-abad-561427f77ac3Symplectic Elements at OxfordOxford University Press2018Brosa Planella, FPlease, CVan Gorder, RUnderstanding 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. |
| spellingShingle | Brosa Planella, F Please, C Van Gorder, R Instability in the self-similar motion of a planar solidification front |
| title | Instability in the self-similar motion of a planar solidification front |
| title_full | Instability in the self-similar motion of a planar solidification front |
| title_fullStr | Instability in the self-similar motion of a planar solidification front |
| title_full_unstemmed | Instability in the self-similar motion of a planar solidification front |
| title_short | Instability in the self-similar motion of a planar solidification front |
| title_sort | instability in the self similar motion of a planar solidification front |
| work_keys_str_mv | AT brosaplanellaf instabilityintheselfsimilarmotionofaplanarsolidificationfront AT pleasec instabilityintheselfsimilarmotionofaplanarsolidificationfront AT vangorderr instabilityintheselfsimilarmotionofaplanarsolidificationfront |