Selection Theory of Dendritic Growth with Anisotropic Diffusion
Dendritic patterns frequently arise when a crystal grows into its own undercooled melt. Latent heat released at the two-phase boundary is removed by some transport mechanism, and often the problem can be described by a simple diffusion model. Its analytic solution is based on a perturbation expansio...
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| Format: | Article |
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Wiley
2015-01-01
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| Series: | Advances in Condensed Matter Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/529036 |
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| author | Martin von Kurnatowski Klaus Kassner |
| author_facet | Martin von Kurnatowski Klaus Kassner |
| author_sort | Martin von Kurnatowski |
| collection | DOAJ |
| description | Dendritic patterns frequently arise when a crystal grows into its own undercooled melt. Latent heat released at the two-phase boundary is removed by some transport mechanism, and often the problem can be described by a simple diffusion model. Its analytic solution is based on a perturbation expansion about the case without capillary effects. The length scale of the pattern is determined by anisotropic surface tension, which provides the mechanism for stabilizing the dendrite. In the case of liquid crystals, diffusion can be anisotropic too. Growth is faster in the direction of less efficient heat transport (inverted growth). Any physical solution should include this feature. A simple spatial rescaling is used to reduce the bulk equation in 2D to the case of isotropic diffusion. Subsequently, an eigenvalue problem for the growth mode results from the interface conditions. The eigenvalue is calculated numerically and the selection problem of dendritic growth with anisotropic diffusion is solved. The length scale is predicted and a quantitative description of the inverted growth phenomenon is given. It is found that anisotropic diffusion cannot take the stabilizing role of anisotropic surface tension. |
| format | Article |
| id | doaj-art-5b502d91d259407c860bc82bfdf92fcf |
| institution | OA Journals |
| issn | 1687-8108 1687-8124 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
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| series | Advances in Condensed Matter Physics |
| spelling | doaj-art-5b502d91d259407c860bc82bfdf92fcf2025-08-20T02:05:13ZengWileyAdvances in Condensed Matter Physics1687-81081687-81242015-01-01201510.1155/2015/529036529036Selection Theory of Dendritic Growth with Anisotropic DiffusionMartin von Kurnatowski0Klaus Kassner1Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, 39016 Magdeburg, GermanyInstitut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, 39016 Magdeburg, GermanyDendritic patterns frequently arise when a crystal grows into its own undercooled melt. Latent heat released at the two-phase boundary is removed by some transport mechanism, and often the problem can be described by a simple diffusion model. Its analytic solution is based on a perturbation expansion about the case without capillary effects. The length scale of the pattern is determined by anisotropic surface tension, which provides the mechanism for stabilizing the dendrite. In the case of liquid crystals, diffusion can be anisotropic too. Growth is faster in the direction of less efficient heat transport (inverted growth). Any physical solution should include this feature. A simple spatial rescaling is used to reduce the bulk equation in 2D to the case of isotropic diffusion. Subsequently, an eigenvalue problem for the growth mode results from the interface conditions. The eigenvalue is calculated numerically and the selection problem of dendritic growth with anisotropic diffusion is solved. The length scale is predicted and a quantitative description of the inverted growth phenomenon is given. It is found that anisotropic diffusion cannot take the stabilizing role of anisotropic surface tension.http://dx.doi.org/10.1155/2015/529036 |
| spellingShingle | Martin von Kurnatowski Klaus Kassner Selection Theory of Dendritic Growth with Anisotropic Diffusion Advances in Condensed Matter Physics |
| title | Selection Theory of Dendritic Growth with Anisotropic Diffusion |
| title_full | Selection Theory of Dendritic Growth with Anisotropic Diffusion |
| title_fullStr | Selection Theory of Dendritic Growth with Anisotropic Diffusion |
| title_full_unstemmed | Selection Theory of Dendritic Growth with Anisotropic Diffusion |
| title_short | Selection Theory of Dendritic Growth with Anisotropic Diffusion |
| title_sort | selection theory of dendritic growth with anisotropic diffusion |
| url | http://dx.doi.org/10.1155/2015/529036 |
| work_keys_str_mv | AT martinvonkurnatowski selectiontheoryofdendriticgrowthwithanisotropicdiffusion AT klauskassner selectiontheoryofdendriticgrowthwithanisotropicdiffusion |