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Effect of buoyancy-driven convection on steady state dendritic growth in a binary alloy |
| Chen Ming-Wen (陈明文)a, Wang Bao (王宝)a, Wang Zi-Dong (王自东)b |
a School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;
b School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China |
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Abstract The effect of buoyancy-driven convection on the steady state dendritic growth in an undercooled binary alloy is studied. For the case of the moderate modified Grashof number, the uniformly valid asymptotic solution in the entire region of space is obtained by means of the matched asymptotic expansion method. The analytical results show that the buoyancy-driven convection has a significant effect on the needle-like interface of dendritic growth. Due to the buoyancy-driven convection, the needle-like interface shape of the crystal is changed. When the Peclet number that is not affected by the buoyant flow is less than a certain critical value, the interface shape of the dendrite becomes thinner as the Grashof number increases; when it is larger than the critical value, the interface shape becomes fatter as the Grashof number increases. In the undercooled binary alloy the morphology number plays an active role in the interface shape and leads to the buoyancy effect that is different from the situation for the pure melt. The smaller the morphology number is, the more significant change the interface shape has. As the Peclet number further increases, the effect of buoyancy on the interface diminishes eventually.
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Received: 03 February 2013
Revised: 12 June 2013
Accepted manuscript online:
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PACS:
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68.70.+w
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(Whiskers and dendrites (growth, structure, and nonelectronic properties))
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81.10.Mx
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(Growth in microgravity environments)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10972030), the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant No. FRF-BR-11-034B), and the Overseas Distinguished Scholar Program of the Ministry of Education of China (Grant No. MS2010bjkj005). |
Corresponding Authors:
Chen Ming-Wen, Wang Zi-Dong
E-mail: chenmw@ustb.edu.cn;wangzd@mater.ustb.edu.cn
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Cite this article:
Chen Ming-Wen (陈明文), Wang Bao (王宝), Wang Zi-Dong (王自东) Effect of buoyancy-driven convection on steady state dendritic growth in a binary alloy 2013 Chin. Phys. B 22 116805
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