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A model is developed to investigate the effects of far field flow on the solidification of a spherical particle from the melt, under the influence of thermal and solute flow. The stability of the spherical interface is studied and the growth rate of the interface perturbation is calculated. The perturbation to the maximum growth rate becomes larger when the spherical radius increases. The downwind side of the interface is more unstable than the upwind side. The effect of far field flow reduces the critical radius of the spherical crystal.
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Keywords:
- spherical crystal /
- far field flow /
- interface stability /
- Trivedi criterion
[1] Mullins W W, Sekerka R F 1963 J. Appl. Phys. 34 323
[2] Trivedi R 1980 J. Cryst. Growth 48 93
[3] Vogel A, Cantor B 1977 J. Cryst. Growth 37 309
[4] Li T, Lin X, Huang W D 2006 Acta Mater. 54 4815
[5] Delves R T 1971 J. Cryst. Growth 8 13
[6] Coriell S R, McFadden G B, Boisvert R F, Sekerka R F 1984 J. Cryst. Growth 69 15
[7] Brattkus K, Davis S H 1988 J. Cryst. Growth 89 423
[8] Forth S A, Wheeler A A 1989 J. Fluid Mech. 202 339
[9] Davis S H, Schulze T P 1996 Metall. Mater. Trans. 27A 583
[10] Lin X, Li T, Wang L L, Su Y P, Huang W D 2004 Acta Phys. Sin. 53 3971(in Chinese)[林 鑫、李 涛、王琳琳、苏云鹏、黄卫东 2004 物理学报 53 3971]
[11] Huang W D, Lin X, Li T, Wang L L, Inatomi Y 2004 Acta Phys. Sin. 53 3978(in Chinese)[黄卫东、林 鑫、李 涛、王 琳琳、Inatomi Y 2004 物理学报 53 3978] 〖12] Chen Y J, Chen C L 2008 Acta Phys. Sin. 57 4585(in Chinese)[陈玉娟、陈长乐 2008 物理学报 57 4585]
[12] Sun D K, Zhu M F, Yang C R, Pan S Y, Dai T 2009 Acta Phys. Sin. 58 S285 (in Chinese)[孙东科、朱鸣芳、杨朝蓉、潘诗琰、戴 挺 2009 物理学报 58 S285]
[13] Xiong B, Tang Z M, Hu W R 1991 Acta Phys. Sin. 40 1809(in Chinese)[熊 斌、唐泽眉、胡文瑞 1991物理学报 40 1809]
[14] Wang J Y, Chen C L, Zhai W, Jin K X 2009 Acta Phys. Sin. 58 6554(in Chinese)[王建元、陈长乐、翟 薇、金克新 2009物理学报 58 6554]
[15] Chen M W, Wang Z D, Xu J J 2007 Sci. China E 37 644(in Chinese)[陈明文、王自东、徐鉴君 2007 中国科学 E 37 644]
[16] Chen M W, Wang Z D, Sun R J 2007 Acta Phys. Sin. 56 1819(in Chinese)[陈明文、王自东、孙仁济 2007 物理学报 56 1819]
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[1] Mullins W W, Sekerka R F 1963 J. Appl. Phys. 34 323
[2] Trivedi R 1980 J. Cryst. Growth 48 93
[3] Vogel A, Cantor B 1977 J. Cryst. Growth 37 309
[4] Li T, Lin X, Huang W D 2006 Acta Mater. 54 4815
[5] Delves R T 1971 J. Cryst. Growth 8 13
[6] Coriell S R, McFadden G B, Boisvert R F, Sekerka R F 1984 J. Cryst. Growth 69 15
[7] Brattkus K, Davis S H 1988 J. Cryst. Growth 89 423
[8] Forth S A, Wheeler A A 1989 J. Fluid Mech. 202 339
[9] Davis S H, Schulze T P 1996 Metall. Mater. Trans. 27A 583
[10] Lin X, Li T, Wang L L, Su Y P, Huang W D 2004 Acta Phys. Sin. 53 3971(in Chinese)[林 鑫、李 涛、王琳琳、苏云鹏、黄卫东 2004 物理学报 53 3971]
[11] Huang W D, Lin X, Li T, Wang L L, Inatomi Y 2004 Acta Phys. Sin. 53 3978(in Chinese)[黄卫东、林 鑫、李 涛、王 琳琳、Inatomi Y 2004 物理学报 53 3978] 〖12] Chen Y J, Chen C L 2008 Acta Phys. Sin. 57 4585(in Chinese)[陈玉娟、陈长乐 2008 物理学报 57 4585]
[12] Sun D K, Zhu M F, Yang C R, Pan S Y, Dai T 2009 Acta Phys. Sin. 58 S285 (in Chinese)[孙东科、朱鸣芳、杨朝蓉、潘诗琰、戴 挺 2009 物理学报 58 S285]
[13] Xiong B, Tang Z M, Hu W R 1991 Acta Phys. Sin. 40 1809(in Chinese)[熊 斌、唐泽眉、胡文瑞 1991物理学报 40 1809]
[14] Wang J Y, Chen C L, Zhai W, Jin K X 2009 Acta Phys. Sin. 58 6554(in Chinese)[王建元、陈长乐、翟 薇、金克新 2009物理学报 58 6554]
[15] Chen M W, Wang Z D, Xu J J 2007 Sci. China E 37 644(in Chinese)[陈明文、王自东、徐鉴君 2007 中国科学 E 37 644]
[16] Chen M W, Wang Z D, Sun R J 2007 Acta Phys. Sin. 56 1819(in Chinese)[陈明文、王自东、孙仁济 2007 物理学报 56 1819]
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