The effect of two-dimensional shear flow on the stability of a crystal interface in the supercooled melt

doi:10.1088/1674-1056/21/8/086401

Abstract A model is developed based on the time-related thermal diffusion equations to investigate the effects of two-dimensional shear flow on the stability of a crystal interface in the supercooled melt of pure substance. Similar to the three-dimensional shear flow as described in our previous paper, the two-dimensional shear flow can also be found to reduce the growth rate of perturbation amplitude. However, compared with the case of Laplace equation for steady state thermal diffusion field, due to the existence of time partial derivatives of the temperature fields in diffusion equation the absolute value of the gradients of the temperature fields increases, therefore destabilizing the interface. The circular interface is more unstable than in the case of Laplace equation without time partial derivatives. The critical stability radius of the crystal interface increases with shearing rate increasing. The stability effect of shear flow decreases remarkably with the increase of melt undercooling.

Keywords: spherical crystal shear flow interface stability Trivedi criterion

Received: 21 December 2011
Revised: 10 February 2012
Accepted manuscript online:

PACS:	64.70.D-	(Solid-liquid transitions)
	64.70.dg	(Crystallization of specific substances)
	81.10.Fq	(Growth from melts; zone melting and refining)
	81.30.Fb	(Solidification)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 50771083 and 50901061), the National Basic Research Program of China (Grant No. 2011CB610402), the Fund of the State Key Laboratory of Solidification Processing in Northwestern Polytechnical University, China (Grant Nos. 02-TZ-2008 and 36-TP-2009), and the Program of Introducing Talents of Discipline to Universities, China (Grant No. 08040).

Corresponding Authors: Lin Xin
E-mail: xlin@nwpu.edu.cn

Cite this article:

Cao Bin (曹斌), Lin Xin (林鑫), Wang Meng (王猛), Huang Wei-Dong (黄卫东 ) The effect of two-dimensional shear flow on the stability of a crystal interface in the supercooled melt 2012 Chin. Phys. B 21 086401

[1]	Mullins W W and Sekerka R F 1963 J. Appl. Phys. 34 323
[2]	Mullins W W and Sekerka R F 1964 J. Appl. Phys. 35 444
[3]	Trivedi R 1980 J. Crystal Growth 48 93
[4]	Vogel A and Cantor B 1977 J. Crystal Growth 37 309
[5]	Li T, Lin X and Huang W D 2006 Acta Materialia 54 4815
[6]	Tong L L, Lin X, Zhao L N and Huang W D 2009 Acta Metallurgica Sinica 45 737
[7]	Coriell S R, McFadden G B, Boisvert R F and Sekerka R F 1984 J. Crystal Growth 69 15
[8]	Brattkus K and Davis S H 1988 J. Crystal Growth 89 423
[9]	Schulze T P and Davis S H 1994 J. Crystal Growth 143 317
[10]	Schulze T P and Davis S H 1995 J. Crystal Growth 149 253
[11]	Davis S H and Schulze T P 1996 Metall. Mater. Trans. 27A 583
[12]	Lin X, Li T, Wang L L, Su Y P and Huang W D 2004 Acta Phys. Sin. 53 3971 (in Chinese)
[13]	Zhao D W and Li J F 2009 Acta Phys. Sin. 58 7094 (in Chinese)
[14]	Sun D K, Zhu M F, Yang C R, Pan S Y and Dai T 2009 Acta Phys. Sin. 58 285 (in Chinese)
[15]	Xing H, Chen C L, Jin K X, Tan X Y and Fan F 2010 Acta Phys. Sin. 59 8218 (in Chinese)
[16]	Chen M W, Wang Z D and Xu J J 2007 Sci. Sin. Tech. 37 644
[17]	Chen M W, Wang Z D and Sun R J 2007 Acta Phys. Sin. 56 1819
[18]	Chen M W, Ni F, Wang Y L, Wang Z D and Xie J X 2011 Acta Phys. Sin. 60 068103 (in Chinese)
[19]	Cao B, Lin X and Huang W D 2011 Acta Phys. Sin. 60 066403 (in Chinese)
[20]	Cao B, Lin X, Wang M and Huang W D 2011 J. Crystal Growth 327 140

[1]	Gravity-capillary waves modulated by linear shear flow in arbitrary water depth Shaofeng Li(李少峰), Jinbao Song(宋金宝), and Anzhou Cao(曹安州). Chin. Phys. B, 2020, 29(12): 124702.
[2]	A nonlinear Schrödinger equation for gravity waves slowly modulated by linear shear flow Shaofeng Li(李少峰), Juan Chen(陈娟), Anzhou Cao(曹安州), Jinbao Song(宋金宝). Chin. Phys. B, 2019, 28(12): 124701.
[3]	Characteristics and generation of elastic turbulence in a three-dimensional parallel plate channel using direct numerical simulation Hong-Na Zhang(张红娜), Feng-Chen Li(李凤臣), Xiao-Bin Li(李小斌), Dong-Yang Li(李东阳), Wei-Hua Cai(蔡伟华), Bo Yu(宇波). Chin. Phys. B, 2016, 25(9): 094701.
[4]	Hydrodynamics of passing-over motion during binary droplet collision in shear flow Cheng-Yao Wang(王程遥), Cheng-Bin Zhang(张程宾), Xiang-Yong Huang(黄庠永), Xiang-Dong Liu(刘向东), Yong-Ping Chen(陈永平). Chin. Phys. B, 2016, 25(10): 108202.
[5]	Axisymmetric wave propagation in gas shear flow confined by a rigid-walled pipeline Chen Yong (陈勇), Huang Yi-Yong (黄奕勇), Chen Xiao-Qian (陈小前), Bai Yu-Zhu (白玉铸), Tan Xiao-Dong (谭晓栋). Chin. Phys. B, 2015, 24(4): 044301.
[6]	Out-of-plane shear flow effects on fast magnetic reconnection in a two-dimensional hybrid simulation model Wang Lin (王琳), Wang Xian-Qu (王先驱), Wang Xiao-Gang (王晓钢), Liu Yue (刘悦). Chin. Phys. B, 2014, 23(2): 025203.
[7]	Electro–magnetic control of shear flow over a cylinder for drag reduction and lift enhancement Zhang Hui (张辉), Fan Bao-Chun (范宝春), Chen Zhi-Hua (陈志华), Chen Shuai (陈帅), Li Hong-Zhi (李鸿志). Chin. Phys. B, 2013, 22(10): 104701.
[8]	Coupling effect of Brownian motion and laminar shear flow on colloid coagulation:a Brownian dynamics simulation study Xu Sheng-Hua(徐升华), Sun Zhi-Wei(孙祉伟), Li Xu(李旭), and Jin Tong Wang . Chin. Phys. B, 2012, 21(5): 054702.
[9]	Linear stability analysis on a spherical particle growing from a binary melt under the far-field flow Cao Bin(曹斌), Lin Xin(林鑫), Wang Meng(王猛), and Huang Wei-Dong(黄卫东) . Chin. Phys. B, 2012, 21(5): 056401.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

The effect of two-dimensional shear flow on the stability of a crystal interface in the supercooled melt

Cite this article:

Online attention