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A two-dimensional (2D) lattice Boltzmann method (LBM) model was developed to simulate liquid-liquid phase separation of monotectic alloys, which is controlled by the diffusive growth, the collisions and coagulations, and the Ostwald ripening of the minority liquid droplets. The present model combines the features of the multiphase flow model proposed by Shan-Chen and the mesoscopic interparticle potentials developed by Oin. In addition, a source term is introduced in the LB evolution equations to account for the phase transformation. The proposed LBM model was applied to simulate single droplet growth, coagulation of two droplets and multi-droplet growth during the liquid-liquid phase separation process of a monotectic alloy. The simulation shows that the single droplet growth in the two-liquid phase is controlled by diffusion and that the initial nonequilibrium composition approaches to equilibrium. The coagulation velocity of two droplets is influenced by surface tension, which is in accordance with the trend of the analytical prediction. It is found that the liquid-liquid phase separation process is obviously impacted by the collisions and coagulations and the Ostwald ripening of the droplets.
[1] ［1］Li H L, Zhao J Z 2008 Appl. Phy. Lett. 92 241902
[2] ［2］Huang Q, Luo X H, Li Y Y 2005 Adv. Space Res. 36 86
[3] ［3］Ratke L, Dieffenbach S 1995 Mater. Sci. Eng. R 15 263
[4] ［4］Fan Z, Ji S, Zhang J 2001 Mater. Sci. Technol. 17 837
[5] ［5］Zhai W, Wang N, Wei B B 2007 Acta Phys. Sin. 56 2353 (in Chinese) ［翟薇、 王楠、 魏柄波 2007 56 2353］
[6] ［6］Zhao J Z, Hu Z Q, Ratke L 2004 Acta Metall. Sin. 40 27 (in Chinese) ［赵九洲、 胡壮麒、 Ratke L 2004 金属学报 40 27］
[7] ［7］Cui H B, Guo J J, Su Y Q, et al 2007 Acta Metall. Sin. 43 907 (in Chinese) ［崔红保、 郭景杰、 苏彦庆等 2007 金属学报 43 907］
[8] ［8］Chen S, Doolen G D 1998 Annu. Rev. Fluid Mech. 30 329
[9] ［9］Raabe D 2004 Modelling Simul. Mater. Sci. Eng. 12 R13
[10] ］Wang H L, Chai Z H, G Z L 2009 Chin. J. Comput. Phys. 26 389 (in Chinese) ［王华龙、 柴振华、 郭照立 2009 计算物理 26 389］
[11] ］Chai Z H, Guo Z L, Shi B C 2007 J. Appl. Phys. 101 104913
[12] ］Xu Y S, Li H B, Fang H P, Huang G X 2004 Acta Phys. Sin. 53 773 (in Chinese) ［许友生、 李华兵、 方海平、 黄国翔 2004 53 773］
[13] ］Feng S D, Zhong L H, Gao S T, Dong P 2007 Acta Phys. Sin. 56 1238 (in Chinese) ［冯士德、 钟霖浩、 高守亭、 Dong Ping 2007 56 1238］
[14] ］Sun D K, Zhu M F, Pan S Y, Raabe D 2009 Acta Mater. 57 1755
[15] ］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 58 S285］
[16] ］Wagner A J, Giraud L, Scott C E 2000 Comput. Phys. Commun. 129 227
[17] ］Yang Z L, Dinh T N, Nourgaliev R R, Sehgal B R 2001 Int. J. Therm. Sci. 204 143
[18] ］Shan X , Chen H 1993 Phys. Rev. E 47 1815
[19] ］Shan X, Chen H 1994 Phys. Rev. E 49 2941
[20] ］Qin R S 2006 Phys. Rev. E 73 066703
[21] ］Nishizawa T (written), Hao S M (translated) 2006 Thermodynamics of Microstructure (1st ed) (Beijing: Chemical Industry Press) p106 (in Chinese) ［西泽泰二 著，郝士明 译 2006 微观组织热力学(第一版) (北京：化学工业出版社) 第106页］
[22] ］Eggers J, Lister J R, Stone H A 1999 J. Fluid. Mech. 401 293
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[1] ［1］Li H L, Zhao J Z 2008 Appl. Phy. Lett. 92 241902
[2] ［2］Huang Q, Luo X H, Li Y Y 2005 Adv. Space Res. 36 86
[3] ［3］Ratke L, Dieffenbach S 1995 Mater. Sci. Eng. R 15 263
[4] ［4］Fan Z, Ji S, Zhang J 2001 Mater. Sci. Technol. 17 837
[5] ［5］Zhai W, Wang N, Wei B B 2007 Acta Phys. Sin. 56 2353 (in Chinese) ［翟薇、 王楠、 魏柄波 2007 56 2353］
[6] ［6］Zhao J Z, Hu Z Q, Ratke L 2004 Acta Metall. Sin. 40 27 (in Chinese) ［赵九洲、 胡壮麒、 Ratke L 2004 金属学报 40 27］
[7] ［7］Cui H B, Guo J J, Su Y Q, et al 2007 Acta Metall. Sin. 43 907 (in Chinese) ［崔红保、 郭景杰、 苏彦庆等 2007 金属学报 43 907］
[8] ［8］Chen S, Doolen G D 1998 Annu. Rev. Fluid Mech. 30 329
[9] ［9］Raabe D 2004 Modelling Simul. Mater. Sci. Eng. 12 R13
[10] ］Wang H L, Chai Z H, G Z L 2009 Chin. J. Comput. Phys. 26 389 (in Chinese) ［王华龙、 柴振华、 郭照立 2009 计算物理 26 389］
[11] ］Chai Z H, Guo Z L, Shi B C 2007 J. Appl. Phys. 101 104913
[12] ］Xu Y S, Li H B, Fang H P, Huang G X 2004 Acta Phys. Sin. 53 773 (in Chinese) ［许友生、 李华兵、 方海平、 黄国翔 2004 53 773］
[13] ］Feng S D, Zhong L H, Gao S T, Dong P 2007 Acta Phys. Sin. 56 1238 (in Chinese) ［冯士德、 钟霖浩、 高守亭、 Dong Ping 2007 56 1238］
[14] ］Sun D K, Zhu M F, Pan S Y, Raabe D 2009 Acta Mater. 57 1755
[15] ］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 58 S285］
[16] ］Wagner A J, Giraud L, Scott C E 2000 Comput. Phys. Commun. 129 227
[17] ］Yang Z L, Dinh T N, Nourgaliev R R, Sehgal B R 2001 Int. J. Therm. Sci. 204 143
[18] ］Shan X , Chen H 1993 Phys. Rev. E 47 1815
[19] ］Shan X, Chen H 1994 Phys. Rev. E 49 2941
[20] ］Qin R S 2006 Phys. Rev. E 73 066703
[21] ］Nishizawa T (written), Hao S M (translated) 2006 Thermodynamics of Microstructure (1st ed) (Beijing: Chemical Industry Press) p106 (in Chinese) ［西泽泰二 著，郝士明 译 2006 微观组织热力学(第一版) (北京：化学工业出版社) 第106页］
[22] ］Eggers J, Lister J R, Stone H A 1999 J. Fluid. Mech. 401 293
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