溶液中球形晶体溶解的分析

王小慧; 陈明文; 王自东

doi:10.7498/aps.65.038701

摘要

从物质溶液浓度变化角度考虑了球形晶体在溶液中溶解随表面张力的变化, 利用渐近方法求出了在溶液中球形晶体溶解的浓度和界面的近似解析解, 能够计算出溶解过程中球形晶体溶解的浓度、界面演化形态. 研究了表面张力对于溶液中溶质浓度分布、球晶界面形态和溶解速度的影响. 结果表明, 表面张力促进了球形晶体在溶液中的溶解. 随着表面张力参数增大, 溶液中在界面前沿的溶质浓度升高, 球形晶体的溶解速度增大; 随着时间的增加, 溶解速度逐渐变大, 球形晶体半径逐渐变小, 直至溶解结束.

关键词:

Abstract

Dissolution has attracted considerable attention since the dissolution is a common phenomenon in nature, and is of fundamental interest to reveal the morphology evolutions and microstructures of materials in materials science and pharmaceutical industry. A lot of research has been made in the field of crystal dissolution. And the solid-liquid interfacial energy is recognized as playing a key role in a wide range of material phenomena.The goal of the present study is to present analytical results for the dissolution of spherical crystal with the consideration of surface tension. In this review, we introduce the recent progress of spherical particle dissolution through similar studies. In our paper, a mathematical model is proposed to describe the dissolution process of a spherical crystal with moving boundary. The effect of surface tension through the Gibbs-Thomson condition is included in the mathematical model. And the dissolution of the spherical crystal is considered from the perspective of the concentration change of the solution. An asymptotic solution of the concentration and morphology for a spherical crystal in the dissolution is obtained by using the matched asymptotic expansion method. The results show that the surface tension has great effects on the concentration and interface shape of spherical crystal dissolution. As the surface tension parameter increases, the radius of the crystal decreases, the velocity of the spherical dissolution and the concentration of the solution increase. We have the conclusion that surface tension accelerates the dissolution process of the spherical crystal. And the larger the surface tension parameter, the faster the dissolution rate is and the shorter the dissolution time. The particle radius decreases with time going by, and the dissolution velocity increases with time increasing until the dissolution is completed. The concentration of the dissolution and interface shape of the spherical crystal can be calculated with the results obtained in this paper. It is shown that our analytical results accord well with the results obtained from the numerical results of Vermolen et al. [Vermolen F J, Vuik C, Zwaag S V D 2003 Mater. Sci. Eng. A 347 265].

Keywords:

作者及机构信息

1.
北京科技大学数理学院, 北京 100083;

2.
北京科技大学材料科学与工程学院, 北京 100083

通信作者: 陈明文, chenmw@ustb.edu.cn;wangzd@mater.ustb.edu.cn ; 王自东, chenmw@ustb.edu.cn;wangzd@mater.ustb.edu.cn

基金项目: 国家自然科学基金(批准号: 10972030)资助的课题.

Authors and contacts

1.
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;

2.
School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China

Corresponding author: Chen Ming-Wen, chenmw@ustb.edu.cn;wangzd@mater.ustb.edu.cn ; Wang Zi-Dong, chenmw@ustb.edu.cn;wangzd@mater.ustb.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 10972030).

参考文献

[1]	Daculsi G, Legeros R Z, Mitre D 1989 Calcif. Tissue Int. 45 95
[2]	Lttge A 2006 J. Electron. Spectrosc. Rerat. Phenom. 150 248
[3]	Plomp E R, Rooijen R V, Akimoto H, Frossati G, Jochensen R, Saarloos W V 2001 J. Low Temp. Phys. 124 169
[4]	Lu K, Sheng H W, Jin C H 1997 Chin. J. Marer. Res. 11 658 (in Chinese) [卢珂, 生红卫, 金朝晖 1997 材料研究学报 11 658]
[5]	Kofman R, Cheyssac P, Aouaj A, Lereah Y, Deutscher G, Ben-David T, Penisson J M, Bourret A 1994 Surf. Sci. 303 231
[6]	Huang Z X, Zheng Q S 1998 Acta Mech. Sin. 30 247 (in Chinese) [黄再兴, 郑泉水 1998 力学学报 30 247]
[7]	Lu M, Huang H L, Yu D H, Liu W Q, Wei W H 2015 Acta Phys. Sin. 64 106101 (in Chinese) [卢敏, 黄惠莲, 余冬海, 刘维清, 魏望和 2015 64 106101]
[8]	He A M, Qin C S, Shao J L, Wang P 2009 Acta Phys. Sin. 58 2667 (in Chinese) [何安民, 秦承森, 邵建立, 王裴 2009 58 2667]
[9]	Tong Z H, Liu H T, Chang J Z, An K 2012 Acta Phys. Sin. 61 024401 (in Chinese) [仝志辉, 刘汉涛, 常建忠, 安康 2012 61 024401]
[10]	Zhang Y X, Walker D, Lesher C E 1989 Contrib. Mineral. Petrol. 102 492
[11]	Rice R G, Dob D D 2006 Chem. Eng. Sci. 61 775
[12]	Dong X X, He L J, Mi G B, Li P J 2014 Chin. Phys. B 23 110204
[13]	Lupulescu A, Glicksman M E, Koss M B 2005 J. Cryst. Growth 276 549
[14]	Font F, Myers T G, Mitchell S L 2015 Microfluid. Nanofluid. 18 233
[15]	Wu B S, Tillman P, McCue S W, Hill J M 2009 J. Nanosci. Nanotechnol. 9 885
[16]	Vermolen F J, Vuik C, Zwaag S V D 2003 Mater. Sci. Eng. A 347 265

施引文献

[1]	Daculsi G, Legeros R Z, Mitre D 1989 Calcif. Tissue Int. 45 95
[2]	Lttge A 2006 J. Electron. Spectrosc. Rerat. Phenom. 150 248
[3]	Plomp E R, Rooijen R V, Akimoto H, Frossati G, Jochensen R, Saarloos W V 2001 J. Low Temp. Phys. 124 169
[4]	Lu K, Sheng H W, Jin C H 1997 Chin. J. Marer. Res. 11 658 (in Chinese) [卢珂, 生红卫, 金朝晖 1997 材料研究学报 11 658]
[5]	Kofman R, Cheyssac P, Aouaj A, Lereah Y, Deutscher G, Ben-David T, Penisson J M, Bourret A 1994 Surf. Sci. 303 231
[6]	Huang Z X, Zheng Q S 1998 Acta Mech. Sin. 30 247 (in Chinese) [黄再兴, 郑泉水 1998 力学学报 30 247]
[7]	Lu M, Huang H L, Yu D H, Liu W Q, Wei W H 2015 Acta Phys. Sin. 64 106101 (in Chinese) [卢敏, 黄惠莲, 余冬海, 刘维清, 魏望和 2015 64 106101]
[8]	He A M, Qin C S, Shao J L, Wang P 2009 Acta Phys. Sin. 58 2667 (in Chinese) [何安民, 秦承森, 邵建立, 王裴 2009 58 2667]
[9]	Tong Z H, Liu H T, Chang J Z, An K 2012 Acta Phys. Sin. 61 024401 (in Chinese) [仝志辉, 刘汉涛, 常建忠, 安康 2012 61 024401]
[10]	Zhang Y X, Walker D, Lesher C E 1989 Contrib. Mineral. Petrol. 102 492
[11]	Rice R G, Dob D D 2006 Chem. Eng. Sci. 61 775
[12]	Dong X X, He L J, Mi G B, Li P J 2014 Chin. Phys. B 23 110204
[13]	Lupulescu A, Glicksman M E, Koss M B 2005 J. Cryst. Growth 276 549
[14]	Font F, Myers T G, Mitchell S L 2015 Microfluid. Nanofluid. 18 233
[15]	Wu B S, Tillman P, McCue S W, Hill J M 2009 J. Nanosci. Nanotechnol. 9 885
[16]	Vermolen F J, Vuik C, Zwaag S V D 2003 Mater. Sci. Eng. A 347 265

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