固体表面液滴铺展与润湿接触线的移动分析

焦云龙; 刘小君; 逄明华; 刘焜

doi:10.7498/aps.65.016801

摘要

液滴在固体表面上的铺展行为与润湿特性对许多工业生产过程的研究具有重要意义. 根据液滴在光滑表面上的受力情况, 建立了液滴平壁铺展的动力学模型. 应用润滑近似方法和二维Navier-Stokes方程, 建立了液滴沿理想表面铺展的动量和连续性方程. 根据建立的方程, 应用数值解法求解并详细分析了液滴在铺展过程中膜厚、接触线铺展半径以及铺展速度随时间的变化关系. 研究结果表明: 液滴的铺展过程可分为扩展和收缩两个阶段, 铺展过程伴随着表面能、动能以及各种势能的相互转化, 液滴最终的铺展半径大小由固体基面固有的润湿特性所决定; 液滴在铺展过程中出现的坍塌效应与弯曲液面处的Laplace压力差有关; 铺展半径随时间变化的标定律近似满足1/7次方标度律.

关键词:

Abstract

Droplet spreading behavior on a substrate is closely bound up with the wettability of the substrate, and plays a critical role in many industrial applications, such as lubrication, painting, coating, and mineral flotation. In this paper, a dynamical model of droplet spreading on a smooth substrate is established through a mechanical analysis. According to the lubrication approximation theory and Navier-Stokes equation, a general nonlinear evolution equation or equations are derived, including the momentum equation, the continuity equation, and the evolution equation of film thickness. We adopt numerical methods to solve these equations, and also quantitatively analyze the relation among film thickness, spreading radius, speed of wetting contact line and time in detail. The results show that the droplet spreading process is mainly divided into two phases, namely expansion phase and contraction phase. Moreover, the spreading process is along with mutual transformation among surface energy, kinetic energy, and different kinds of potential energies. In addition, the final spreading radius Rf of droplet is determined by the inherent wettability of solid surface, and the collapse effect, which emerges at t=0.006 s in the spreading process, is related to Laplace pressure difference of curved liquid surface. Finally, by controlling the droplet size, we obtain the scaling law of droplet spreading radius with time, which approximately meets R ～ t1/7. The scaling law is validated both experimentally and numerically. The results of this study are expected to enhance our knowledge of the movement of wetting contact line and also provide some guidance for the wetting theory.

Keywords:

作者及机构信息

1.
合肥工业大学摩擦学研究所, 合肥 230009

通信作者: 刘焜, liukun@hfut.edu.cn

基金项目: 国家自然科学基金(批准号: 51375132)和高等学校博士学科点专项科研基金(批准号: 20120111110026)资助的课题.

Authors and contacts

1.
Institute of Tribology, Hefei University of Technology, Hefei 230009, China

Corresponding author: Liu Kun, liukun@hfut.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51375132) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120111110026).

参考文献

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[3]	Yuan Q Z, Zhao Y P 2013 Sci. Rep. 3 1944
[4]	Young T 1805 Phil. Trans. 95 65
[5]	Wenzel R N 1936 J. Ind. Eng. Chem. 28 988
[6]	Cassie A B D, Baxter S 1944 Trans. Faraday. Soc. 40 546
[7]	Lafuma A, Qur D 2003 Nat. Mater. 2 457
[8]	Mei M F, Yu B M, Luo L, Cai J C 2010 Chin. Phys. Lett. 27 076802
[9]	Wang Y X, Chen S 2015 Acta Phys. Sin. 64 054701 (in Chinese) [王宇翔, 陈硕 2015 物理学报 64 054701]
[10]	Blake T D 1969 J. Colloid Interf. Sci. 299 1
[11]	Oron A, Davis S H, Bankoff S G 1997 Rev. Mod. Phys. 69 931
[12]	de Gennes P G 1985 Rev. Mod. Phys. 57 827
[13]	Das S, Marchand A, Andreotti B, Snoeijer J H 2011 Phys. Fluids 23 072006
[14]	Yu Y S 2010 Ph. D. Dissertation (Beijing: Institute of Mechanics, Chinese Academy of Sciences) (in Chinese) [余迎松 2010 博士学位论文 (北京: 中国科学院力学研究所)]
[15]	Wang X D, Peng X F, He J C, Liu T 2002 J. Eng. Thermophys. 23 67 (in Chinese) [王晓东, 彭晓峰, 阂敬春, 刘涛 2002 工程热物理学报 23 67]
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[17]	Wang X D, Peng X F, Wang B X 2003 J. Basic Sci. Eng. 11 396 (in Chinese) [王晓东, 彭晓峰, 王补宣 2003 应用基础与工程科学学报 11 396]
[18]	Wang X D, Peng X F, Li D Z 2004 J. Chem. Ind. Eng. 55 402 (in Chinese) [王晓东, 彭晓峰, 李笃中 2004 化工学报 55 402]
[19]	Cao X P, Jiang Y M 2005 Acta Phys. Sin. 54 2202 (in Chinese) [曹晓平, 蒋亦民 2005 物理学报 54 2202]
[20]	Zhou J C, Geng X G, Lin K J, Zhang Y J, Zang D Y 2014 Acta Phys. Sin. 63 216801 (in Chinese) [周建臣, 耿兴国, 林可君, 张永健, 臧渡洋 2014 物理学报 63 216801]
[21]	Chen S, Tao Y, Shen S Q, Li D W 2014 Acta Mech. Sin. 46 329 (in Chinese) [陈石, 陶英, 沈胜强, 李德伟 2014 力学学报 46 329]
[22]	Barenblatt G I, Beretta E, Bertsch M 1977 Proc. Nat. Acad. Sci. 94 10024
[23]	Seong J K, Myoung W M, Kwang R L, Dae Y L, Woung S C, Ho Y K 2011 J. Fluid Mech. 680 477
[24]	Yuan Q Z, Zhao Y P 2013 J. Fluid Mech. 716 171
[25]	Navier C L M H 1823 Memories. De France VI. 6 389
[26]	Yuan Q Z, Zhao Y P 2010 Phys. Rev. Lett. 104 246101

施引文献

[1]	Becker J, Grun G 2005 J. Phys.: Condens. Mat. 17 291
[2]	Liu X C 2010 Ph. D. Dissertation (Xi'an: Northwest University) (in Chinese) [刘小川 2010 博士学位论文 (西安: 西北大学)]
[3]	Yuan Q Z, Zhao Y P 2013 Sci. Rep. 3 1944
[4]	Young T 1805 Phil. Trans. 95 65
[5]	Wenzel R N 1936 J. Ind. Eng. Chem. 28 988
[6]	Cassie A B D, Baxter S 1944 Trans. Faraday. Soc. 40 546
[7]	Lafuma A, Qur D 2003 Nat. Mater. 2 457
[8]	Mei M F, Yu B M, Luo L, Cai J C 2010 Chin. Phys. Lett. 27 076802
[9]	Wang Y X, Chen S 2015 Acta Phys. Sin. 64 054701 (in Chinese) [王宇翔, 陈硕 2015 物理学报 64 054701]
[10]	Blake T D 1969 J. Colloid Interf. Sci. 299 1
[11]	Oron A, Davis S H, Bankoff S G 1997 Rev. Mod. Phys. 69 931
[12]	de Gennes P G 1985 Rev. Mod. Phys. 57 827
[13]	Das S, Marchand A, Andreotti B, Snoeijer J H 2011 Phys. Fluids 23 072006
[14]	Yu Y S 2010 Ph. D. Dissertation (Beijing: Institute of Mechanics, Chinese Academy of Sciences) (in Chinese) [余迎松 2010 博士学位论文 (北京: 中国科学院力学研究所)]
[15]	Wang X D, Peng X F, He J C, Liu T 2002 J. Eng. Thermophys. 23 67 (in Chinese) [王晓东, 彭晓峰, 阂敬春, 刘涛 2002 工程热物理学报 23 67]
[16]	Wang X D, Peng X F, Li D Z 2003 Sci. China Ser. E 33 625 (in Chinese) [王晓东, 彭晓峰, 李笃中 2003 中国科学E辑 33 625]
[17]	Wang X D, Peng X F, Wang B X 2003 J. Basic Sci. Eng. 11 396 (in Chinese) [王晓东, 彭晓峰, 王补宣 2003 应用基础与工程科学学报 11 396]
[18]	Wang X D, Peng X F, Li D Z 2004 J. Chem. Ind. Eng. 55 402 (in Chinese) [王晓东, 彭晓峰, 李笃中 2004 化工学报 55 402]
[19]	Cao X P, Jiang Y M 2005 Acta Phys. Sin. 54 2202 (in Chinese) [曹晓平, 蒋亦民 2005 物理学报 54 2202]
[20]	Zhou J C, Geng X G, Lin K J, Zhang Y J, Zang D Y 2014 Acta Phys. Sin. 63 216801 (in Chinese) [周建臣, 耿兴国, 林可君, 张永健, 臧渡洋 2014 物理学报 63 216801]
[21]	Chen S, Tao Y, Shen S Q, Li D W 2014 Acta Mech. Sin. 46 329 (in Chinese) [陈石, 陶英, 沈胜强, 李德伟 2014 力学学报 46 329]
[22]	Barenblatt G I, Beretta E, Bertsch M 1977 Proc. Nat. Acad. Sci. 94 10024
[23]	Seong J K, Myoung W M, Kwang R L, Dae Y L, Woung S C, Ho Y K 2011 J. Fluid Mech. 680 477
[24]	Yuan Q Z, Zhao Y P 2013 J. Fluid Mech. 716 171
[25]	Navier C L M H 1823 Memories. De France VI. 6 389
[26]	Yuan Q Z, Zhao Y P 2010 Phys. Rev. Lett. 104 246101

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