搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

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

引用本文:
Citation:

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

Analyses of droplet spreading and the movement of wetting line on a solid surface

Jiao Yun-Long, Liu Xiao-Jun, Pang Ming-Hua, Liu Kun
PDF
导出引用
  • 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.
    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.
      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.
      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).
    [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

  • [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

  • [1] 张晓林, 黄军杰. 楔形体上复合液滴润湿铺展行为的格子Boltzmann方法研究. 物理学报, 2023, 72(2): 024701. doi: 10.7498/aps.72.20221472
    [2] 叶学民, 张湘珊, 李明兰, 李春曦. 自润湿流体液滴的热毛细迁移特性. 物理学报, 2018, 67(18): 184704. doi: 10.7498/aps.67.20180660
    [3] 程广贵, 张忠强, 丁建宁, 袁宁一, 许多. 石墨表面熔融硅的润湿行为研究. 物理学报, 2017, 66(3): 036801. doi: 10.7498/aps.66.036801
    [4] 叶学民, 李永康, 李春曦. 受热基底上的液滴铺展及换热特性. 物理学报, 2016, 65(23): 234701. doi: 10.7498/aps.65.234701
    [5] 郭进利. 非均齐超网络中标度律的涌现富者愈富导致幂律分布吗?. 物理学报, 2014, 63(20): 208901. doi: 10.7498/aps.63.208901
    [6] 郭进利, 祝昕昀. 超网络中标度律的涌现. 物理学报, 2014, 63(9): 090207. doi: 10.7498/aps.63.090207
    [7] 李丽, 李萍萍, 柯见洪, 夏海江, 林振权. 两种类粒子间的聚集与完全湮没竞争过程的标度行为. 物理学报, 2014, 63(11): 118201. doi: 10.7498/aps.63.118201
    [8] 邱丰, 王猛, 周化光, 郑璇, 林鑫, 黄卫东. Pb液滴在Ni基底润湿铺展行为的分子动力学模拟. 物理学报, 2013, 62(12): 120203. doi: 10.7498/aps.62.120203
    [9] 董宇蔚, 蔡世民, 尚明生. 电子商务中人类活动的标度行为实证研究. 物理学报, 2013, 62(2): 028901. doi: 10.7498/aps.62.028901
    [10] 毕菲菲, 郭亚丽, 沈胜强, 陈觉先, 李熠桥. 液滴撞击固体表面铺展特性的实验研究. 物理学报, 2012, 61(18): 184702. doi: 10.7498/aps.61.184702
    [11] 朱标, 李萍萍, 柯见洪, 林振权. 全局耦合网络上的两种类集团的聚集-湮没反应动力学. 物理学报, 2012, 61(6): 066802. doi: 10.7498/aps.61.066802
    [12] 谭振兵, 马丽, 刘广同, 吕力, 杨昌黎. 石墨烯量子霍尔平台与平台之间转变的标度律关系. 物理学报, 2011, 60(10): 107204. doi: 10.7498/aps.60.107204
    [13] 张丽萍, 温荣吉. 含有广义守恒律的生长方程标度奇异性的直接标度分析. 物理学报, 2009, 58(8): 5186-5190. doi: 10.7498/aps.58.5186
    [14] 郭进利, 汪丽娜. 幂律指数在1与3之间的一类无标度网络. 物理学报, 2007, 56(10): 5635-5639. doi: 10.7498/aps.56.5635
    [15] 何 阅, 姜玉梅, 申 影, 何大韧. 一个分段连续系统中的胖奇异集激变. 物理学报, 2005, 54(3): 1071-1080. doi: 10.7498/aps.54.1071
    [16] 范建平, 侯榆青, 汪颖梅, 何大韧, 吴顺光. V型阵发李雅普诺夫指数标度律的验证. 物理学报, 1998, 47(7): 1084-1089. doi: 10.7498/aps.47.1084
    [17] 朱顺泉, 谢发根, 胡岗. Duffing方程的分叉结构及其标度特性. 物理学报, 1992, 41(10): 1638-1646. doi: 10.7498/aps.41.1638
    [18] 吕燕南, 丁鄂江. 弱耦合满迭代中的标度行为. 物理学报, 1992, 41(4): 550-553. doi: 10.7498/aps.41.550
    [19] 刘鸿, 陈暧球, 李白文. Rb原子里德伯态的l混合跃迁截面及标度律. 物理学报, 1991, 40(12): 1909-1914. doi: 10.7498/aps.40.1909
    [20] 王光瑞, 陈式刚. 超临界圆映象的混沌测度及其标度律. 物理学报, 1990, 39(11): 1705-1713. doi: 10.7498/aps.39.1705
计量
  • 文章访问数:  7859
  • PDF下载量:  532
  • 被引次数: 0
出版历程
  • 收稿日期:  2015-04-28
  • 修回日期:  2015-08-25
  • 刊出日期:  2016-01-05

/

返回文章
返回