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

疏水表面振动液滴模态演化与流场结构的数值模拟

叶欣 单彦广

引用本文:
Citation:

疏水表面振动液滴模态演化与流场结构的数值模拟

叶欣, 单彦广

Numerical simulation of modal evolution and flow field structure of vibrating droplets on hydrophobic surface

Ye Xin, Shan Yan-Guang
PDF
HTML
导出引用
  • 为了研究疏水表面垂直振动液滴的运动规律, 本文建立了振动液滴的三维模型, 考虑了振动液滴的动态接触角变化过程, 通过流体体积函数和连续表面张力(volume of fluid-continue surface force, VOF-CSF)方法实现了液滴受迫振动的数值模拟, 得到了液滴的四种模态(2, 4, 6和8)动态演化过程、内部流场结构以及动态接触角的变化规律. 随着振动加速度的改变, 液滴可表现出丰富的模态, 而具体模态依赖于振动加速度的频率变化. 以此为基础, 本文对液滴的内部流场结构做了进一步的分析. 在模态2和模态4时, 液滴内部流动从底部向上产生“Y”型流动, 而在模态6和模态8时呈现对称的涡流动. 且共振模态阶数越高, 液滴内部速度平均值越大. 液滴振动时的动态接触角明显偏离静态接触角, 表明液滴振动模型有必要考虑动态接触角. 模拟结果与文献中的实验结果做了对比, 结果符合良好.
    In order to understand the evolution and flow structure within vertical vibrating droplets on hydrophobic surfaces, a three-dimensional model of the vibrating droplet is developed, and the dynamic contact angle of the vibrating droplet is considered. The numerical simulations are performed for the droplet attached to the vertical vibrating plane by the VOF-CSF method, and the four resonance modes of the droplets are obtained. The evolution of modes (2, 4, 6, and 8), internal flow structures and the variation of the dynamic contact angle are predicted. With the change of the vibration acceleration, the droplet can express a wealth of modes, and the specific mode depends on the frequency of the vibrating acceleration. Based on this model, in this paper the internal flow field structure of the droplet is further analyzed. In mode 2 and mode 4, a Y-shaped flow is generated from the bottom of the droplet, while in mode 6 and mode 8, there is a symmetrical eddy flow. And the higher the order of the resonance mode, the larger the average value of the internal velocity of the droplet is. The dynamic contact angle of the vibrating droplet obviously deviates from the static contact angle, indicating the necessity to consider the dynamic contact angle in simulating the vertical vibrating of droplet. The simulation results are compared with the experimental results from the literature, showing that they are in good agreement with each other.
      通信作者: 单彦广, shan@usst.edu.cn
    • 基金项目: 国家自然科学基金 (批准号: 51676130)资助的课题
      Corresponding author: Shan Yan-Guang, shan@usst.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51676130)
    [1]

    Singhal V, Garimella S V, Raman A 2004 Appl. Mech. Rev. 57 191Google Scholar

    [2]

    Vukasinovic B, Smith M K, Glezer A 2004 Phys. Fluid 16 306Google Scholar

    [3]

    Nisisako T, Torri T 2007 Adv. Mater. 19 1489Google Scholar

    [4]

    Shan Y G, Wang Y L, Coyle T 2013 Appl. Therm. Eng. 51 690Google Scholar

    [5]

    高超, 袁俊杰, 曹进军, 杨荟楠, 单彦广 2019 物理学报 68 140204Google Scholar

    Gao C, Yuan J J, Cao J J, Yang H N, Shan Y G 2019 Acta Phys. Sin. 68 140204Google Scholar

    [6]

    张永建 2015 博士学位论文 (西安: 西北工业大学)

    Zhang Y J 2015 Ph. D. Dissertation (Xian: Northwestern Polytechnical University) (in Chinese)

    [7]

    Kabi P, Chattopadhyay B, Bhattacharyya S, Chaudhuri S, Basu S 2018 Langmuir 34 12642Google Scholar

    [8]

    Kelvin L 1882 Mathematical and Physical Papers (London: Cambridge University Press) pp178−181

    [9]

    Rayleigh L 1879 Proc. R. Soc. London 29 71Google Scholar

    [10]

    Lamb H 1932 Hydrodynamics (London: Cambridge University press) p606

    [11]

    Strani M, Sabetta F 1984 J. Fluid Mech. 141 233Google Scholar

    [12]

    Ko S H, Lee S J, Kang K H 2009 Appl. Phys. Lett. 94 194102Google Scholar

    [13]

    邵学鹏, 解文军 2012 物理学报 61 134302Google Scholar

    Shao X P, Xie W J 2012 Acta Phys. Sin. 61 134302Google Scholar

    [14]

    Brunet P, Eggers J, Deegan R D 2009 Eur. Phys. J-Spec. Top. 166 11Google Scholar

    [15]

    Noblin X, Buguin A, Brochard-Wyart F 2009 Eur. Phys. J. E 166 7Google Scholar

    [16]

    Dong L, Chaudhury A, Chaudhury M K 2006 Eur. Phys. J. E 21 231Google Scholar

    [17]

    周建臣, 耿兴国, 林可君, 张永建, 臧渡洋 2014 物理学报 63 216801Google Scholar

    Zhou J C, Geng X G, Lin K J, Zhang Y J, Zang D Y 2014 Acta Phys. Sin. 63 216801Google Scholar

    [18]

    Noblin X, Buguin A, Brochard-Wyart F 2004 Eur. Phys. J. E 14 395Google Scholar

    [19]

    Shin Y S, Lim H C 2014 Eur. Phys. J. E 37 1Google Scholar

    [20]

    Kim H, Lim H C 2015 J. Phys. Chem. B 119 6740Google Scholar

    [21]

    Park C S, Kim H, Lim H C 2016 Exp. Therm. Fluid Sci. 78 112Google Scholar

    [22]

    Ramos S M M 2008 Nucl. Instrum. Methods Phys. Res., Sect. B 266 3143Google Scholar

    [23]

    Ehrhorn J, Semke W 2013 Folia Parasit. 5 243Google Scholar

    [24]

    Li Y and Umemura A 2014 Int. J. Multiphase Flow 60 64Google Scholar

    [25]

    James A J, Smith M K and Glezer A 2003 J. Fluid Mech. 476 29Google Scholar

    [26]

    王瑞金, 张凯, 王刚 2007 Fluent技术基础与应用实例 (北京: 清华大学出版社) 第136−150页

    Wang R J, Zhang K, Wang G 2007 Fluent Technology Foundation and Application Examples (Beijing: Tsinghua University Press) pp136−150 (in Chinese)

    [27]

    Brackbill J U, Kothe D B, Zemach C 1992 J. Comput. Phys. 100 335Google Scholar

    [28]

    Chernova A A, Kopysov S P, Tonkov L E 2016 IOP Conference Series: Mater. Sci. Eng. 158 1Google Scholar

    [29]

    Kistler S F 1993 Wettability (New York: Marcel Dekker) pp311−429

  • 图 1  三维模拟计算区域(3 mm × 3 mm × 3 mm)

    Fig. 1.  3D computational domain (3 mm × 3 mm × 3 mm).

    图 2  疏水表面上液滴共振模态(2, 4, 6和8)的模拟结果与实验结果对比 (a)实验结果[20]; (b) 模拟结果

    Fig. 2.  Comparisons of the resonance modes (2, 4, 6, and 8) of a vibrating water drop on a hydrophobic surface: (a) Experimental results[20]; (b) simulation results.

    图 3  液滴在2, 4, 6和8共振模态下一个振动周期内形貌变化的实验[21]与模拟结果对比

    Fig. 3.  Comparisons between the experimental[21] and simulation results of the droplet shape evolution during one cycle of the vibration at resonance modes 2, 4, 6 and 8.

    图 4  在2, 4, 6和8模态下液滴内部的三维流场图

    Fig. 4.  The three-dimensional flow field inside the droplet at modes 2, 4, 6, and 8.

    图 5  液滴在2, 4, 6和8共振模态下内部流动结构的实验[20]与模拟结果对比 (a) 模态2; (b) 模态4; (c) 模态6; (d) 模态8

    Fig. 5.  Comparisons between the experimental[20]and simulation results of the internal flow structure of the droplet during the vibration at modes 2, 4, 6 and 8: (a) Mode 2; (b) mode 4; (c) mode 6; (d) mode 2.

    图 6  在2, 4, 6和8共振模态下液滴内部平均速度随时间的变化

    Fig. 6.  The variations of the velocity with time at modes 2, 4, 6, and 8.

    图 7  在模态2时液滴振动幅值随时间的变化. Num.1: 动态接触角; Num.2: 静态接触角; Exp.: 实验[20]

    Fig. 7.  The variations of droplet vibration amplitude with time at mode 2. Num.1: dynamic wetting angle; Num.2: static contact angle; Exp.: experiment[20].

    图 8  在2, 4, 6和8共振模态下液滴动态接触角随时间的变化

    Fig. 8.  The variations of the dynamic contact angle with time at modes 2, 4, 6, and 8.

    图 9  在2, 4, 6和8共振模态下液滴润湿面积随时间的变化

    Fig. 9.  The variations of the wetting area with time at modes 2, 4, 6, and 8.

    表 1  共振频率的理论值和实验值对比

    Table 1.  Comparisons of theoretical and experimental results for resonance frequency of a 5 ${\text{μ}}\mathrm{L}$ droplet.

    Mode nRayleigh方程
    计算值 f/Hz
    共振频率
    实验值 f/Hz
    29685
    4288226
    6526469
    8804635
    下载: 导出CSV

    表 2  液滴在模态2, 4, 6和8下中心底部的平均垂直速度的实验[20]与模拟对比

    Table 2.  Comparisons between the experimental[20] and simulation results of averaged vertical velocity at the central bottom region of the droplet in modes 2, 4, 6, and 8.

    模态模拟速度值/(mm·s–1)实验速度值/(mm·s–1)
    21.760.36
    43.370.79
    610.433.87
    811.053.61
    下载: 导出CSV
  • [1]

    Singhal V, Garimella S V, Raman A 2004 Appl. Mech. Rev. 57 191Google Scholar

    [2]

    Vukasinovic B, Smith M K, Glezer A 2004 Phys. Fluid 16 306Google Scholar

    [3]

    Nisisako T, Torri T 2007 Adv. Mater. 19 1489Google Scholar

    [4]

    Shan Y G, Wang Y L, Coyle T 2013 Appl. Therm. Eng. 51 690Google Scholar

    [5]

    高超, 袁俊杰, 曹进军, 杨荟楠, 单彦广 2019 物理学报 68 140204Google Scholar

    Gao C, Yuan J J, Cao J J, Yang H N, Shan Y G 2019 Acta Phys. Sin. 68 140204Google Scholar

    [6]

    张永建 2015 博士学位论文 (西安: 西北工业大学)

    Zhang Y J 2015 Ph. D. Dissertation (Xian: Northwestern Polytechnical University) (in Chinese)

    [7]

    Kabi P, Chattopadhyay B, Bhattacharyya S, Chaudhuri S, Basu S 2018 Langmuir 34 12642Google Scholar

    [8]

    Kelvin L 1882 Mathematical and Physical Papers (London: Cambridge University Press) pp178−181

    [9]

    Rayleigh L 1879 Proc. R. Soc. London 29 71Google Scholar

    [10]

    Lamb H 1932 Hydrodynamics (London: Cambridge University press) p606

    [11]

    Strani M, Sabetta F 1984 J. Fluid Mech. 141 233Google Scholar

    [12]

    Ko S H, Lee S J, Kang K H 2009 Appl. Phys. Lett. 94 194102Google Scholar

    [13]

    邵学鹏, 解文军 2012 物理学报 61 134302Google Scholar

    Shao X P, Xie W J 2012 Acta Phys. Sin. 61 134302Google Scholar

    [14]

    Brunet P, Eggers J, Deegan R D 2009 Eur. Phys. J-Spec. Top. 166 11Google Scholar

    [15]

    Noblin X, Buguin A, Brochard-Wyart F 2009 Eur. Phys. J. E 166 7Google Scholar

    [16]

    Dong L, Chaudhury A, Chaudhury M K 2006 Eur. Phys. J. E 21 231Google Scholar

    [17]

    周建臣, 耿兴国, 林可君, 张永建, 臧渡洋 2014 物理学报 63 216801Google Scholar

    Zhou J C, Geng X G, Lin K J, Zhang Y J, Zang D Y 2014 Acta Phys. Sin. 63 216801Google Scholar

    [18]

    Noblin X, Buguin A, Brochard-Wyart F 2004 Eur. Phys. J. E 14 395Google Scholar

    [19]

    Shin Y S, Lim H C 2014 Eur. Phys. J. E 37 1Google Scholar

    [20]

    Kim H, Lim H C 2015 J. Phys. Chem. B 119 6740Google Scholar

    [21]

    Park C S, Kim H, Lim H C 2016 Exp. Therm. Fluid Sci. 78 112Google Scholar

    [22]

    Ramos S M M 2008 Nucl. Instrum. Methods Phys. Res., Sect. B 266 3143Google Scholar

    [23]

    Ehrhorn J, Semke W 2013 Folia Parasit. 5 243Google Scholar

    [24]

    Li Y and Umemura A 2014 Int. J. Multiphase Flow 60 64Google Scholar

    [25]

    James A J, Smith M K and Glezer A 2003 J. Fluid Mech. 476 29Google Scholar

    [26]

    王瑞金, 张凯, 王刚 2007 Fluent技术基础与应用实例 (北京: 清华大学出版社) 第136−150页

    Wang R J, Zhang K, Wang G 2007 Fluent Technology Foundation and Application Examples (Beijing: Tsinghua University Press) pp136−150 (in Chinese)

    [27]

    Brackbill J U, Kothe D B, Zemach C 1992 J. Comput. Phys. 100 335Google Scholar

    [28]

    Chernova A A, Kopysov S P, Tonkov L E 2016 IOP Conference Series: Mater. Sci. Eng. 158 1Google Scholar

    [29]

    Kistler S F 1993 Wettability (New York: Marcel Dekker) pp311−429

  • [1] 张超, 布龙祥, 张智超, 樊朝霞, 凡凤仙. 丁二酸-水纳米气溶胶液滴表面张力的分子动力学研究. 物理学报, 2023, 72(11): 114701. doi: 10.7498/aps.72.20222371
    [2] 赵豪, 吴志豪, 胡晓红, 凡凤仙, 苏明旭. 外加液滴条件下固体细颗粒声凝并特性. 物理学报, 2023, 72(6): 064702. doi: 10.7498/aps.72.20221912
    [3] 刘博, 邢朴, 丁松, 谢明军, 冯林, 时晓天. 一种新的可计算可压缩流动的预处理方法. 物理学报, 2022, 71(12): 124701. doi: 10.7498/aps.71.20220102
    [4] 闫晨帅, 徐进良. 超临界压力CO2在水平圆管内流动传热数值分析. 物理学报, 2020, 69(4): 044401. doi: 10.7498/aps.69.20191513
    [5] 左娟莉, 杨泓, 魏炳乾, 侯精明, 张凯. 气力提升系统气液两相流数值模拟分析. 物理学报, 2020, 69(6): 064705. doi: 10.7498/aps.69.20191755
    [6] 周剑宏, 童宝宏, 王伟, 苏家磊. 油滴撞击油膜层内气泡的变形与破裂过程的数值模拟. 物理学报, 2018, 67(11): 114701. doi: 10.7498/aps.67.20180133
    [7] 魏梦举, 陈力, 伍涛, 张鸿雁, 崔海航. 微尺度空泡溃灭驱使微球运动的机理研究. 物理学报, 2017, 66(16): 164702. doi: 10.7498/aps.66.164702
    [8] 马理强, 苏铁熊, 刘汉涛, 孟青. 微液滴振荡过程的光滑粒子动力学方法数值模拟. 物理学报, 2015, 64(13): 134702. doi: 10.7498/aps.64.134702
    [9] 刘颖刚, 车伏龙, 贾振安, 傅海威, 王宏亮, 邵敏. 微纳光纤布拉格光栅折射率传感特性研究. 物理学报, 2013, 62(10): 104218. doi: 10.7498/aps.62.104218
    [10] 王勇, 林书玉, 莫润阳, 张小丽. 含气泡液体中气泡振动的研究. 物理学报, 2013, 62(13): 134304. doi: 10.7498/aps.62.134304
    [11] 刘邱祖, 寇子明, 韩振南, 高贵军. 基于格子Boltzmann方法的液滴沿固壁铺展动态过程模拟. 物理学报, 2013, 62(23): 234701. doi: 10.7498/aps.62.234701
    [12] 陈石, 王辉, 沈胜强, 梁刚涛. 液滴振荡模型及与数值模拟的对比. 物理学报, 2013, 62(20): 204702. doi: 10.7498/aps.62.204702
    [13] 胡海豹, 鲍路瑶, 黄苏和. 纳米通道内液态微流动密度分布特性数值模拟研究. 物理学报, 2013, 62(12): 124705. doi: 10.7498/aps.62.124705
    [14] 马理强, 刘谋斌, 常建忠, 苏铁熊, 刘汉涛. 液滴冲击液膜问题的光滑粒子动力学模拟. 物理学报, 2012, 61(24): 244701. doi: 10.7498/aps.61.244701
    [15] 马理强, 常建忠, 刘汉涛, 刘谋斌. 液滴溅落问题的光滑粒子动力学模拟. 物理学报, 2012, 61(5): 054701. doi: 10.7498/aps.61.054701
    [16] 朱昌盛, 王军伟, 王智平, 冯力. 受迫流动下的枝晶生长相场法模拟研究. 物理学报, 2010, 59(10): 7417-7423. doi: 10.7498/aps.59.7417
    [17] 赵啦啦, 刘初升, 闫俊霞, 蒋小伟, 朱艳. 不同振动模式下颗粒分离行为的数值模拟. 物理学报, 2010, 59(4): 2582-2588. doi: 10.7498/aps.59.2582
    [18] 王晓南, 邸洪双, 梁冰洁, 夏小明. 热连轧粗轧调宽轧制过程边角部金属流动三维数值模拟. 物理学报, 2009, 58(13): 84-S88. doi: 10.7498/aps.58.84
    [19] 董建军, 曹磊峰, 陈 铭, 谢常青, 杜华冰. 微聚焦菲涅耳波带板聚焦特性研究. 物理学报, 2008, 57(5): 3044-3047. doi: 10.7498/aps.57.3044
    [20] 任明星, 李邦盛, 杨 闯, 傅恒志. 微尺度型腔内液态金属流动规律模拟研究. 物理学报, 2008, 57(8): 5063-5071. doi: 10.7498/aps.57.5063
计量
  • 文章访问数:  4658
  • PDF下载量:  140
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-01-24
  • 修回日期:  2021-02-17
  • 上网日期:  2021-06-20
  • 刊出日期:  2021-07-20

/

返回文章
返回