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液滴撞击固体表面是一种广泛存在于工农业生产中的现象. 随着微纳技术的发展, 纳米液滴撞击行为的定量描述有待完善. 采用分子动力学模拟纳米水滴撞击柱状粗糙铜固体表面的动态行为. 分别在液滴速度为2—15 Å/ps, 五种方柱高度和六种固体表面特征能的情况下分析液滴的动态特征. 结果表明, 随着液滴初始速度V0的增加, 其最终稳定状态先由Cassie态(V0 = 2—3 Å/ps)转变为Wenzel态(V0 = 4—10 Å/ps), 然后再次呈现Cassie态(V0 = 11—13 Å/ps). 当V0 > 13 Å/ps时, 液滴发生弹跳. 液滴最大铺展时间tmax与V0关系曲线中存在拐点, 并针对不同速度区域提出tmax与V0的关系式. 随着方柱高度的增加, 液滴的稳定状态由Wenzel向Cassie态转变, 液滴稳定状态的铺展半径逐渐减小. 固体表面特征能εs的增大使得液滴的铺展能力增强, 液滴铺展后的回缩现象逐渐减弱直至消失.Droplets’ impinging on a solid surface is a common phenomenon in industry and agriculture. With the development of micro and nano technology, the quantitative descriptions of impinging behaviors for nanodroplets are expected to be further explored. Molecular dynamics (MD) simulation is adopted to investigate the behaviors of water nanodroplets impinging on cooper surfaces which have been decorated with square nanopillars. The dynamical characteristics of nanodroplets are analyzed at 5 different pillar heights, 6 different surface characteristic energy values, and a wide range of droplet velocities. The results show that there is no obvious difference among the dynamical behaviors for nanodroplets, whose radii are in a range from 35 to 45 Å, impinging on a solid surface. With the increase of droplet velocity, the wetting pattern of steady nanodroplets first transfers from Cassie state (V0 = 2–3 Å/ps) to Wenzel state (V0 = 4–10 Å/ps), then it returns to the Cassie state (V0 = 11–13 Å/ps) again. Nanodroplets bounce off the solid surface when V0 > 13 Å/ps. The relationship between the maximum spreading time and droplet velocity is presented. Inflection points in the curve of the relationship are discovered and their formation mechanism is studied. The spreading factors of steady states for nanodroplets with velocity lower than 9 Å/ps are nearly the same; however, they decrease gradually for nanodroplets with velocity higher than 9 Å/ps. In addition, the increasing height of square nanopillars facilitates the transition from Wenzel state to Cassie state and reduces the spreading radius of steady nanodroplets. The mechanism, which yields Wenzel state when the nanodroplets impinge on solid surface with lower height nanopillars, is investigated. In the spreading stage, spreading radii of nanodroplets impinging on surfaces with different height nanopillars are almost identical. The influence of nanopillar height mainly plays a role in the retraction stage of droplets and it fades away as the height further increases. Moreover, the higher surface characteristic energy benefits the spreading of nanodroplets and reduces the retraction time. Especially, nanodroplets do not experience retraction stage, and the spreading stage is kept until the nanodroplets reach a stable state when the surface characteristic energy is increased to 0.714 kcal/mol. Compared with the spreading factor, the centroid height of nanodroplet is very sensitive to the change of surface characteristic energy.
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Keywords:
- nanodroplet /
- molecular dynamics simulations /
- impinge /
- dynamic behavior
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图 3 液滴尺寸对铺展时间t的影响 (a) 液滴在光滑固体表面上; (b) 液滴在柱状固体表面上
Fig. 3. Effects of droplets size on spreading time: (a) Droplets on the flat solid surfaces; (b) droplets on the nanopillared solid surfaces.
图 4 不同速度的液滴撞击柱状固体表面的动态行为
Fig. 4. Dynamic behaviors of droplets with various velocities impinging on nanopillared solid surfaces.
图 5 液滴质心高度h随铺展时间t的变化
Fig. 5. Time evolution of central height of droplets with different velocities.
图 6 最大铺展时间tmax随速度V0的变化
Fig. 6. The dependence of the maximum spreading time of droplets on velocities.
图 7 不同速度液滴的最大铺展状态
Fig. 7. The maximum spreading states of droplets with different velocities.
图 8 不同初始速度的液滴铺展因子β随时间t的变化 (a) V0 = 3—9 Å/ps; (b) V0 = 11—15 Å/ps
Fig. 8. Time evolution of spreading factor for droplets with different velocities: (a) V0 = 3−9 Å/ps; (b) V0 = 11−15 Å/ps.
图 9 不同初始速度液滴的最大铺展因子βmax
Fig. 9. The maximum spreading factor of droplets with different velocities.
图 10 液滴撞击不同方柱高度固体表面的稳定状态
Fig. 10. Steady states of droplets impinging on solid surfaces with nanopillars of different height.
图 12 不同方柱高度对液滴质心高度的影响
Fig. 12. Effects of nanopillars with different height on centroid height of droplets.
图 13 方柱高度对铺展因子的影响
Fig. 13. Dependence of spreading factor on the height of nanopillars.
图 14 方柱高度对铺展半径R的影响
Fig. 14. Dependence of spreading radius on the height of nanopillars.
图 15 液滴撞击不同特征能柱状固体表面的质心高度
Fig. 15. Centroid height of droplets impinging on surfaces with different characteristic energy.
图 16 液滴撞击具有不同特征能方柱表面时的铺展因子
Fig. 16. Time evolution of spreading factor of droplets impinging on surfaces with different characteristic energy.
表 1 液滴撞击柱状固体表面稳定状态时的润湿模式
Table 1. Wetting patterns of steady state of droplets impinging on nanopillared solid surfaces.
V0/(Å·ps–1) 2—3 4—10 11—13 14—15 润湿模式 Cassie Wenzel Cassie 弹跳 
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表 2 液滴撞击不同高度柱状表面后的稳定态润湿模式
Table 2. Wetting patterns of steady state of droplets impinging on surfaces with different height nanopillars.
方柱
高度H1 H2 H3 H4 H5 10.845 Å 14.460 Å 18.075 Å 21.690 Å 25.305 Å 润湿
模式Wenzel Wenzel Cassie Cassie Cassie
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表 3 不同
${\varepsilon _{\rm{s}}}$ 固体表面对应的${\varepsilon _{{\rm{s \text- o}}}}$ 及液滴接触角$ \theta $ Table 3. Corresponding
${\varepsilon _{{\rm{s \text- o}}}}$ and contact angles of droplets for solid surfaces with different${\varepsilon _{\rm{s}}}$ .${\varepsilon _{\rm{s}}}$/(kcal·mol–1) ${\varepsilon _{\rm{s}}}$/(kcal·mol–1) 接触角$ \theta $/$ (°) $ ${\varepsilon _{{\rm{s1}}}} = 0.5{\varepsilon _{{\rm{Cu}}}} = 0.119$ 0.139 125.9 ${\varepsilon _{{\rm{s2}}}} = 1.5{\varepsilon _{{\rm{Cu}}}} = 0.357$ 0.241 97.1 ${\varepsilon _{{\rm{s3}}}} = 2.0{\varepsilon _{{\rm{Cu}}}} = 0.476$ 0.278 80 ${\varepsilon _{{\rm{s4}}}} = 3.0{\varepsilon _{{\rm{Cu}}}} = 0.714$ 0.341 63 ${\varepsilon _{{\rm{s5}}}} = 4.0{\varepsilon _{{\rm{Cu}}}} = 0.952$ 0.394 45 ${\varepsilon _{{\rm{s6}}}} = 5.0{\varepsilon _{{\rm{Cu}}}} = 1.190$ 0.440 22
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[1] Galliker P, Schneider J, Eghlidi H, Kress S, Sandoghdar V, Poulikakos D 2012 Nat. Commun. 3 782
Google Scholar
[2] Bergeron V, Bonn D, Martin J Y, Vovelle L 2000 Nature 405 772
Google Scholar
[3] Zhou Z F, Chen B, Wang R, Wang G X 2017 Exp. Therm. Fluid Sci. 82 189
Google Scholar
[4] Chen X L, Li X M, Shao J Y, An N L, Tian H M, Wang C, Han T Y, Wang L, Lu B H 2017 Small 13 1604245
Google Scholar
[5] Pan K L, Chou P C, Tseng Y J 2009 Phys. Rev. E 80 036301
Google Scholar
[6] Deng X, Mammen L, Butt H, Vollmer D 2012 Science 335 67
Google Scholar
[7] Wang N, Xiong D S, Deng Y L, Shi Y, Wang K 2015 ACS. Appl. Mater. Interfaces 7 6260
Google Scholar
[8] Peng Y, He Y X, Yang S A, Ben S, Cao M Y, Li K, Liu K, Jiang L 2015 Adv. Funct. Mater. 25 5967
Google Scholar
[9] Rioboo R, Tropea C, Marengo M 2001 Atomization Spray. 11 155
Google Scholar
[10] 施其明, 贾志海, 林琪焱 2016 化工进展 35 3818
Google Scholar
Shi Q M, Jia Z H, Lin Q Y 2016 Chem. Ind. Eng. Prog. 35 3818
Google Scholar
[11] 彭家略, 郭浩, 尤天涯, 纪献兵, 徐进良 2021 物理学报 70 044701
Google Scholar
Peng J L, Guo H, You T Y, Ji X B, Xu J L 2021 Acta Phys. Sin. 70 044701
Google Scholar
[12] 顾秦铭, 张朝阳, 周晖, 张凯峰, 徐坤, 朱浩 2020 机械工程学报 56 223
Google Scholar
Gu Q M, Zhang C Y, Zhou H, Zhang K F, Xu K, Zhu H 2020 J. Mech. Eng. 56 223
Google Scholar
[13] Qi H C, Wang T Y, Che Z Z 2020 Phys. Rev. E 101 043114
Google Scholar
[14] Gao S, Liao Q W, Liu W, Liu Z C 2018 J. Phys. Chem. Lett. 9 13
Google Scholar
[15] Gao S, Liao Q W, Liu W, Liu Z C 2017 Langmuir 33 12379
Google Scholar
[16] Xie F F, Lv S H, Yang Y R, Wang X D 2020 J. Phys. Chem. Lett. 11 2818
Google Scholar
[17] 邱丰, 王猛, 周化光, 郑璇, 林鑫, 黄卫东 2013 物理学报 62 120203
Google Scholar
Qiu F, Wang M, Zhou H G, Zheng X, Lin X, Huang W D 2013 Acta Phys. Sin. 62 120203
Google Scholar
[18] Liu H Y, Chu F Q, Zhang J, Wen D S 2020 Phys. Rev. Fluids 5 074201
Google Scholar
[19] Wang Y B, Wang X D, Yang Y R, Chen M 2019 J. Phys. Chem. C. 123 12841
Google Scholar
[20] Yin Z J, Ding Z L, Zhang W F, Su R, Chai F T, Yu P 2020 Comput. Mater. Sci. 183 109814
Google Scholar
[21] Zhang M Y, Ma L J, Wang Q, Hao P, Zheng X 2020 Colloids Surf., A 604 125291
Google Scholar
[22] Jorgensen W L, Chandrasekhar J, Madura J D, Impey R W, Klein M L 1983 J. Chem. Phys. 79 926
Google Scholar
[23] Fu T, Wu N, Lu C, Wang J B, Wang Q L 2019 Mol. Simul. 45 35
Google Scholar
[24] Plimpton S 1995 J. Comput. Phys. 117 1
Google Scholar
[25] Song F H, Li B Q, Li Y 2015 Phys. Chem. Chem. Phys. 17 5543
Google Scholar
[26] Gonzalez-Valle C U, Kumar S, Ramos-Alvarado B 2018 The Journal of Physical Chemistry C 122 7179
Google Scholar
[27] Koishi T, Yasuoka K, Zeng X C 2017 Langmuir 33 10184
Google Scholar
[28] Cordeiro J, Desai S 2017 ASME J. Micro Nano-Manuf. 5 031008
Google Scholar
[29] 向恒 2008 博士学位论文 (北京: 清华大学)
Xiang H 2008 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese)
[30] Chen L, Wang S Y, Xiang X, Tao W Q 2020 Comput. Mater. Sci. 171 109223
Google Scholar
[31] 陈正隆 2007 分子模拟的实践与理论 (北京: 化学工业出版社) 第8页
Chen Z L 2007 Practice and Theory of Molecular Simulations (Beijing: Chemical Industry Press) p8 (in Chinese)
[32] Bekele S, Evans O G, Tsige M 2020 J. Phys. Chem.C. 124 20109
Google Scholar
[33] Essmann U, Perera L, Berkowitz M, Darden T, Lee H, Pedersen L 1995 J. Chem. Phys. 103 8577
[34] Hoover W G 1985 Phys. Rev. A 31 1695
Google Scholar
[35] Song F H, Li B Q, Liu C 2013 Langmuir 29 4266
Google Scholar
[36] 章佳健 2020 博士学位论文 (合肥: 中国科学技术大学)
Zhang J J 2020 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese)
[37] 成中军, 杜明, 来华, 张乃庆, 孙克宁 2013 高等学校化学学报 34 606
Google Scholar
Cheng Z J, Du M, Lai H, Zhang N Q, Sun K N 2013 Chem. J. Chin. Univ. 34 606
Google Scholar
[38] Hu H B, Chen L B, Bao L Y, Huang S H 2014 Chin. Phys. B. 23 074702
Google Scholar
[39] Wenzel R N 1936 Ind. Eng. Chem. 28 988
Google Scholar
[40] Cassie A B D, Baxter S 1944 Trans. Farad. Soc. 40 546
Google Scholar
[41] 焦云龙, 刘小君, 刘焜 2016 力学学报 48 353
Google Scholar
Jiao Y L, Liu X J, Liu K 2016 Chin J. Theor. Appl. Mech. 48 353
Google Scholar
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