Please wait a minute...
Chin. Phys. B, 2019, Vol. 28(1): 016801    DOI: 10.1088/1674-1056/28/1/016801
CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES Prev   Next  

Approximate expression of Young's equation and molecular dynamics simulation for its applicability

Shu-Wen Cui(崔树稳)1,2, Jiu-An Wei(魏久安)2,3, Wei-Wei Liu(刘伟伟)1, Ru-Zeng Zhu(朱如曾)2, Qian Ping(钱萍)4
1 Department of Physics and Information Engineering, Cangzhou Normal University, Cangzhou 061001, China;
2 State Key Laboratory of Nonlinear Mechanics(LNM) and Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Science, Beijing 100190, China;
3 Silfex, a Division of Lam Research, 950 South Franklin Street, Eaton, Ohio, 45320, USA;
4 Department of Physics, University of Science and Technology Beijing, Beijing 100083, China
Abstract  

In 1805, Thomas Young was the first to propose an equation (Young's equation) to predict the value of the equilibrium contact angle of a liquid on a solid. On the basis of our predecessors, we further clarify that the contact angle in Young's equation refers to the super-nano contact angle. Whether the equation is applicable to nanoscale systems remains an open question. Zhu et al.[College Phys. 4 7 (1985)] obtained the most simple and convenient approximate formula, known as the Zhu-Qian approximate formula of Young's equation. Here, using molecular dynamics simulation, we test its applicability for nanodrops. Molecular dynamics simulations are performed on argon liquid cylinders placed on a solid surface under a temperature of 90 K, using Lennard-Jones potentials for the interaction between liquid molecules and between a liquid molecule and a solid molecule with the variable coefficient of strength a. Eight values of a between 0.650 and 0.825 are used. By comparison of the super-nano contact angles obtained from molecular dynamics simulation and the Zhu-Qian approximate formula of Young's equation, we find that it is qualitatively applicable for nanoscale systems.

Keywords:  molecular dynamics simulation      Young's equation      surface tension      Zhu-Qian approximate formula of Young'      s equation  
Received:  15 June 2018      Revised:  31 October 2018      Published:  05 January 2019
PACS:  68.08.Bc (Wetting)  
  68.03.Cd (Surface tension and related phenomena)  
  61.46.Fg (Nanotubes)  
  87.10.Tf (Molecular dynamics simulation)  
Fund: 

Project supported by the National Natural Science Foundation of China (Grant No. 11072242), the Key Scientific Studies Program of Hebei Province Higher Education Institute, China (Grant No. ZD2018301), and Cangzhou National Science Foundation, China (Grant No. 177000001).

Corresponding Authors:  Ru-Zeng Zhu     E-mail:  zhurz@lnm.imech.ac.cn

Cite this article: 

Shu-Wen Cui(崔树稳), Jiu-An Wei(魏久安), Wei-Wei Liu(刘伟伟), Ru-Zeng Zhu(朱如曾), Qian Ping(钱萍) Approximate expression of Young's equation and molecular dynamics simulation for its applicability 2019 Chin. Phys. B 28 016801

[1] Young T 1805 Philos. Trans. R. Soc. London 95 65
[2] Jameson G J and del Cerro M C G 1976 J. Chem. Soc. Furaduy I. 72 883
[3] White L R 1977 J. Chem. Soc. Faraday Trans 1. 73 390
[4] Gibbs J W 1957 The Collected Works of J Willard Gibbs (London: Yale University Press)
[5] Johnson R E 1959 J. Phys. Chem. 63 1655
[6] Barber A H, Cohen S R and Wagner H D 2004 Phys. Rev. Lett. 92 186103
[7] Delmas M, Monthioux M and Ondarc T 2011 Phys. Rev. Lett. 106 136102
[8] Roura P and Fort J 2004 J. Colloid Interface Sci. 272 420
[9] Ingebrigtsen T and Toxvaerd S 2007 J. Phys. Chem. C 111 8518
[10] Snoeijer J H and Andreotti B 2008 Phys. Fluids 20 057101
[11] Sikkenk J H, Indekeu J O and Menu G 1988 J. Stat. Phys. 52 23
[12] Nijmeijer M J P, Bruin C and Bakker A F 1990 Phys. Rev. A 42 6052
[13] Kimura T and Maruyama S 2002 Microscale Therm. Eng. 6 3
[14] Maruyama S, Kimura T and Lu M C 2002 Therm. Sci. & Eng. 6 23
[15] Seveno D, Blake T D and de Coninck J 2013 Phys. Rev. Lett. 111 096101
[16] Wang C, Lu H, Wang Z, Xiu P, Zhou B, Zuo G, Wan R, Hu J and Fang H 2009 Phys. Rev. Lett. 103 137801
[17] Nishida S, Surblys D, Yamaguchi Y, Kuroda K, Kagawa M, Nakajima T and Fujimura H 2014 J. Chem. Phys. 140 074707
[18] Fernandez-Toledano J C, Blake T D, Lambert P and de Coninck J 2017 Adv. Colloid Interface Sci. 245 102
[19] Cui S W, Zhu R Z, Wei J A, Wang X S, Yang H X, Xu S H and Sun Z W 2015 Acta Phys. Sin. 64 116802 (in Chinese)
[20] Berim G O and Ruckenstein E 2009 J. Chem. Phys. 130 044709
[21] Maruyama S 2000 Advances in Numerical Heat Transfer (Vol. 2) (Minkowycz W J and Sparrow E M Ed.) (New York: Taylor & Francis) p.189
[22] Sinha S 2004 Molecular dynamics simulation of interfacial tension and contact angle of Lennard-Jones fluid (Ph.D. Dissertation) (University of California, Los Angeles)
[23] Shi B 2006 Molecular dynamics simulation of the surface tension and contact angle of argon and water (Ph.D. Dissertation) (University of California, Los Angeles)
[24] Zhu R Z and Qian S W 1985 College Phys. 4 7 (in Chinese)
[25] Zhu R Z 1992 Mech. Eng. 14 14 (in Chinese)
[26] Adamson A M and Gast A P 1997 Physical Chemistry of Surfaces (New Jersey: Wiley-Interscience Press)
[27] Allen M P and Tildesley D J 1989 Computer Simulation of Liquids (New York: Oxford University Press)
[28] Leroy F and Müller-Plathe F 2010 J. Chem. Phys. 133 044110
[29] Grzelak E M and Errington J R 2008 J. Chem. Phys. 128 014710
[30] Nishida S, Surblys D, Yamaguchi Y, Kuroda K, Kagawa M, Nakajima T and Fujimura H 2014 J. Chem. Phys. 140 074707
[1] Tolman length of simple droplet: Theoretical study and molecular dynamics simulation
Shu-Wen Cui(崔树稳), Jiu-An Wei(魏久安), Qiang Li(李强), Wei-Wei Liu(刘伟伟), Ping Qian(钱萍), and Xiao Song Wang(王小松). Chin. Phys. B, 2021, 30(1): 016801.
[2] Size effect of He clusters on the interactions with self-interstitial tungsten atoms at different temperatures
Jinlong Wang(王金龙), Wenqiang Dang(党文强), Daping Liu(刘大平), Zhichao Guo(郭志超). Chin. Phys. B, 2020, 29(9): 093101.
[3] Oscillation of S5 helix under different temperatures in determination of the open probability of TRPV1 channel
Tie Li(李铁), Jun-Wei Li(李军委), Chun-Li Pang(庞春丽), Hailong An(安海龙), Yi-Zhao Geng(耿轶钊), Jing-Qin Wang(王景芹). Chin. Phys. B, 2020, 29(9): 098701.
[4] Different potential of mean force of two-state protein GB1 and downhill protein gpW revealed by molecular dynamics simulation
Xiaofeng Zhang(张晓峰), Zilong Guo(郭子龙), Ping Yu(余平), Qiushi Li(李秋实), Xin Zhou(周昕), Hu Chen(陈虎). Chin. Phys. B, 2020, 29(7): 078701.
[5] Balancing strength and plasticity of dual-phase amorphous/crystalline nanostructured Mg alloys
Jia-Yi Wang(王佳怡), Hai-Yang Song(宋海洋), Min-Rong An(安敏荣), Qiong Deng(邓琼), Yu-Long Li(李玉龙). Chin. Phys. B, 2020, 29(6): 066201.
[6] Molecular dynamics simulation of thermal conductivity of silicone rubber
Wenxue Xu(徐文雪), Yanyan Wu(吴雁艳), Yuan Zhu(祝渊), Xin-Gang Liang(梁新刚). Chin. Phys. B, 2020, 29(4): 046601.
[7] Anisotropic plasticity of nanocrystalline Ti: A molecular dynamics simulation
Minrong An(安敏荣), Mengjia Su(宿梦嘉), Qiong Deng(邓琼), Haiyang Song(宋海洋), Chen Wang(王晨), Yu Shang(尚玉). Chin. Phys. B, 2020, 29(4): 046201.
[8] Fractional variant of Stokes-Einstein relation in aqueous ionic solutions under external static electric fields
Gan Ren(任淦), Shikai Tian(田时开). Chin. Phys. B, 2020, 29(3): 036101.
[9] Lump and interaction solutions to the (3+1)-dimensional Burgers equation
Jian Liu(刘健), Jian-Wen Wu(吴剑文). Chin. Phys. B, 2020, 29(3): 030201.
[10] Alternative constitutive relation for momentum transport of extended Navier-Stokes equations
Guo-Feng Han(韩国锋), Xiao-Li Liu(刘晓丽), Jin Huang(黄进), Kumar Nawnit, and Liang Sun(孙亮). Chin. Phys. B, 2020, 29(12): 124701.
[11] Find slow dynamic modes via analyzing molecular dynamics simulation trajectories
Chuanbiao Zhang(张传彪), Xin Zhou(周昕). Chin. Phys. B, 2020, 29(10): 108706.
[12] Structural and dynamical mechanisms of a naturally occurring variant of the human prion protein in preventing prion conversion
Yiming Tang(唐一鸣), Yifei Yao(姚逸飞), Guanghong Wei(韦广红). Chin. Phys. B, 2020, 29(10): 108710.
[13] Density functional calculations of efficient H2 separation from impurity gases (H2, N2, H2O, CO, Cl2, and CH4) via bilayer g-C3N4 membrane
Yuan Guo(郭源), Chunmei Tang(唐春梅), Xinbo Wang(王鑫波), Cheng Wang(王成), Ling Fu(付玲). Chin. Phys. B, 2019, 28(4): 048102.
[14] A nonlocal Burgers equation in atmospheric dynamical system and its exact solutions
Xi-Zhong Liu(刘希忠), Jun Yu(俞军), Zhi-Mei Lou(楼智美), Xian-Min Qian(钱贤民). Chin. Phys. B, 2019, 28(1): 010201.
[15] Alkyl group functionalization-induced phonon thermal conductivity attenuation in graphene nanoribbons
Caiyun Wang(王彩云), Shuang Lu(鲁爽), Xiaodong Yu(于晓东), Haipeng Li(李海鹏). Chin. Phys. B, 2019, 28(1): 016501.
No Suggested Reading articles found!