Please wait a minute...
Friction  2022, Vol. 10 Issue (2): 200-208    doi: 10.1007/s40544-020-0396-x
Research Article     
Oscillating friction of nanoscale capillary bridge
Shuai WU1,2,Yuqing HE3,4,Quanshui ZHENG1,2,3,Ming MA2,3,4,*()
1 Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
2 Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
3 State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China
4 Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
Download: PDF (3255 KB)      HTML
Export: BibTeX | EndNote (RIS)      


The presence of a capillary bridge between solid surfaces is ubiquitous under ambient conditions. Usually, it leads to a continuous decrease of friction as a function of bridge height. Here, using molecular dynamics we show that for a capillary bridge with a small radius confined between two hydrophilic elastic solid surfaces, the friction oscillates greatly when decreasing the bridge height. The underlying mechanism is revealed to be a periodic ordered-disordered transition at the liquid-solid interfaces. This transition is caused by the balance between the surface tension of the liquid-vapor interface and the elasticity of the surface. This balance introduces a critical size below which the friction oscillates. Based on the mechanism revealed, a parameter-free analytical model for the oscillating friction was derived and found to be in excellent agreement with the simulation results. Our results describe an interesting frictional phenomenon at the nanoscale, which is most prominent for layered materials.

Key wordscapillary bridge      nano-confinement      elasticity      atomically smooth surface     
Received: 06 September 2019      Published: 17 January 2022
Fund:  Thousand Young Talents Program and the National Natural Science Foundation of China(11632009)
Corresponding Authors: Ming MA     E-mail:
About author: Shuai WU. He received his bachelor degree in civil engineering in 2012 from Nanchang University, Nanchang, China. Then, he studied for his doctorate in the Department of Engineering Mechanics at Tsinghua University. His research interests include nano/micro mechanics and super hydrophobicity.|Ming MA. He received his Ph.D. degree in engineering mechanics from Tsinghua University, China, in 2011. He joined the State Key Laboratory of Tribology at Tsinghua University since 2016. His current position is an associate professor. His research areas cover nanotribology, nanofluidics, superlubricity, and diffusion on surfaces or under confinement.
Cite this article:

Shuai WU,Yuqing HE,Quanshui ZHENG,Ming MA. Oscillating friction of nanoscale capillary bridge. Friction, 2022, 10(2): 200-208.

URL:     OR

Fig. 1 (a) A schematic of the simulation system; the liquid is embedded between two solid plates. The upper plate is pulled by a spring with the other moving at constant speed, and the lower plate is fixed. (b) Each plate is composed of two layers of atoms. The outer layers (grey) were frozen and the inner layers (red) were equilibrated at room temperature. (c) The magnitude of shear and normal force experienced by the plate as a function of the distance between plates.
Fig. 2 (a) In a typical periodic phase for the height varying from 2.69 to 1.77 (h=2.69, 2.45, 2.31, 2.18, 2.09, 2.00, 1.88, 1.77), the number of liquid layers changes from 4 to 3; this number can be easily obtained by counting the peaks. Correspondingly, the structure factor between the solid and the neighboring liquid layer is shown in (b-d), which indicates an ordered- (b for 4 layers, d for 3 layers) disordered (c for 3 layers) transition. (e, f) Lateral force and normal force for h=2.45 and 1.77, respectively.
Fig. 3 Comparison of FL and FN for a capillary bridge with (a) r=9.52 and (b) r=11.50 when h is 5.0. As r increases, the oscillating dependence of FL on h disappears, but remains for FN.
Fig. 4 (a) Schematic of the deformation of the plate and the capillary bridge under the pressure differential caused by surface tension. The magnitude of the deformation is enlarged for better visibility. (b) The corresponding shear force as a function of height.
2) is plotted as a solid curve.
Fig. 5 Phase diagram of the shear modes characterized by contact angle and elastic modulus. The stepped mode is in red and the continuous mode is in blue. The critical transition as predicted by Eq. (2) is plotted as a solid curve.
SolidLiquid E * θδγ h r c
Silicon[C4C1im][ NTf2]~20035~10.040.1-0.54.2-6.3
Table 1 Critical radius rc for some typical capillary bridge systems, H is about 1 nm in each condition, E*=E/(1-v2), the effective elastic modulus.
[1]   Xiao X, Qian L. Investigation of humidity-dependent capillary force. Langmuir 16: 8153-8158 (2000)
[2]   Choe H, Hong M H, Seo Y, Lee K, Kim G, Cho Y, Ihm J, Jhe W. Formation, manipulation, and elasticity measurement of a nanometric column of water molecules. Phys Rev Lett 95: 187801 (2005)
[3]   Bocquet L, Charlaix E, Ciliberto S, Crassous J. Moisture- nduced ageing in granular media and the kinetics of capillary condensation. Nature 396: 735 (1998)
[4]   Restagno F, Bocquet L, Biben T. Metastability and nucleation in capillary condensation. Phys Rev Lett 84: 2433-2436 (2000)
[5]   Jang J, Schatz G C, Ratner M A. How narrow can a meniscus be? Phys Rev Lett 92: 085504 (2004)
[6]   D?rmann M, Schmid H-J. Simulation of capillary bridges between nanoscale particles. Langmuir 30: 1055-1062 (2014)
[7]   Gennes P G D, Brochard-Wyart F, Quéré D. Capillarity and Wetting Phenomena. Springer, 2004.
[8]   Cheng S, Robbins M O. Capillary adhesion at the nanometer scale. Phys Rev E 89: 062402 (2014)
[9]   Cheng S, Robbins M O. Nanocapillary adhesion between parallel plates. Langmuir 32: 7788 (2016)
[10]   Valenzuela G E, Rozas R E, Toledo P G. Molecular dynamics simulation of nanoforces between substrates mediated by liquid bridges: Controlling separation and force fluctuations. J Phys Chem C 121: 25986-25993 (2017)
[11]   Riedo E, Lévy F, Brune H. Kinetics of capillary condensation in nanoscopic sliding friction. Phys Rev Lett 88: 185505 (2002)
[12]   Lancaster J K. A review of the influence of environmental humidity and water on friction, lubrication and wear. Tribol Int 23: 371-389 (1990)
[13]   Popov V L. Contact Mechanics and Friction: Physical Principles and Applications, 2nd Ed. Springer, 2017.
[14]   Raviv U, Laurat P, Klein J. Fluidity of water confined to subnanometre films. Nature 413: 51-54 (2001)
[15]   Zangi R, Mark A E. Monolayer ice. Phys Rev Lett 91: 025502 (2003)
[16]   Jinesh K B, Frenken J W M. Experimental evidence for ice formation at room temperature. Phys Rev Lett 101: 036101 (2008)
[17]   Cao W, Wang J, Ma M. Mechano-nanofluidics: Water transport through CNTs by mechanical actuation. Microfluid Nanofluid 22: 125 (2018)
[18]   Bo N J P, Spencer N D. Sliding friction: Physical principles and applications. Phys Today 52: 66-68 (1999)
[19]   Szoszkiewicz R, Riedo E. Nucleation time of nanoscale water bridges. Phys Rev Lett 95: 135502 (2005)
[20]   Noel O, Mazeran P-E, Nasrallah H. Sliding velocity dependence of adhesion in a nanometer-sized contact. Phys Rev Lett 108: 015503 (2012)
[21]   Barel I, Filippov A E, Urbakh M. Formation and rupture of capillary bridges in atomic scale friction. J Chem Phys 137: 164706 (2012)
[22]   Capozza R, Barel I, Urbakh M. Effect of Capillary Condensation on Nanoscale Friction. Springer International Publishing, 2015.
[23]   Lee M, Kim B, Kim J, Jhe W. Noncontact friction via capillary shear interaction at nanoscale, Nat Commun 6: 7359 (2015)
[24]   Becker T, Mugele F. Nanofluidics: Viscous dissipation in layered liquid films. Phys Rev Lett 91: 166104 (2003)
[25]   Bureau L. Nonlinear rheology of a nanoconfined simple fluid. Phys Rev Lett 104: 218302 (2010)
[26]   Geringer V, Liebmann M, Echtermeyer T, Runte S, Schmidt M, Ruckamp R, Lemme M C, Morgenstern M. Intrinsic and extrinsic corrugation of monolayer graphene deposited on SiO2. Phys Rev Lett 102: 076102 (2009)
[27]   Tunuguntla R H, Henley R Y, Yao Y C, Pham T A, Wanunu M, Noy A. Enhanced water permeability and tunable ion selectivity in subnanometer carbon nanotube porins. Science 357: 792 (2017)
[28]   Ouyang W, Ma M, Zheng Q, Urbakh M. Frictional properties of nanojunctions including atomically thin sheets. Nano Lett 16: 1878-1883 (2016)
[29]   Plimpton S. Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117: 1-19 (1995)
[30]   Neek-Amal M, Peeters F M, Grigorieva I V, Geim A K. Commensurability effects in viscosity of nanoconfined water. ACS Nano 10: 3685-3692 (2016)
[31]   Falk K, Sedlmeier F, Joly L, Netz R R, Bocquet L. Molecular origin of fast water transport in carbon nanotube membranes: Superlubricity versus curvature dependent friction. Nano Lett 10: 4067 (2010)
[32]   Allen M P, Tildesley D J. Computer Simulation of Liquids. New York (US): Oxford University Press, 1987.
[33]   Wu S, Ma M. A contact angle hysteresis model based on the fractal structure of contact line. J Colloid Interface Sci 505: 995-1000 (2017)
[34]   Timoshenko S P, Woinowsky-Krieger S. Theory of Plates and Shells. McGraw-hill, 1959.
[35]   Ge X, Halmans T, Li J, Luo J. Molecular behaviors in thin film lubrication-Part three: Superlubricity attained by polar and nonpolar molecules. Friction 7: 625-636 (2019)
[36]   Liu L, Zhou M, Jin L, Li L, Mo Y, Su G, Li X, Zhu H, Tian Y. Recent advances in friction and lubrication of graphene and other 2D materials: Mechanisms and applications. Friction 7: 199-216 (2019)
[37]   Gongyang Y, Ouyang W, Qu C, Urbakh M, Quan B, Ma M, Zheng Q. Temperature and velocity dependent friction of a microscale graphite-DLC heterostructure. Friction 8: 462-470 (2020)
[38]   Ma M, Tocci G, Michaelides A, Aeppli G. Fast diffusion of water nanodroplets on graphene. Nature Mater 15: 66-71 (2016)
[39]   Sung B, Kim J, Stambaugh C, Chang S J. Direct measurement of activation time and nucleation rate in capillary-condensed water nanomeniscus. Appl Phys Lett 103: 236102 (2013)
[40]   Giovambattista N, Almeida A B, Alencar A M, Buldyrev S V. Validation of capillarity theory at the nanometer scale by atomistic computer simulations of water droplets and bridges in contact with hydrophobic and hydrophilic surfaces. J Phys Chem C 120: 1597-1608 (2016)
[41]   Duan H, Wang J, Karihaloo B L. Theory of elasticity at the nanoscale. Adv Appl Mech 42: 1-68 (2009)
[42]   Piner R D, Zhu J, Xu F, Hong S, Mirkin C A. "Dip-pen" nanolithography. Science 283: 661-663 (1999)