1932
0
  1. Home
  2. A-Z Publications
  3. Annual Review of Fluid Mechanics
  4. Volume 56, 2024
  5. Article

Annual Review of Fluid Mechanics

Volume 56, 2024

Molecular Mechanics of Liquid and Gas Slip Flow

Abstract

By taking into account the inhomogeneity introduced by the presence of a solid boundary, slip-flow theory extends the range of applicability of the venerable Navier–Stokes description to smaller scales and into the regime where confinement starts to be important. Due to the inherently atomistic nature of solid–fluid interactions at their interface, slip flow can be described, at least in principle, predictively at this level. This review aims to summarize our current understanding of slip flow at the atomistic level in dilute gases and dense liquids. The discussion extends over the similarities and differences between slip in gases and liquids, characterization and measurement of slip by molecular simulation methods, models for predicting slip, and open questions requiring further investigation.

Keyword(s): kinetic theory, molecular dynamics, slip, small-scale hydrodynamics, solid–fluid interface
Loading

Article metrics loading...

/content/journals/10.1146/annurev-fluid-121021-014808
2024-01-19
2024-04-29
Loading full text...

Full text loading...

/deliver/fulltext/fluid/56/1/annurev-fluid-121021-014808.html?itemId=/content/journals/10.1146/annurev-fluid-121021-014808&mimeType=html&fmt=ahah

Literature Cited

  1. Alexeev D, Chen J, Walther JH, Giapis KP, Angelikopoulos P, Koumoutsakos P. 2015. Kapitza resistance between few-layer graphene and water: liquid layering effects. Nano Lett. 15:5744
     [Google Scholar]
  2. Allen MP, Tildesley DJ. 1989. Computer Simulation of Liquids Oxford, UK: Oxford Univ. Press
  3. Alosious S, Kannam SK, Sathian SP, Todd BD. 2019. Prediction of Kapitza resistance at fluid-solid interfaces. J. Chem. Phys. 151:194502
     [Google Scholar]
  4. Aoki K. 2001. Dynamics of rarefied gas flows: asymptotic and numerical analyses of the Boltzmann equation Paper presented at 39th Aerospace Sciences Meeting and Exhibit Reno, NV: AIAA Pap. 2001-0874
  5. Aoki K, Baranger C, Hattori M, Kosuge S, Martalo G et al. 2017. Slip boundary conditions for the compressible Navier-Stokes. J. Stat. Phys. 169:744–81
     [Google Scholar]
  6. Arkilic EB, Breuer KS, Schmidt MA. 2001. Mass flow and tangential momentum accommodation in silicon micromachined channels. J. Fluid Mech. 437:29–43
     [Google Scholar]
  7. Barrat JL, Bocquet L. 1999. Influence of wetting properties on hydrodynamic boundary conditions at a fluid/solid interface. Faraday Discuss. 112:119–28
     [Google Scholar]
  8. Bedeaux D, Albano AM, Mazur P. 1976. Boundary conditions and non-equilibrium thermodynamics. Physica A 82:438–62
     [Google Scholar]
  9. Bhatnagar PL, Gross EP, Krook M. 1954. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94:511–25
     [Google Scholar]
  10. Bird GA. 1994. Molecular Gas Dynamics and the Direct Simulation of Gas Flows Oxford, UK: Oxford Univ. Press
  11. Blake TD. 1990. Slip between a liquid and a solid: D.M. Tolstoi's (1952) theory reconsidered. Colloids Surf. 47:135–45
     [Google Scholar]
  12. Blake TD. 1993. Dynamic contact angles and wetting kinetics. Wettability JC Berg 251–309. Boca Raton, FL: CRC Press
     [Google Scholar]
  13. Blake TD. 2006. The physics of moving wetting lines. J. Colloid Interface Sci. 299:1–13
     [Google Scholar]
  14. Blake TD, De Coninck J. 2011. Dynamics of wetting and Kramer's theory. Eur. Phys. J. Spec. Top. 197:249–64
     [Google Scholar]
  15. Blake TD, Fernandez-Toledano J-C, Doyen G, De Coninck J. 2015. Forced wetting and hydrodynamic assist. Phys. Fluids 27:112101
     [Google Scholar]
  16. Blake TD, Haynes JM. 1969. Kinetics of liquid/liquid displacement. J. Colloid Interface Sci. 30:421–23
     [Google Scholar]
  17. Blake TD, Clarke A, De Coninck J, de Ruijter MJ. 1997. Contact angle relaxation during droplet spreading: comparison between molecular kinetic theory and molecular dynamics. Langmuir 13:064291
     [Google Scholar]
  18. Bocquet L, Barrat J-L. 1994. Hydrodynamic boundary conditions, correlation functions, and Kubo relations for confined fluids. Phys. Rev. E 49:3079–92
     [Google Scholar]
  19. Bocquet L, Charlaix E. 2010. Nanofluidics, from bulk to interfaces. Chem. Soc. Rev. 39:1073–95
     [Google Scholar]
  20. Bonn D, Eggers J, Indekeu J, Meunier J, Rolley E. 2009. Wetting and spreading. Rev. Model. Phys. 81:739–805
     [Google Scholar]
  21. Boon JP, Yip S. 1991. Molecular Hydrodynamics New York: Dover
  22. Bowles AP, Honig CDF, Ducker WA. 2011. No-slip boundary condition for weak solid-liquid interactions. J. Phys. Chem. C 115:8613–21
     [Google Scholar]
  23. Braun OM, Kivshar YS. 1998. Nonlinear dynamics of the Frenkel–Kontorova model. Phys. Rep. 306:1–108
     [Google Scholar]
  24. Brochard-Wyart F, de Gennes PG. 1992. Dynamics of partial wetting. Adv. Colloid Interface Sci. 39:1–11
     [Google Scholar]
  25. Camargo D, de la Torre JA, Delgado-Buscalioni R, Chejne F, Español P. 2019. Boundary conditions derived from a microscopic theory of hydrodynamics near solids. J. Chem. Phys. 150:144104
     [Google Scholar]
  26. Cercignani C. 1964. Higher order slip according to the linearized Boltzmann equation Rep. As-64-19 Univ. Calif. Berkeley:
  27. Cercignani C. 1988. The Boltzmann Equation and Its Applications New York: Springer-Verlag
  28. Cercignani C, Lampis M. 1971. Kinetic models and gas-surface interactions. Transp. Theory Stat. Phys. 1:101–14
     [Google Scholar]
  29. Cheng L, Fenter P, Nagy KL, Schlegel ML, Sturchio NC. 2001. Molecular-scale density oscillations in water adjacent to a mica surface. Phys. Rev. Lett. 87:156103
     [Google Scholar]
  30. Cottin-Bizonne C, Steinberger A, Cross B, Raccurt O, Charlaix E. 2008. Nanohydrodynamics: the intrinsic flow boundary condition on smooth surfaces. Langmuir 24:1165–72
     [Google Scholar]
  31. Cross B, Barraud C, Picard C, Léger L, Restagno F, Charlaix E. 2018. Wall slip of complex fluids: interfacial friction versus slip length. Phys. Rev. Fluids 3:062001
     [Google Scholar]
  32. De Coninck J, Blake TD. 2008. Wetting and molecular dynamics simulations of simple liquids. Annu. Rev. Mater. Res. 38:1–22
     [Google Scholar]
  33. de la Torre JA, Duque-Zumajo D, Camargo D, Español P. 2019. Microscopic slip boundary conditions in unsteady fluid flows. Phys. Rev. Lett. 123:264501
     [Google Scholar]
  34. de Ruijter MJ, Blake TD, De Coninck J. 1999. Dynamic wetting studied by molecular modeling simulations of droplet spreading. Langmuir 15:7836–47
     [Google Scholar]
  35. Duque-Zumajo D, de la Torre JA, Camargo D, Español P. 2019. Discrete hydrodynamics near solid walls: non-Markovian effects and the slip boundary condition. Phys. Rev. E 100:062133
     [Google Scholar]
  36. Eyring H. 1936. Viscosity, plasticity, and diffusion as examples of absolute reaction rates. J. Chem. Phys. 4:283–91
     [Google Scholar]
  37. Falk K, Sedlmeier F, Joly L, Netz RR, Bocquet L. 2010. Molecular origin of fast water transport in carbon nanotube membranes: superlubricity versus curvature dependent friction. Nano Lett. 10:4067–73
     [Google Scholar]
  38. Frenkel D, Smit B. 2002. Understanding Molecular Simulation San Diego, CA: Academic Press
  39. Giannakopoulos AE, Sofos F, Karakasidis TE, Liakopoulos A. 2012. Unified description of size effects of transport properties of liquids flowing in nanochannels. Int. J. Heat Mass Transf. 55:5087–92
     [Google Scholar]
  40. Glasstone S, Laidler KJS, Eyring H. 1941. The Theory of Rate Processes: The Kinetics of Chemical Reactions, Viscosity, Diffusion and Electrochemical Phenomena New York: McGraw-Hill
  41. Graur IA, Perrier P, Ghozlani W, Meolans JG. 2009. Measurements of tangential momentum accommodation coefficient for various gases in plane microchannel. Chem. Soc. Rev. 21:102004
     [Google Scholar]
  42. Gravelle S, Joly L, Detcheverry F, Ybert C, Cottin-Bizonne C, Bocquet L. 2013. Optimizing water permeability through the hourglass shape of aquaporins. PNAS 110:16367–72
     [Google Scholar]
  43. Hadjiconstantinou NG. 2003. Comment on Cercignani's second-order slip coefficient. Phys. Fluids 15:2352–54
     [Google Scholar]
  44. Hadjiconstantinou NG. 2005. Oscillatory shear-driven gas flows in the transition and free-molecular-flow regimes. Phys. Fluids 17:100611
     [Google Scholar]
  45. Hadjiconstantinou NG. 2006. The limits of Navier-Stokes theory and kinetic extensions for describing small-scale gaseous hydrodynamics. Phys. Fluids 18:111301
     [Google Scholar]
  46. Hadjiconstantinou NG. 2021. An atomistic model for the Navier slip condition. J. Fluid Mech. 912:A26
     [Google Scholar]
  47. Hadjiconstantinou NG, Garcia AL, Bazant MZ, He G. 2003. Statistical error in particle simulations of hydrodynamic phenomena. J. Comp. Phys. 187:274–97
     [Google Scholar]
  48. Hadjiconstantinou NG, Swisher MM. 2022a. An atomistic model for the thermal resistance of a fluid-solid interface. J. Fluid Mech. 934:R2
     [Google Scholar]
  49. Hadjiconstantinou NG, Swisher MM. 2022b. On the equivalence of nonequilibrium and equilibrium measurements of slip in molecular dynamics simulations. Phys. Rev Fluids 7:114203
     [Google Scholar]
  50. Hänggi P, Talkner P, Borkovec M. 1990. Reaction-rate theory: fifty years after Kramers. Rev. Model. Phys. 62:251–341
     [Google Scholar]
  51. Hansen JS, Todd BD, Daivis PJ. 2011. Prediction of fluid velocity slip at solid surfaces. Phys. Rev. E 84:016313
     [Google Scholar]
  52. Hatzikiriakos SG. 2012. Wall slip of molten polymers. Prog. Polymer Sci. 37:624–43
     [Google Scholar]
  53. Heyes DM, Dini D, Castigliola L, Dyre JC. 2019. Transport coefficients of the Lennard-Jones fluid close to the freezing line. J. Chem. Phys. 151:204502
     [Google Scholar]
  54. Hirschfelder JO, Curtiss CF, Bird RB. 1955. Molecular Theory of Gases and Liquids New York: Wiley
  55. Hollway LH. 1966. New statistical models for kinetic theory: method of construction. Phys. Fluids 9:1658–73
     [Google Scholar]
  56. Homolle TMM, Hadjiconstantinou NG. 2007. A low-variance deviational simulation Monte Carlo for the Boltzmann equation. J. Comput. Phys. 226:2341–58
     [Google Scholar]
  57. Huisman WJ, Peters JF, Zwanenburg MJ, de Vries SA, Derry TE et al. 1997. Layering of a liquid metal in contact with a hard wall. Nature 390:379–81
     [Google Scholar]
  58. Joseph S, Aluru NR. 2008. Why are carbon nanotubes fast transporters of water?. Nano Lett. 8:452–58
     [Google Scholar]
  59. Kavokine N, Netz RR, Bocquet L. 2021. Fluids at the nanoscale: from continuum to subcontinuum transport. Annu. Rev. Fluid Mech. 53:377–410
     [Google Scholar]
  60. Keeler JS, Blake TD, Lockerby DA, Sprittles JE. 2022. Putting the micro into the macro: a molecularly augmented hydrodynamic model of dynamic wetting applied to flow instabilities during forced dewetting. J. Fluid Mech. 953:A17
     [Google Scholar]
  61. Lauga E, Brenner M, Stone HA 2007. Microfluidics: the no slip boundary condition. Handbook of Experimental Fluid Mechanics C Tropea, A Yarin, JF Foss 1219–40. New York: Springer
     [Google Scholar]
  62. Lichter S, Roxin A, Mandre S. 2004. Mechanisms for liquid slip at solid surfaces. Phys. Rev. Lett. 93:8086001
     [Google Scholar]
  63. Martini A, Hsu H-Y, Patankar NA, Lichter S. 2008a. Slip at high shear rates. Phys. Rev. Lett. 100:20206001
     [Google Scholar]
  64. Martini A, Roxin A, Snurr RQ, Wang Q, Lichter S. 2008b. Molecular mechanisms of liquid slip. J. Fluid Mech. 600:257–69
     [Google Scholar]
  65. Mashayak SY, Aluru NR. 2012. Coarse-grained potential model for structural prediction of nanoconfined water. J. Chem. Theory Comput. 8:1828–40
     [Google Scholar]
  66. Mashayak SY, Motevaselian MH, Aluru NR. 2015. An EQT-CDFT approach to determine thermodynamic properties of confined fluids. J. Chem. Phys. 142:244116
     [Google Scholar]
  67. Maxwell JC. 1879. On stresses in rarefied gases arising from inequalities of temperature. Philos. Trans. R. Soc. 170:231–56
     [Google Scholar]
  68. Navier M. 1823. Mémoire sur les lois du mouvement des fluides. Mem. Acad. Sci. 6:389–440
     [Google Scholar]
  69. Niavarani A, Priezjev NV. 2008. Slip boundary conditions for shear flow of polymer melts past atomically flat surfaces. Phys. Rev. E 77:041606
     [Google Scholar]
  70. Oga H, Yamaguchi Y, Omory T, Merabia S, Joly L. 2019. Green-Kubo measurement of liquid-solid friction in finite-size systems. J. Chem. Phys. 151:054502
     [Google Scholar]
  71. Pahlavan AA, Freund JB. 2011. Effect of solid properties on slip at the fluid-solid interface. Phys. Rev. E 83:021602
     [Google Scholar]
  72. Peraud JPM, Hadjiconstantinou NG. 2016. Extending the range of validity of Fourier's law into the kinetic transport regime via asymptotic solution of the phonon Boltzmann transport equation. Phys. Rev. B 93:045424
     [Google Scholar]
  73. Perez-Hernandez G, Schmidt B. 2013. Anisotropy of the water–carbon interaction: molecular simulations of water in low-diameter carbon nanotubes. Phys. Chem. Chem. Phys. 15:4995–5006
     [Google Scholar]
  74. Priezjev NV. 2007. Rate-dependent slip boundary conditions for simple fluids. Phys. Rev. E 75:051605
     [Google Scholar]
  75. Priezjev NV. 2009. Shear rate threshold for the boundary slip in dense polymer melts. Phys. Rev. E 80:031608
     [Google Scholar]
  76. Priezjev NV, Darhuber AA, Troian SM. 2005. Slip behavior in liquid films on surfaces of patterned wettability: comparison between continuum and molecular dynamics simulations. Phys. Rev. E 71:4041608
     [Google Scholar]
  77. Priezjev NV, Troian SM. 2006. Influence of periodic wall roughness on the slip behavior at liquid/solid interfaces: molecular scale simulations versus continuum predictions. J. Fluid Mech. 554:25–46
     [Google Scholar]
  78. Radtke GA, Hadjiconstantinou NG, Takata S, Aoki K. 2012. On the second-order temperature jump coefficient of a dilute gas. J. Fluid Mech. 707:331–41
     [Google Scholar]
  79. Radtke GA, Wagner W, Hadjiconstantinou NG. 2011. Low-noise Monte Carlo simulation of the variable hard sphere gas. Phys. Fluids 23:030606
     [Google Scholar]
  80. Raghunathan AV, Park JH, Aluru NR. 2007. Interatomic potential-based semiclassical theory for Lennard-Jones fluids. J. Chem. Phys. 127:174701
     [Google Scholar]
  81. Risken H. 1989. The Fokker-Planck Equation: Methods of Solution and Applications New York: Springer
  82. Ruckenstein E, Rajora PJ. 1983. On the no slip boundary condition of hydrodynamics. J. Colloid Interface Sci. 96:488–91
     [Google Scholar]
  83. Sadr M, Hadjiconstantinou NG. 2023. A variance-reduced direct Monte Carlo simulation method for solving the Boltzmann equation over a wide range of rarefaction. J. Comput. Phys. 472:111677
     [Google Scholar]
  84. Secchi E, Marbach S, Nigues A, Stein D, Siria A, Bocquet L. 2016. Massive radius-dependent flow slippage in carbon nanotubes. Nature 537:210–13
     [Google Scholar]
  85. Sendner C, Horinek D, Bocquet L, Netz RR. 2009. Interfacial water at hydrophobic and hydrophilic surfaces: slip, viscosity and diffusion. Langmuir 25:10768–81
     [Google Scholar]
  86. Sharipov F. 2003. Application of the Cercignani-Lampis scattering kernel to calculations of rarefied flows. II. Slip and jump coefficients. Eur. J. Mech. B/Fluids 22:133–43
     [Google Scholar]
  87. Sharipov F. 2011. Data on the velocity slip and temperature jump on a gas-solid interface. J. Phys. Chem. Ref. Data 40:023101
     [Google Scholar]
  88. Sharipov F, Seleznev V. 1998. Data on internal rarefied gas flows. J. Phys. Chem. Ref. Data 27:657–706
     [Google Scholar]
  89. Sone Y. 2007. Molecular Gas Dynamics: Theory, Techniques, and Applications Boston: Birkhäuser
  90. Steele WA. 1973. The physical interaction of gases with crystalline solids. I. Gas-solid energies and properties of isolated adsorbed atoms. Surf. Sci. 36:317–52
     [Google Scholar]
  91. Takata S, Aoki K, Hattori M, Hadjiconstantinou NG. 2012. Parabolic temperature profile and second-order temperature jump of slightly rarefied gas in an unsteady two-surface problem. Phys. Fluids 24:032002
     [Google Scholar]
  92. Takata S, Hattori M. 2012a. Asymptotic theory for the time-dependent behavior of a slightly rarefied gas over a smooth solid boundary. J. Stat. Phys 147:1182–215
     [Google Scholar]
  93. Takata S, Hattori M. 2012b. On the second-order slip and jump coefficients for the general theory of slip flow. AIP Conf. Proc. 28th Int. Symp. Rarefied Gas Dyn. 1501:59–66
     [Google Scholar]
  94. Thompson PA, Troian SM. 1997. A general boundary condition for liquid flow at solid surfaces. Nature 389:6649360–62
     [Google Scholar]
  95. Tolstoi DM. 1952. Molecular theory for slippage of liquids over solid surfaces. Dokl. Acad. Nauk SSSR 85:1089
     [Google Scholar]
  96. Vincenti WG, Kruger CH. 1965. Introduction to Physical Gas Dynamics New York: Wiley
  97. Wakabayashi M, Ohwada T, Golse F. 1996. Numerical analysis of the shear and thermal creep flows of a rarefied gas over the plane wall of a Maxwell-type boundary condition on the basis of the linearized Boltzmann equation for hard-sphere molecules. Eur. J. Mech. B/Fluids 15:175–201
     [Google Scholar]
  98. Wang GJ, Damone A, Benfenati F, Poesio P, Beretta G-P, Hadjiconstantinou NG. 2019. Physics of nanoscale immiscible fluid displacement. Phys. Rev. Fluids 4:124203
     [Google Scholar]
  99. Wang GJ, Hadjiconstantinou N. 2015. Why are fluid densities so low in carbon nanotubes?. Phys. Fluids 27:052006
     [Google Scholar]
  100. Wang GJ, Hadjiconstantinou NG. 2017. Molecular mechanics and structure of the fluid-solid interface in simple fluids. Phys. Rev. Fluids 2:094201
     [Google Scholar]
  101. Wang GJ, Hadjiconstantinou NG. 2018. Layered fluid structure and anomalous diffusion under nanoconfinement. Langmuir 34:6976–82
     [Google Scholar]
  102. Wang GJ, Hadjiconstantinou NG. 2019. A universal molecular-kinetic scaling relation for slip of a simple fluid at a solid boundary. Phys. Rev. Fluids 4:064291
     [Google Scholar]
  103. Wenski TE, Olson T, Rettner CT, Garcia AL. 1998. Simulations of air slider bearings with realistic gas-surface scattering. J. Tribol. 120:639–41
     [Google Scholar]
  104. Zwanzig R, Mountain RD. 1965. High-frequency elastic moduli of simple fluids. J. Chem. Phys. 43:4464–71
     [Google Scholar]
/content/journals/10.1146/annurev-fluid-121021-014808
Loading
Molecular Mechanics of Liquid and Gas Slip Flow
Annual Review of Fluid Mechanics 56, 435 (2024); https://doi.org/10.1146/annurev-fluid-121021-014808
/content/journals/10.1146/annurev-fluid-121021-014808
/content/journals/10.1146/annurev-fluid-121021-014808
Loading

Data & Media loading...

  • Article Type: Review Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error