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Density and confinement effects on fluid velocity slip

Carlos Corral-Casas*, Yichong Chen, Matthew K. Borg, and Livio Gibelli†

  • Institute for Multiscale Themofluids, School of Engineering, The University of Edinburgh, Edinburgh EH9 3FB, United Kingdom

  • *c.corral-casas@imperial.ac.uk
  • †Corresponding author: livio.gibelli@ed.ac.uk
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Phys. Rev. Fluids 9, 034201 – Published 11 March, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.034201

Abstract

Understanding the velocity slip of fluids in channels of molecular length scales is essential for accurately manipulating their flow in engineering applications, such as in water desalination or, by reversing the process, osmotic power generation. This study addresses two major open questions, namely (a) the range of validity of the Navier-Stokes equations with slip boundary conditions in describing fluid flows within channels of molecular confinement, and (b) the effect of fluid density and confinement as well as surface properties, such as microscopic roughness and curvature, on fluid slippage along walls. Using a hard-sphere fluid model and describing the fluid-wall interactions by the Maxwell scattering kernel, an event-driven molecular dynamics simulation study was performed in planar and cylindrical channels of different sizes and accommodation coefficients with varying fluid densities. The results show that the well-known criterion for the slip solution, which is valid in rarefied conditions, also holds for a dense gas, i.e., the predictive accuracy improves with decreasing Knudsen numbers, as long as the channel size is larger than about ten molecular diameters. We also find that the key quantity influencing the friction coefficient of a fluid is the peak density at the walls, rather than the nominal density, the fluid confinement, or the channel curvature, as found in previous studies. In particular, higher nominal densities lead to higher density peaks, and therefore a decrease in slip, while tighter confinements lead to lower density peaks, and therefore an increase in slip, regardless of channel geometry. Furthermore, the velocity slip depends on the microscopic roughness via the Smoluchowski factor. These findings are a stepping stone towards a deeper understanding of the molecular mechanisms underlying fluid velocity slip in molecular-scale channels.

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References (51)

  1. M. Gad-el Hak, The fluid mechanics of microdevices-The Freeman Scholar Lecture, J. Fluids Eng. 121, 5 (1999).
  2. G. M. Kremer, An Introduction to the Boltzmann Equation and Transport Processes in Gases, 1st ed. (Springer, Berlin, 2010).
  3. N. G. Hadjiconstantinou, The limits of Navier-Stokes theory and kinetic extensions for describing small-scale gaseous hydrodynamics, Phys. Fluids 18, 111301 (2006).
  4. E. H. Kennard, Kinetic Theory of Gases, with an Introduction to Statistical Mechanics (McGraw-Hill, New York, 1938).
  5. W. Sparreboom, A. van den Berg, and J. C. Eijkel, Transport in nanofluidic systems: A review of theory and applications, New J. Phys. 12, 015004 (2010).
  6. N. Kavokine, R. R. Netz, and L. Bocquet, Fluids at the nanoscale: From continuum to subcontinuum transport, Annu. Rev. Fluid Mech. 53, 377 (2021).
  7. J. N. Israelachvili, Solvation, structural, and hydration forces, in Intermolecular and Surface Forces, 3rd ed., edited by J. N. Israelachvili (Academic Press, Boston, 2011), Chap. 15, pp. 341–380.
  8. G. J. Wang and N. G. Hadjiconstantinou, Why are fluid densities so low in carbon nanotubes? Phys. Fluids 27, 052006 (2015).
  9. L. Wu, H. Liu, J. M. Reese, and Y. Zhang, Non-equilibrium dynamics of dense gas under tight confinement, J. Fluid Mech. 794, 252 (2016).
  10. C. Corral-Casas, J. Li, M. K. Borg, and L. Gibelli, Knudsen minimum disappearance in molecular-confined flows, J. Fluid Mech. 945, A28 (2022).
  11. W. G. Pollard and R. D. Present, On gaseous self-diffusion in long capillary tubes, Phys. Rev. 73, 762 (1948).
  12. C. Cercignani and A. Daneri, Flow of a rarefied gas between two parallel plates, J. Appl. Phys. 34, 3509 (1963).
  13. M. Majumder, N. Chopra, R. Andrews, and B. J. Hinds, Enhanced flow in carbon nanotubes, Nature (London) 438, 44 (2005).
  14. J. K. Holt, H. G. Park, Y. Wang, M. Stadermann, A. B. Artyukhin, C. P. Grigoropoulos, A. Noy, and O. Bakajin, Fast mass transport through sub-2-nanometer carbon nanotubes, Science 312, 1034 (2006).
  15. M. Whitby, L. Cagnon, M. Thanou, and N. Quirke, Enhanced fluid flow through nanoscale carbon pipes, Nano Lett. 8, 2632 (2008).
  16. Q. Sheng, L. Gibelli, J. Li, M. K. Borg, and Y. Zhang, Dense gas flow simulations in ultra-tight confinement, Phys. Fluids 32, 092003 (2020).
  17. G. Hummer, J. C. Rasaiah, and J. P. Noworyta, Water conduction through the hydrophobic channel of a carbon nanotube, Nature (London) 414, 188 (2001).
  18. A. I. Skoulidas, D. M. Ackerman, J. K. Johnson, and D. S. Sholl, Rapid transport of gases in carbon nanotubes, Phys. Rev. Lett. 89, 185901 (2002).
  19. J. A. Thomas and A. J. H. McGaughey, Reassessing fast water transport through carbon nanotubes, Nano Lett. 8, 2788 (2008).
  20. I. Bitsanis, T. K. Vanderlick, M. Tirrell, and H. T. Davis, A tractable molecular theory of flow in strongly inhomogeneous fluids, J. Chem. Phys. 89, 3152 (1988).
  21. K. P. Travis, B. D. Todd, and D. J. Evans, Departure from Navier-Stokes hydrodynamics in confined liquids, Phys. Rev. E 55, 4288 (1997).
  22. X. D. Din and E. E. Michaelides, Kinetic theory and molecular dynamics simulations of microscopic flows, Phys. Fluids 9, 3915 (1997).
  23. P. A. Thompson and M. O. Robbins, Shear flow near solids: Epitaxial order and flow boundary conditions, Phys. Rev. A 41, 6830 (1990).
  24. P. A. Thompson and S. M. Troian, A general boundary condition for liquid flow at solid surfaces, Nature (London) 389, 360 (1997).
  25. J. L. Barrat and L. Bocquet, Influence of wetting properties on hydrodynamic boundary conditions at a fluid/solid interface, Faraday Discuss. 112, 119 (1999).
  26. C. Sendner, D. Horinek, L. Bocquet, and R. R. Netz, Interfacial water at hydrophobic and hydrophilic surfaces: Slip, viscosity, and diffusion, Langmuir 25, 10768 (2009).
  27. N. V. Priezjev and S. M. Troian, Influence of periodic wall roughness on the slip behaviour at liquid/solid interfaces: Molecular-scale simulations versus continuum predictions, J. Fluid Mech. 554, 25 (2006).
  28. S. Lichter, A. Roxin, and S. Mandre, Mechanisms for liquid slip at solid surfaces, Phys. Rev. Lett. 93, 086001 (2004).
  29. A. Martini, A. Roxin, R. Q. Snurr, Q. Wang, and S. Lichter, Molecular mechanisms of liquid slip, J. Fluid Mech. 600, 257 (2008).
  30. F.-C. Wang and Y.-P. Zhao, Slip boundary conditions based on molecular kinetic theory: The critical shear stress and the energy dissipation at the liquid–solid interface, Soft Matter 7, 8628 (2011).
  31. G. J. Wang and N. G. Hadjiconstantinou, Universal molecular-kinetic scaling relation for slip of a simple fluid at a solid boundary, Phys. Rev. Fluids 4, 064201 (2019).
  32. N. V. Priezjev, Rate-dependent slip boundary conditions for simple fluids, Phys. Rev. E 75, 051605 (2007).
  33. N. G. Hadjiconstantinou, An atomistic model for the Navier slip condition, J. Fluid Mech. 912, A26 (2021).
  34. N. G. Hadjiconstantinou and M. M. Swisher, On the equivalence of nonequilibrium and equilibrium measurements of slip in molecular dynamics simulations, Phys. Rev. Fluids 7, 114203 (2022).
  35. K. Falk, F. Sedlmeier, L. Joly, R. R. Netz, and L. Bocquet, Molecular origin of fast water transport in carbon nanotube membranes: Superlubricity versus curvature dependent friction, Nano Lett. 10, 4067 (2010).
  36. S. K. Kannam, B. D. Todd, J. S. Hansen, and P. J. Daivis, Interfacial slip friction at a fluid-solid cylindrical boundary, J. Chem. Phys. 136, 244704 (2012).
  37. B. Shan, P. Wang, R. Wang, Y. Zhang, and Z. Guo, Molecular kinetic modelling of nanoscale slip flow using a continuum approach, J. Fluid Mech. 939, A9 (2022).
  38. J. S. Hansen, B. D. Todd, and P. J. Daivis, Prediction of fluid velocity slip at solid surfaces, Phys. Rev. E 84, 016313 (2011).
  39. C. L. Navier, Mémoire sur les lois du Mouvement des Fluides, Mémoires de l'Académie Royale des Sciences de l'Institut de France 6, 389 (1823).
  40. L. Bocquet and J. L. Barrat, Flow boundary conditions from nano- to micro-scales, Soft Matter 3, 685 (2007).
  41. C. Herrero, T. Omori, Y. Yamaguchi, and L. Joly, Shear force measurement of the hydrodynamic wall position in molecular dynamics, J. Chem. Phys. 151, 041103 (2019).
  42. N. F. Carnahan and K. E. Starling, Equation of state for nonattracting rigid spheres, J. Chem. Phys. 51, 635 (1969).
  43. T. Pöschel and T. Schwager, Event-driven molecular dynamics, in Computational Granular Dynamics: Models and Algorithms, 1st ed. (Springer, Berlin, 2005), pp. 135–189.
  44. M. G. Verbeek, Smoluchowski thermostat: A realistic introduction of the tangential momentum accommodation coefficient, Phys. Rev. E 81, 046701 (2010).
  45. S. Varghese, J. S. Hansen, and B. D. Todd, Improved methodology to compute the intrinsic friction coefficient at solid-liquid interfaces, J. Chem. Phys. 154, 184707 (2021).
  46. L. Gibelli, Velocity slip coefficients based on the hard-sphere Boltzmann equation, Phys. Fluids 24, 022001 (2012).
  47. K. P. Travis and K. E. Gubbins, Poiseuille flow of Lennard-Jones fluids in narrow slit pores, J. Chem. Phys. 112, 1984 (2000).
  48. A. Frezzotti, A particle scheme for the numerical solution of the Enskog equation, Phys. Fluids 9, 1329 (1997).
  49. J. A. Thomas and A. J. H. McGaughey, Density, distribution, and orientation of water molecules inside and outside carbon nanotubes, J. Chem. Phys. 128, 084715 (2008).
  50. S. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys. 117, 1 (1995).
  51. P. Spijker, A. J. Markvoort, S. V. Nedea, and P. A. J. Hilbers, Computation of accommodation coefficients and the use of velocity correlation profiles in molecular dynamics simulations, Phys. Rev. E 81, 011203 (2010).

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Phys. Rev. Fluids 9, 034201– Published 11 March, 2024
  • Received 22 May 2023
  • Accepted 6 February 2024
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