Molecular Dynamics of Slow Viscous Flows

  • J. R. Banavar
  • J. Koplik
  • J. F. Willemsen
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 53)


We use molecular dynamics techniques to study the microscopic aspects of several slow viscous flows past a solid wall, where both fluid and wall have a molecular structure. Systems of several thousand molecules are found to exhibit reasonable continuum behavior, albeit with significant thermal fluctuations. In Couette and Poiseuille flow of liquids we find the no—slip boundary condition arises naturally as a consequence of molecular roughness, and that the velocity and stress fields agree with the solutions of the Stokes equations. At lower densities slip appears, which can be incorporated into a flow—independent slip—length boundary condition. An immiscible two—fluid system is simulated by a species—dependent intermolecular interaction. We observe a static meniscus whose contact angle agrees with simple estimates and, when motion occurs, velocity—dependent advancing and receding angles. The local velocity field near a moving contact line shows a breakdown of the no—slip condition.


Contact Angle Contact Line Poiseuille Flow Slip Length Slip Boundary Condition 
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  1. 1.
    S. Goldstein, ed., “Modern Developments in Fluid Dynamics” (Oxford University Press, Oxford, 1938), Appendix. We thank G. M. Homsy for bringing this reference to our attention.MATHGoogle Scholar
  2. 2.
    G. K. Batchelor, “An Introduction to Fluid Dynamics” (Cambridge University Press, Cambridge, 1967).MATHGoogle Scholar
  3. 3.
    C. Huh and L. E. Scriven, J. Coll. Int. Sci. 35, 85 (1971).CrossRefGoogle Scholar
  4. 4.
    E. B. Dussan V., Ann. Rev. Fluid Mech. 11, 371 (1979).ADSCrossRefGoogle Scholar
  5. 5.
    P. G. De Gennes, Rev. Mod. Phys. 57, 827 (1985).ADSCrossRefGoogle Scholar
  6. 6.
    J. N. Israelachvili, P. M. McGuiggan and A. M. Homola, Science 240, 189 (1988).ADSCrossRefGoogle Scholar
  7. 7.
    D. D. Awschalom and J. Warnock, Phys. Rev. B 35, 6779 (1987).ADSCrossRefGoogle Scholar
  8. 8.
    M. P. Allen and D. J. Tildesley “Computer Simulation of Liquids” (Clarendon Press, Oxford, 1987).MATHGoogle Scholar
  9. 9.
    G. Coccotti and W. G. Hoover, eds., “Molecular-Dynamics Simulation of Statistical Mechanics Systems” (North-Holland, Amsterdam, 1986).Google Scholar
  10. 10.
    J. M. Haile, “A Primer on the Computer Simulation of Atomic Fluids by Molecular Dynamics” (Clemson University, Clemson, SC, 1980).Google Scholar
  11. 11.
    E. Meiburg, Phys. Fluids 29, 3107 (1986); D. C. Rapoport, Phys. Rev. A 36, 3288 (1987).ADSCrossRefGoogle Scholar
  12. 12.
    M. Mareschal and E. Kestamont, Nature 329, 427 (1987); J. Stat. Phys. 48, 1187 (1987); D. C. Rapoport, Phys. Rev. Lett. 60, 2480 (1988).ADSCrossRefGoogle Scholar
  13. 13.
    B. J. Alder and T. E. Wainwright, Phys. Rev. A 1, 18 (1970); W. E. Alley and B. J. Alder, ibid. 27, 3158 (1983); W. E. Alley and B. J. Alder, Phys. Today 37 (1), 56 (1984).ADSCrossRefGoogle Scholar
  14. 14.
    J. Koplik, J. R. Banavar and J. F. Willemsen, Phys. Rev. Lett. 60, 1282 (1988); Phys. Fluids A 1, 781 (1889).Google Scholar
  15. 15.
    J. C. Maxwell, Phil. Trans. Roy. Soc. 170, 231 (1867); see also R. Jackson, “Transport in Porous Catalysts” (Elsevier, Amsterdam, 1977).Google Scholar
  16. 16.
    G. N. Patterson, “Molecular Flow of Gases” (Wiley, New York, 1956); D. K. Bhattacharya and G. C. Lie, Phys. Rev. Lett. 62, 897 (1989).MATHGoogle Scholar
  17. 17.
    E. B. Dussan, and S. H. Davis, J. Fluid Mech. 65, 71 (1974).ADSMATHCrossRefGoogle Scholar
  18. 18.
    G. E. P. Elliot and A. C. Riddiford, J. Coll. Int. Sci. 23, 389 (1967).CrossRefGoogle Scholar
  19. 19.
    Y. Pomeau and A. Pumir, C. R Acad. Sci. 299, 909 (1984).Google Scholar
  20. 20.
    A. Nir, private communication (1988).Google Scholar
  21. 21.
    E. B. Dussan, J. Fluid Mech. 77, 665 (1976).ADSMATHCrossRefGoogle Scholar
  22. 22.
    S. Richardson, J. Fluid Mech. 59, 707 (1973); L. M. Hocking, J. Fluid Mech. 76, 801 (1976).ADSMATHCrossRefGoogle Scholar
  23. 23.
    K. M. Jansons, J. Fluid Mech. 154, 1 (1985); Phys. Fluids 31, 15 (1988).MathSciNetADSMATHCrossRefGoogle Scholar
  24. 24.
    J. N. Israelachvili and G. E. Adams, J. Chem. Soc. Faraday-Trans. I 74, 975 (1978).CrossRefGoogle Scholar
  25. 25.
    J. N. Israelachvili, “Intermolecular and Surface Forces” (Academic, London, 1985).Google Scholar
  26. 26.
    F. F. Abraham, J. Chem. Phys. 68, 3713 (1978); see also F. F. Abraham, Rept. Progr. Phys. 45, 1113 (1982).ADSCrossRefGoogle Scholar
  27. 27.
    S. Toxvaerd, J. Chem. Phys. 74, 1998 (1981).ADSCrossRefGoogle Scholar
  28. 28.
    J. J. Magda, M. Tirrell and H. T. Davis, J. Chem. Phys. 83, 1888 (1985).ADSCrossRefGoogle Scholar
  29. 29.
    J. Q. Broughton and G. H. Gilmer, J. Chem. Phys., 64, 5759 (1986), and earlier references therein.ADSCrossRefGoogle Scholar
  30. 30.
    J. Talion, Phys. Rev. Lett. 57, 1328 (1986).ADSCrossRefGoogle Scholar
  31. 31.
    P. A. Thompson and M. O. Robbins, Phys. Rev. Lett. 63, 766 (1989).ADSCrossRefGoogle Scholar
  32. 32.
    W. T. Ashurst and W. G. Hoover, Phys. Rev. A 11, 658 (1975).ADSCrossRefGoogle Scholar
  33. 33.
    S. A. Mikhailenko, B. G. Dudar and V. A. Schmidt, Sov. J. Low Temp. Phys. 1, 109 (1975).Google Scholar
  34. 34.
    W. G. Hoover, D. J. Evans, R. B. Hickman, A. J. C. Ladd, W. T. Ashurst and B. Moran, Phys. Rev. A 22, 1690 (1980).Google Scholar
  35. 35.
    D. M. Heyes, J. J. Kim, C. J. Montrose and T. A. Litovitz, J. Chem Phys. 73, 3987 (1980).ADSCrossRefGoogle Scholar
  36. 36.
    J.-P. Ryckaert, A. Bellemans, G. Cicotti, and G. A. Paolini, Phys. Rev. Lett. 60, 128 (1988).ADSCrossRefGoogle Scholar
  37. 37.
    J. H. Irving and J. G. Kirkwood, J. Chem. Phys. 18, 817 (1950).MathSciNetADSCrossRefGoogle Scholar
  38. 38.
    F. Y. Kafka and E. B. Dussan, J. Fluid Mech. 95, 539 (1979); E. B. Dussan V., AIChE J. 23, 131 (1977).MathSciNetADSMATHCrossRefGoogle Scholar
  39. 39.
    Although their solution cannot be correct down to the contact line, it can represent an outer or matching solution when combined with a slip boundary condition in the inner region near the wall; see Ref. 38.Google Scholar
  40. 40.
    D. D. Joseph, K. Nguyen and G. S. Beavers, J. Fluid Mech. 141, 319 (1984).ADSMATHCrossRefGoogle Scholar
  41. 41.
    K. Moffatt, J. Fluid Mech. 18, 1 (1964).ADSMATHCrossRefGoogle Scholar
  42. 42.
    G. K. Batchelor, “Theoretical and Applied Mechanics”, W. T. Kolter, ed. (North-Holland, Amsterdam, 1976).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • J. R. Banavar
    • 1
  • J. Koplik
    • 2
  • J. F. Willemsen
    • 3
  1. 1.Department of Physics and Materials Research LaboratoryPennsylvania State UniversityUniversity ParkUSA
  2. 2.Benjamin Levich Institute and Department of PhysicsCity College of the City University of New YorkNew YorkUSA
  3. 3.RSMAS — AMP, 4600 Rickenbacker CausewayUniversity of MiamiMiamiUSA

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