Abstract
Modelling fluid flows past a surface is a general problem in science and engineering, and requires some assumption about the nature of the fluid motion (the boundary condition) at the solid interface. One of the simplest boundary conditions is the no-slip condition1,2, which dictates that a liquid element adjacent to the surface assumes the velocity of the surface. Although this condition has been remarkably successful in reproducing the characteristics of many types of flow, there exist situations in which it leads to singular or unrealistic behaviourâfor example, the spreading of a liquid on a solid substrate3,4,5,6,7,8, corner flow9,10 and the extrusion of polymer melts from a capillary tube11,12,13. Numerous boundary conditions that allow for finite slip at the solid interface have been used to rectify these difficulties4,5,11,13,14. But these phenomenological models fail to provide a universal picture of the momentum transport that occurs at liquid/solid interfaces. Here we present results from molecular dynamics simulations of newtonian liquids under shear which indicate that there exists a general nonlinear relationship between the amount of slip and the local shear rate at a solid surface. The boundary condition is controlled by the extent to which the liquid âfeelsâ corrugations in the surface energy of the solid (owing in the present case to the atomic close-packing). Our generalized boundary condition allows us to relate the degree of slip to the underlying static properties and dynamic interactions of the walls and the fluid.
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References
Lamb, H. Hydrodynamics (Dover, New York, (1932)).
Batchelor, G. K. An Introduction to Fluid Dynamics (Cambridge Univ. Press, (1967)).
Huh, C. & Scriven, L. E. Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid. Interface. Sci. 35, 85â101 (1971).
Hocking, L. M. Amoving fluid interface on a rough surface. J. Fluid Mech. 76, 801â817 (1976).
Dussan, E. B. On the spreading of liquids on solid surfaces: static and dynamic contact lines. Annu. Rev. Fluid. Mech. 11, 371â400 (1979).
Koplik, J., Banavar, J. R. & Willemsen, J. F. Molecular dynamics of Poiseuille flow and moving contact lines. Phys. Rev. Lett. 60, 1282â1285 (1988); Molecular dynamics of fluid flow at solid surfaces. Phys. Fluids A 1, 781â794 (1989).
Thompson, P. A. & Robbins, M. O. Simulations of contact line motion: slip and the dynamic contact angle. Phys. Rev. Lett. 63, 766â769 (1989).
Thompson, P. A., Brinkerhoff, W. B. & Robbins, M. O. Microscopic studies of static and dynamic contact angles. J. Adhesion Sci. Technol. 7, 535â554 (1993).
Moffatt, H. K. Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18, 1â18 (1964).
Koplik, J. & Banavar, J. R. Corner flow in the sliding plate problem. Phys. Fluids 7, 3118â3125 (1995).
Pearson, J. R. A. & Petrie, C. J. S. in Polymer Systems: Deformation and Flow (eds Wetton, R. E. & Whorlow, R. W.) 163â187 (Macmillian, London, (1968)).
Richardson, S. On the no-slip boundary condition. J. Fluid Mech. 59, 707â719 (1973).
Denn, L. M. Issues in viscoelastic fluid mechanics. Annu. Rev. Fluid Mech. 22, 13â34 (1990).
Durbin, P. A. Considerations on the moving contact-line singularity, with application to frictional drag on a slender drop. J. Fluid Mech. 197, 157â169 (1988).
Koplik, J. & Banavar, J. R. Continuum deductions from molecular hydrodynamics. Annu. Rev. Fluid Mech. 27, 257â292 (1995).
Thompson, P. A. & Robbins, M. O. Shear flow near solids: epitaxial order and flow boundary conditions. Phys. Rev. A 41, 6830â6837 (1990).
Thompson, P. A. & Robbins, M. O. The origin of stick-slip motion in boundary lubrication. Science 250, 792â794 (1990).
Stevens, M. J. et al. Comparison of shear flow of hexadecane in a confined geometry and in bulk. J. Chem. Phys. 106, 7303â7314 (1997).
Allen, M. & Tildesley, D. Computer Simulation of Liquids (Clarendon, Oxford, (1987)).
Loose, W. & Hess, S. Rheology of dense fluids via nonequilibrium molecular hydrodynamics: shear thinning and ordering transition. Rheol. Acta. 28, 91â101 (1989).
Atwood, B. T. & Schowalter, W. R. Measurements of slip at the wall during flow of high-density polyethylene through a rectangular conduit. Rheol. Acta. 28, 134â146 (1989).
Rozman, M. G., Urbakh, M. & Klafter, J. Stick-slip motion and force fluctuations in a driven two-wave potential. Phys. Rev. Lett. 77, 683â686 (1996).
Acknowledgements
P.A.T. thanks the Exxon Education Foundation and an NSF CAREER award which helped initiate these studies. S.M.T. was supported by the Exxon Education Foundation and the NSF through a Research Initiation and CAREER award, and a seed grant from the MRSEC program of the Princeton Materials Institute.
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Thompson, P., Troian, S. A general boundary condition for liquid flow at solid surfaces. Nature 389, 360â362 (1997). https://doi.org/10.1038/38686
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DOI: https://doi.org/10.1038/38686
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