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Molecular mechanisms of liquid slip

Published online by Cambridge University Press:  26 March 2008

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
Departament de Tecnologia, Universitat Pompeu Fabra, Barcelona, Spain
Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208, USA
Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA
Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA


It is now well-established that the liquid adjacent to a solid need not be stationary – it can slip. How this slip occurs is unclear. We present molecular-dynamics (MD) simulation data and results from an analytical model which support two mechanisms of slip. At low levels of forcing, the potential field generated by the solid creates a ground state which the liquid atoms preferentially occupy. Liquid atoms hop through this energy landscape from one equilibrium site to another according to Arrhenius dynamics. Visual evidence of the trajectories of individual atoms on the solid surface supports the view of localized hopping, independent of the dynamics outside a local neighbourhood. We call this defect slip. At higher levels of forcing, the entire layer slips together, obviating the need for localized defects and resulting in the instantaneous motion of all atoms adjacent to the solid. The appearance of global slip leads to an increase in the number of slipping atoms and consequently an increase in the slip length. Both types of slip observed in the MD simulations are described by a dynamical model in which each liquid atom experiences a force from its neighbouring liquid atoms and the solid atoms of the boundary, is sheared by the overlying liquid, and damped by the solid. In agreement with the MD observations, this model predicts that above a critical value of forcing, localized slipping occurs in which atoms are driven from low-energy sites, but only if there is a downstream site which has been vacated. Also as observed, above a second critical value, all the liquid atoms adjacent to the wall slip. Finally, the dynamical equation predicts that at extremely large values of forcing, the slip length approaches a constant value, in agreement with the MD simulation results.

Copyright © Cambridge University Press 2008

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Blake, T. D. 1990 Slip between a liquid and a solid: D. M. Tolstoi's (1952) theory reconsidered. Colloids Surfaces 47, 135145.Google Scholar
Bocquet, L. & Barrat, J.-L. 2007 Flow boundary conditions from nano- to micro-scales. Soft Matter 3, 685693.Google Scholar
Braun, O. M. & Kivshar, Y. S. 1998 Nonlinear dynamics of the Frenkel–Kontorova model. Phys. Rep. 306, 1108.Google Scholar
Braun, O. M., Kivshar, Yu. S. & Zelenshkaya, I. I. 1990 Kinks in the Frenkel-Kontorova model with long-range interparticle interactions. Phys. Rev. B 41, 71187138.Google Scholar
Eijkel, J. C. T. & van den Berg, A. 2005 Nanofluidics: What it is and what can we expect from it? Microfluid. Nanofluid. 1, 249267.Google Scholar
Floría, L. M. & Mazo, J. J. 1996 Dissipative dynamics of the Frenkel-Kontorova model. Adv. Phys. 45, 505598.Google Scholar
Glasstone, S., Laider, K. H. & Eyring, H. 1941 The Theory of Rate Processes. McGraw-Hill.Google Scholar
Hanggi, P., Talkner, P. & Borkovec, M. 1990 Reaction-rate theory: Fifty years after Kramers. Rev. Mod. Phys. 62, 251341.Google Scholar
Hoffman, R. L. 1983 A study of the advancing interface: II. Theoretical prediction of the dynamic contact angle in liquid-gas systems. J. Colloid Interface. Sci. 94, 470486.Google Scholar
Holt, J. K., Park, H. G., Wang, Y., Stadermann, M., Artyukhin, A. B., Grigoropoulos, C. P., Noy, A. & Bakajin, O. 2006 Fast mass transport through sub-2-nanometer carbon nanotubes. Science 312, 10341037.Google Scholar
Horn, R. G. & Israelachvili, J. N. 1981 Direct measurement of structural forces between two surfaces in a nonpolar liquid. J. Chem. Phys. 75, 14001411.Google Scholar
Koplik, J., Banavar, J. R. & Willemsen, J. F. 1989 Molecular dynamics of fluid flow at solid surfaces. Phys. Fluids A 1, 781794.Google Scholar
Lauga, E., Brenner, M. P. & Stone, H. A. 2005 Microfluidics: The no-slip boundary condition. In Handbook of Experimental Fluid Dynamics (ed. Foss, J., Tropea, C. & Yarin, A.), chap. 15. Springer.Google Scholar
Lichter, S., Martini, A., Snurr, R. Q. & Wang, Q. 2007 Liquid slip as a rate process. Phys. Rev. Lett. 98, 226001.Google Scholar
Lichter, S., Roxin, A. & Mandre, S. 2004 Mechanisms for liquid slip at solid surfaces. Phys. Rev. Lett. 93, 086001.Google Scholar
Majumder, M., Chopra, N., Andrews, R. & Hinds, B. J. 2005 Nanoscale hydrodynamics: enhanced flow in carbon nanotubes. Nature 438, 44.Google Scholar
Martini, A., Liu, Y. C., Snurr, R. Q. & Wang, Q. 2006 Molecular dynamics characterization of thin film viscosity for EHL simulation. Tribol. Lett. 21, 217225.Google Scholar
Neto, C., Evans, D. R., Bonaccurso, E., Butt, H.-J. & Craig, V. S. J. 2005 Boundary slip in Newtonian liquids: A review of experimental studies. Rep. Prog. Phys. 68, 28592897.Google Scholar
Roxin, A. 2004 Five projects in pattern formation, fluid dynamics, and computational neuroscience. PhD thesis, Northwestern University.Google Scholar
Sholl, D. S. & Johnson, J. K. 2006 Making high-flux membranes with carbon nanotubes. Science 312, 10031004.Google Scholar
Sokhan, V. P., Nicholson, D. & Quirke, N. 2001 Fluid flow in nanopores: An examination of hydrodynamic boundary conditions. J. Chem. Phys. 115, 38783887.Google Scholar
Steele, W. A. 1973 The physical interaction of gases with crystalline solids. Surface Sci. 36, 317352.Google Scholar
Thompson, P. A. & Robbins, M. O. 1990 Shear flow near solids: Epitaxial order and flow boundary conditions. Phys. Rev. A 41, 68306837.Google Scholar
Thompson, P. A. & Troian, S. M. 1997 A general boundary condition for liquid flow at solid surfaces. Nature 389, 360362.Google Scholar
Urbakh, M., Klafter, J., Gourdon, D. & Israelachvili, J. 2004 The nonlinear nature of friction. Nature 430, 525528.Google Scholar
Zhu, Y. & Granick, S. 2002 Limits of the hydrodynamics no-slip boundary condition. Phys. Rev. Lett. 88, 106102.Google Scholar