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A general boundary condition for liquid flow at solid surfaces

Author

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  • Peter A. Thompson

    (The Celerity Group)

  • Sandra M. Troian

    (Princeton University)

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 behaviour—for 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 ‘feels’ 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.

Suggested Citation

  • Peter A. Thompson & Sandra M. Troian, 1997. "A general boundary condition for liquid flow at solid surfaces," Nature, Nature, vol. 389(6649), pages 360-362, September.
    • Handle: RePEc:nat:nature:v:389:y:1997:i:6649:d:10.1038_38686
    DOI: 10.1038/38686
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    Citations

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    Cited by:

    1. Wu, Yong Hong & Wiwatanapataphee, B. & Hu, Maobin, 2008. "Pressure-driven transient flows of Newtonian fluids through microtubes with slip boundary," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 5979-5990.
    2. Jing Zhu & Jiahui Cao, 2019. "Effects of Nanolayer and Second Order Slip on Unsteady Nanofluid Flow Past a Wedge," Mathematics, MDPI, vol. 7(11), pages 1-13, November.
    3. Haroon Ur Rasheed & Zeeshan Khan & Saeed Islam & Ilyas Khan & Juan L. G. Guirao & Waris Khan, 2019. "Investigation of Two-Dimensional Viscoelastic Fluid with Nonuniform Heat Generation over Permeable Stretching Sheet with Slip Condition," Complexity, Hindawi, vol. 2019, pages 1-8, December.
    4. Anand, Vishal, 2014. "Slip law effects on heat transfer and entropy generation of pressure driven flow of a power law fluid in a microchannel under uniform heat flux boundary condition," Energy, Elsevier, vol. 76(C), pages 716-732.
    5. Yunmin Ran & Volfango Bertola, 2024. "Achievements and Prospects of Molecular Dynamics Simulations in Thermofluid Sciences," Energies, MDPI, vol. 17(4), pages 1-30, February.
    6. Rahmatipour, Hamed & Azimian, Ahmad-Reza & Atlaschian, Omid, 2017. "Study of fluid flow behavior in smooth and rough nanochannels through oscillatory wall by molecular dynamics simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 159-174.
    7. Balaram Kundu & Sujit Saha, 2022. "Review and Analysis of Electro-Magnetohydrodynamic Flow and Heat Transport in Microchannels," Energies, MDPI, vol. 15(19), pages 1-51, September.
    8. Jafarimoghaddam, A. & Roşca, N.C. & Roşca, A.V. & Pop, I., 2021. "The universal Blasius problem: New results by Duan–Rach Adomian Decomposition Method with Jafarimoghaddam contraction mapping theorem and numerical solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 60-76.
    9. Aurore Quelennec & Jason J. Gorman & Darwin R. Reyes, 2022. "Amontons-Coulomb-like slip dynamics in acousto-microfluidics," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    10. Jun Niu & Ceji Fu & Wenchang Tan, 2012. "Slip-Flow and Heat Transfer of a Non-Newtonian Nanofluid in a Microtube," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-9, May.

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