Tribology Letters

, 67:114 | Cite as

On the Velocity Profile of Couette Flow of Lubricant Within a Micro/Submicro Gap

  • S. L. Han
  • F. GuoEmail author
  • J. Shao
  • Q. H. Bai
  • L. L. Han
Tribology Methods


The hydrodynamic lubrication properties of sliding bearings are influenced by the velocity profile under shear. However, at present, there are very few reports on the velocity profile distribution of the fluid film lubrication in conformal contacts. In this article, an apparatus was built for in situ measurement of the velocity profile of thin oil film under a micro/submicro gap at ambient pressure using a photobleached imaging technique and imaging the shape evolution of the bleached area under shear. The film thickness is calibrated by interferometry. The results show that the velocity profile of oligomer PB450 doped with a fluorescent agent is a typical linear distribution under higher film thickness, which is in accordance with the classical lubrication theory. When the gap of the disk and slider is less than 2 μm, there are obvious partial inhomogeneous shear flows at ambient pressure, and the slip length increases with the decreasing film thickness. Lubricants of different viscosities and molecular structures show an inhomogeneous flow transition at different confinements. Correspondingly, abnormal velocity profile results combined with generalized Reynolds equation could explain the phenomenon that the convergence ratio of the maximum load-carrying capacity is larger than 1.2 experiencing hydrodynamic lubrication. Hence, this work contributes to an improved understanding of rheology as well as more accurate predictions of tribological properties.


Photobleached imaging Slider–disk gap Film thickness Velocity profile Hydrodynamic lubrication 



The authors gratefully acknowledge the financial supports by the National Natural Science Foundation of China (Nos. 51605239, 51775286).

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflicts of interests.


  1. 1.
    Hamrock, B. J.: Fundamentals of Fluid -freq Lubrication, McGraw-Hill, New York (1994)Google Scholar
  2. 2.
    Thompson, P.A., Troian, S.M.: A general boundary condition for liquid flow at solid surfaces. Nature 389, 360–362 (1997)CrossRefGoogle Scholar
  3. 3.
    Barrat, J.L., Lydéric, B.: Large slip effect at a nonwetting fluid-solid interface. Phys. Rev. Lett. 82(23), 4671–4674 (1999)CrossRefGoogle Scholar
  4. 4.
    Bonaccurso, E., Kappl, M., Butt, H.J.: Hydrodynamic force measurements: boundary slip of water on hydrophilic surfaces and electrokinetic effects. Phys. Rev. Lett. 88(7), 076103 (2002)CrossRefGoogle Scholar
  5. 5.
    Spikes, H.A.: The half-wetted bearing. Part 1: extended Reynolds equation. Proc. Inst. Mech. Eng. J 217(1), 1–14 (2003)CrossRefGoogle Scholar
  6. 6.
    Guo, F., Wong, P.L.: Theoretical prediction of hydrodynamic effect by tailored boundary slippage. Proc. Inst. Mech. Eng. J 220(1), 43–48 (2006)CrossRefGoogle Scholar
  7. 7.
    Meng, X.K., Khonsari, M.M.: On the effect of viscosity wedge in micro-textured parallel surfaces. Tribol. Int. 107, 116–124 (2017)CrossRefGoogle Scholar
  8. 8.
    Guo, F., Wong, P.L.: Experimental observation of a dimple-wedge elastohydrodynamic lubricating film. Tribol. Int. 37(2), 119–127 (2004)CrossRefGoogle Scholar
  9. 9.
    Lumma, D., Best, A., Gansen, A., et al.: Flow profile near a wall measured by double-focus fluorescence cross-correlation. Phys. Rev. E 67(5), 056313 (2003)CrossRefGoogle Scholar
  10. 10.
    Li, J.X., Höglund, E., Westerberg, L.G., et al.: µPIV measurement of grease velocity profiles in channels with two different types of flow restrictions. Tribol. Int. 54, 94–99 (2012)CrossRefGoogle Scholar
  11. 11.
    Kuang, C., Wang, G.: A novel far-field nanoscopic velocimetry for nanofluidics. Lab Chip 10(2), 240 (2010)CrossRefGoogle Scholar
  12. 12.
    Pit, R.: Direct experimental evidence of slip in hexadecane: solid interfaces. Phys. Rev. Lett. 85(5), 980 (2000)CrossRefGoogle Scholar
  13. 13.
    Cuenca, A., Bodiguel, H.: Fluorescence photobleaching to evaluate flow velocity and hydrodynamic dispersion in nanoslits. Lab Chip 12(9), 1672–1679 (2012)CrossRefGoogle Scholar
  14. 14.
    Ponjavic, A., Chennaoui, M., Wong, J.S.S.: Through-thickness velocity profile measurements in an elastohydrodynamic contact. Tribol. Lett. 50(2), 261–277 (2013)CrossRefGoogle Scholar
  15. 15.
    Ponjavic, A., di Mare, L., Wong, J.S.S.: Effect of pressure on the flow behavior of polybutene. J. Polym Sci. B 52(10), 708–715 (2014)CrossRefGoogle Scholar
  16. 16.
    Han, S., Li, C., Guo, F., et al.: Velocity profile measurement of oil films in a confined gap based on FRAP. Opt. Preci. Eng. 25(1), 141–147 (2017)CrossRefGoogle Scholar
  17. 17.
    Bai, Q.H., Guo, F., Wong, P.L., et al.: Online measurement of lubricating film thickness in slider-on-disc contact based on dichromatic optical interferometry. Tribol. Lett. 65(4), 145 (2017)CrossRefGoogle Scholar
  18. 18.
    Guo, F., Yang, S.Y., Ma, C., et al.: Experimental study on lubrication film thickness under different interface wettabilities. Tribol. Lett. 54(1), 81–88 (2014)CrossRefGoogle Scholar
  19. 19.
    Guo, F., Wong, P.L., Fu, Z., et al.: Interferometry measurement of lubricating films in slider-on-disc contacts. Tribol. Lett. 39(1), 71–79 (2010)CrossRefGoogle Scholar
  20. 20.
    Brunet, F., Cid, E., Bartoli, A.: Simultaneous image registration and monocular volumetric reconstruction of a fluid flow. In: Proceedings of the British Machine Vision Conference, pp. 83.1–83.11. (2011)Google Scholar
  21. 21.
    Meurisse, M.H., Morales Espejel, G.: Reynolds equation, apparent slip, and viscous friction in a three-layered fluid film. Proc. Inst. Mech. Eng. J 222(3), 369–380 (2008)CrossRefGoogle Scholar
  22. 22.
    Cuenca, A., Bodiguel, H.: Submicron flow of polymer solutions: slippage reduction due to confinement. Phys. Rev. Lett. 110(10), 108304 (2013)CrossRefGoogle Scholar
  23. 23.
    Drummond, C., Israelachvili, J.: Dynamic behavior of confined branched hydrocarbon lubricant fluids under shear. Macromolecules 33(13), 4910–4920 (2000)CrossRefGoogle Scholar
  24. 24.
    Silliman, W.J., Secriven, L.: Separating how near a static contact line: slip at a wall and shape of a free surface. J. Comput. Phys. 34(3), 287–313 (1980)CrossRefGoogle Scholar
  25. 25.
    Neto, C., Evans, D.R., Bonaccurso, E., et al.: Boundary slip in Newtonian liquids: a review of experimental studies. Rep. Prog. Phys. 68(12), 2859 (2005)CrossRefGoogle Scholar
  26. 26.
    H´enot, M., Grzelka, M., Zhang, J., et al.: Temperature-controlled slip of polymer melts on ideal substrates. Phys. Rev. Lett. 121, 177802 (2018)CrossRefGoogle Scholar
  27. 27.
    Ponjavic, A., Wong, J.S.: The effect of boundary slip on elastohydrodynamic lubrication. RSC Adv. 4(40), 20821–20829 (2014)CrossRefGoogle Scholar
  28. 28.
    Yang, P., Wen, S.: A generalized Reynolds equation for non-Newtonian thermal elastohydrodynamic lubrication. J. TRIBOL-T ASME 112(4), 631–636 (1990)CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical and Automotive EngineeringQingdao University of TechnologyQingdaoPeople’s Republic of China
  2. 2.Sinosteel Xingtai Machinery & Mill Roll Co., LTDXingtaiPeople’s Republic of China

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