Skip to main content

Part of the book series: NATO Science Series ((NAII,volume 10))

Abstract

The Navier-Stokes equations can be employed to study fluid motion under ordinary conditions. However, to find solutions to these equations is far from elementary, and in applications we search for ways to simplify them. Such simplification is made particularly easy for lubricant films, where we make use of thin film geometry to derive the Reynolds theory of lubrication. Though the Reynolds equation is employed extensively in numerous technical fields, there are two factors, one geometrical and the other material, that limit its applicability.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  • Albertoni, S., Cercignani, C. and Gotusso, L. (1963), “Numerical Evaluation of the Slip Coefficient”, Phys. Fluids, 6, 993–996.

    Article  Google Scholar 

  • Alexander, F. J., Garcia, A. L. and Aider, B. J. (1994), “Direct Simulation Monte Carlo for Thin Film Bearings”, Phys. Fluids 6(12), 3854–3860.

    Article  CAS  Google Scholar 

  • Ballal, B. and Rivlin, R. S. (1976), “Flow of a Newtonian fluid Between Eccentric Rotating Cylinders”, Arch. Rat. Mech. Anal., 62, 237–274.

    Article  Google Scholar 

  • Bhatnagar, P. L., Gross, E. P. and Krook, M. (1954), “A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems”, Phys. Review, 94, 511–525.

    Article  CAS  Google Scholar 

  • Beskok, A., Karniadakis, G. E. and Trimmer, W. (1996), “Rarefaction and Compressibility in Gas Microflows”, J. Fluids Eng., 118, 448–456.

    Article  CAS  Google Scholar 

  • Bird, G. A. (1994), Molecular Gas Dynamics And The Direct Simulation Of Gas Flows, Clarendon Press, Oxford.

    Google Scholar 

  • Burgdorfer, A. (1959), “The Influence of Molecular Mean Free Path on the Performance of Hydrodynamic Gas Lubricated Bearings”, J. Basic Engr., 81, 94–100.

    Google Scholar 

  • Cercignani, C. (1988), The Boltzman Equation And Its Applications, Springer-Verlag, New York.

    Book  Google Scholar 

  • Cercignani, C. and Daneri, A. (1963), “Flow of a Rarefied Gas Between Two Parallel Plates”, J. Appl. Phys., 34, 3509–3513.

    Article  Google Scholar 

  • Cercignani, C. and Pagani, C. D. (1966), Phys. Fluids, 6, 1167–1175.

    Article  Google Scholar 

  • Chan, D. Y. C. and Horn, R. G. (1985), “The Drainage of Thin Liquid Films Between Solid Surfaces”, J. Chem. Phys., 83, 5311–5324.

    Article  CAS  Google Scholar 

  • Dai, R. X., Dong, Q. M. and Szeri, A. Z. (1992a), “Approximations in Hydrodynamic Lubrication”, J. Tribology, 114, 14–25.

    Article  CAS  Google Scholar 

  • Dai, R. X., Dong, Q. M. and Szeri, A. Z. (1992b), “Flow Between Eccentric Rotating Cylinders: Bifurcation and Stability”, Internat. J. Engrg. Sci., 30, 1323–1340.

    Article  CAS  Google Scholar 

  • Debye, P. and Cleland, R. L. (1959), “Flow of Liquid Hydrocarbons in Porous Vycor”, J. Appl. Phys., 30, 843–849.

    Article  CAS  Google Scholar 

  • Din, X. D. and Michaelides, E. E. (1997), “Kinetic Theory and Molecular Dynamics Simulation of Microscopic Flows”, Phys. Fluids, 9, 3915–3925.

    Article  CAS  Google Scholar 

  • DiPrima, R. C. and Stuart, J. T. (1972), “Non-Local Effects in the Stability of Flow Between Eccentric Rotating Cylinders”, J. Fluid Mech., 54, 393–415.

    Article  Google Scholar 

  • DiPrima, R. C. and Stuart, J. T. (1975), “The Nonlinear Calculation of Taylor Vortex Flow Between Eccentric Rotating Cylinders”, J. Fluid Mech., 67, 85–111.

    Article  Google Scholar 

  • Fukui, S. and Kaneko, R. (1988), “Analysis of Ultra-Thin Gas Film Lubrication Based on Linearized Boltzman Equation”, J. Tribology, 110, 253–261.

    Article  CAS  Google Scholar 

  • Fukui, S. and Kaneko, R. (1990), “A Database for Interpolation of Poiseuille Flow Rates for High Knudsen Number Lubrication Problems”, J. Tribology, 112, 78–83.

    Article  Google Scholar 

  • Gad-el-Hak, M. (1999), ’The Fluid Mechanics of Microdevices-The Freeman Scholar Lecture”, J. Fluids Eng., 121, 5–33.

    Article  Google Scholar 

  • Gao J. P. Luedtke W. D. and Landman U. 1997a “Layering Transitions and Dynamics of Confined Liquid Filmas” Phys. Rev. Lett. 4 705–708

    Article  Google Scholar 

  • Gao J. P., Luedtke, W. D. and Landman, U. (1997b), “Structure and Solvation Forces in Confined Films: Linear and Branched Alkanes”, J. Chem. Phys, 106: (10) 4309–4318.

    Google Scholar 

  • Gross, F. P., Jackson, E. A. and Ziering, S. (1957), “Boundary Value Problems in Kinetic Theory of Gases”, Ann. of Physics, 1, 141–167.

    Article  CAS  Google Scholar 

  • Henderson, D. and Lozada-Cassou, M. (1986), “A Simple Theory for the Force Between Spheres Immersed in Liquid”, J. Colloid and Interface Sci., 114, 180–183.

    Article  CAS  Google Scholar 

  • Ho, C. M. and Tai, Y. C. (1998), “Micro-Electro-Mechanical Systems (MEMS) and Fluid Flows”, Annu. Rev. Fluid Mech., 30, 579–612.

    Article  Google Scholar 

  • Hsia, Y. T. and Domoto, G. A. (1983), “An Experimental Investigation of Molecular Rarefaction Effects in Gas Lubricated Bearings at Ultra-Low Clearances”, J. Tribology, 105, 120–130.

    Google Scholar 

  • Hu, YZ. and Granick, S. (1998), “Microscopic Study of Thin Film Lubrication and its Contribution to Macroscopic”, Tribology. Tribology Letters, 5:(1), 81–88.

    Article  CAS  Google Scholar 

  • Huang, W., Bogy, D. B. and Alexander, F. J. (1967), “Three-Dimensional Direct Simulation Monte Carlo Method for Slider Air Bearing”, Phys. Fluids, 9(6), 1764–1769.

    Article  Google Scholar 

  • Israelachvili, J. N. (1986), “Measurement of the Viscosity of Liquids in Very Thin Films”, J. Coll. Interface Sci., 110, 263–271.

    Article  CAS  Google Scholar 

  • Klein, J. and Kumacheva, E. (1998), “Liquid-to-Solid Transition in Thin Liquid Films Induced by Confinement”, Physica A, 249,206–215.

    Article  CAS  Google Scholar 

  • Koplik, J. and Banavar, J. R. (1995), “Continuum Deductions from Molecular Hydrodynamics”, Annu. Rev. Fluid Mech., 27, 957–992.

    Article  Google Scholar 

  • Koplik, J. and Banavar, J. R. (1998a), “Physics of Fluids at Low Reynolds Numbers — a Molecular Approach”, Computers in Phys., 12, 424–431.

    Article  CAS  Google Scholar 

  • Koplik, J. and Banavar, J. R (1998b), “Molecular Simulation of Viscous Row”, JSME Int. J., B. 41, 3, 53–360.

    Google Scholar 

  • Kogan, M. N. (1969), Rarefied Gas Dynamics, Plenum Press, New York.

    Google Scholar 

  • Loyalka, S. K. (1971), “Kinetic Theory of Thermal Transpiration and Mechanocaloric Effect”, I. J. Chem. Phys., 55, 4497–4503.

    Article  CAS  Google Scholar 

  • Luo, J., Huang, P. and Li, L. K. Y. (1999), “Characteristics of Liquid Lubricant Films at the Nano-Scale”, J. Trib., 121, 872–878.

    Article  CAS  Google Scholar 

  • Matsuoka H. and Kato, T. (1997), “An Ultrathin Liquid Film Lubrication Theory — Calculation Method of Solvation Pressure and its Application to the EHL Problem”, J. Tribology, 119, 217–226.

    Article  CAS  Google Scholar 

  • Migun, N. P. and Prokhorenko, P. P. (1987), “Measurement of the Viscosity of Polar Liquids in Microcapillaries”, Colloid J. USSR, 49, 849–897.

    Google Scholar 

  • Mitsuya, Y. (1993), “Modified Reynolds Equation for Ultra-Thin Film Gas Lubrication Using 1.5 Order Slip Flow Model and Considering Surface Accommodation Coefficient”, J. Tribology, 115, 289–294.

    Article  CAS  Google Scholar 

  • Oran, E. S., Oh, C. K. and Cybyk, B. Z. (1998), “Direct Simulation Monte Carlo: Recent Advances and Applications”, Annu. Rev. Fluid Mech., 30, 403–441.

    Article  Google Scholar 

  • Patir, N, and Cheng, H. S. (1978), “Application of Average How Model to Lubrication Between Rough Sliding Surfaces”, J. Tribology, 101, 220–230.

    Google Scholar 

  • Pfahler, J., Harley, I, Bau, H. and Zemel, J. N. (1991), “Gas and Liquid Flow in Small Channels”, in Symposium on Micromechanical Sensors, Actuators and Systems, (D. Qio et al, eds.), ASME DSC, 32, pp. 49–60.

    Google Scholar 

  • Rettner, C. T. (1997), “Determination of Accommodation Coefficients for N2 at Disk-Drive Air-Bearing Surfaces”, J. Tribology, 119, 588–589.

    Article  CAS  Google Scholar 

  • Reynolds, O. (1986), “On the Theory of Lubrication and its Application to Mr. Beuchamp Tower’s Experiments”, Phil Trans. Roy. Soc, 177, 157–234.

    Google Scholar 

  • Schaaf, S. A. and Sherman, F. S. (1954), “ Skin Friction in Slip Flow”, J. Aero. Sci., 21, 85–90.

    Google Scholar 

  • Szeri, A. Z. (1998), Fluid Film Bearings, Theory And Design, Cambridge University Press. Cambridge, UK

    Book  Google Scholar 

  • Szeri, A. Z. and Al-Sharif, A. (1995), “Flow Between Finite, Steadily Rotating Eccentric Cylinders”, Theoret. Comput. Fluid Dyn., 7, 1–28.

    Article  CAS  Google Scholar 

  • Taylor, G. I. (1923), “Stability of a Viscous Liquid Contained Between Two Rotating Cylinders”, Philos. Trans. Roy., Soc., A 223, 289–343.

    Article  Google Scholar 

  • Thompson, P.A. and Troian, S. M. (1997), “A General Boundary Condition for Liquid Flow at solid surfaces”, Nature, 389, 360–362.

    Article  CAS  Google Scholar 

  • Vincenti, W. G. and Kruger, C. H. (1965), Introduction To Physical Gas Dynamics, John Wiley & Sons, New York.

    Google Scholar 

  • Vohr, J. H. (1968), “An Experimental Study of Taylor Vortices and Turbulence in Flow Between Eccentric, Rotating Cylinders”, Trans. ASME. 90, 285–296.

    Google Scholar 

  • Willis, D. R. (1962), “Comparison of Kinetic Theory Analyses of Linearized Couette Flow”, Phys. Fluids, 5, 127–135.

    Article  Google Scholar 

  • Zienkiewicz, O. C. and Woo, J. (1991),” Incompressibility Without Tears: How to Avoid Restrictions of Mixed Formulation. Internat”, J. Numer. Methods Engrg., 32, 1189–1203.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Szeri, A.Z. (2001). Flow Modeling of Thin Films from Macroscale to Nanoscale. In: Bhushan, B. (eds) Fundamentals of Tribology and Bridging the Gap Between the Macro- and Micro/Nanoscales. NATO Science Series, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0736-8_57

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-0736-8_57

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-6837-3

  • Online ISBN: 978-94-010-0736-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics