Skip to main content
SpringerLink
Log in
Book cover

Slow Rarefied Flows pp 145–163Cite as

Rarefied Lubrication in Mems

  • Chapter

  • 657 Accesses

Part of the book series: Progress in Mathematical Physics ((PMP,volume 41))

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. F.J. Alexander, A.L. Garcia, B.J. Alder, Direct simulation Monte Carlo for thin film bearings, Phys. Fluids, 6, 3854–3860 (1994).

    Article  MATH  Google Scholar 

  2. C. Cercignani, A. Daneri, Flow of a rarefied gas between two parallel plates, Journal of Applied Physics, 34, 3509–3513 (1963).

    Article  MathSciNet  Google Scholar 

  3. C. Cercignani and G. Tironi, New boundary conditions in the transition regime, J. Plasma Phys. 2, 293–310 (1968).

    Article  Google Scholar 

  4. C. Cercignani and G. Tironi, Some applications to the transition regime of a new set of boundary conditions for Navier-Stokes equations, in Rarefied Gas Dynamics, L. Trilling and H. Y. Wachman, Vol I, 281–289, Academic Press, New York (1969).

    Google Scholar 

  5. C. Cercignani, M. Lampis, S. Lorenzani, Variational approach to gas flows in microchannels, Phys. Fluids, 14, 3426–3437 (2004).

    Article  MathSciNet  Google Scholar 

  6. C. Cercignani, M. Lampis, S. Lorenzani, Variational Approach to Plane Poiseuille Flow with General Boundary Conditions, in Rarefied Gas Dynamics, 23rd Int. Symp., A.D. Ketsdever and E.P. Muntz Eds., AIP Conf. Proc. 663, 141–148, New York (2003).

    Google Scholar 

  7. C. Cercignani, M. Lampis, S. Lorenzani, Flow of a Rarefied Gas between Parallel and Almost Parallel Plates, in Rarefied Gas Dynamics, 24th Int. Symp., M. Capitelli Ed., AIP Conf. Proc. 762, pp. 719–724, New York (2005).

    Google Scholar 

  8. J. Fan, C. Shen, Statistical simulation of low-speed unidirectional flows in transitional regime, in Rarefied Gas Dynamics, edited by R. Brun, R. Campargue, R. Gatignol, J.C. Lengrand, Cepadues Editions, Vol. 2, 245–252 (1999)

    Google Scholar 

  9. C. Shen, J. Fan, C. Xie C, Statistical simulation of rarefied gas flows in micro-channels, J. Comp. Physics 189, 512–526 (2003).

    Article  MATH  Google Scholar 

  10. S. Fukui, R. Kaneko, Analysis of ultra-thin gas film lubrication based on linearized Boltzmann equation: first report-derivation of a generalized lubrication equation including thermal creep flow, Journal of Tribology, 110, 253–262 (1988).

    Article  Google Scholar 

  11. S. Fukui, R. Kaneko, Analysis of ultra-thin gas film lubrication based on the linearized Boltzmann equation, JSME International Journal, 30, 1660–1666 (1987).

    Google Scholar 

  12. J._Z. Jiang, C. Shen, J. Fan, Statistical simulation of thin-film bearings in Rarefied Gas Dynamics, 24th Int. Symp., M. Capitelli Ed., AIP Conf. Proc. 762, pp. 180–185, New York (2005).

    Google Scholar 

  13. X. Nie, G. D. Doolen, S. Chen, Lattice Boltzmann simulation of fluid flows in MEMS, J. Stat. Phys., 107, 279–289 (2002)

    Article  MATH  Google Scholar 

  14. K. C. Pong, C.M., Ho, J. Q. Liu, Y. C. Tai, Non-linear pressure distribution in uniform microchannels, ASME, FED 197, Application of Microfabrication to Fluid Mechanics, 51–56 (1994)

    Google Scholar 

  15. O. Reynolds, On the theory of lubrication and its application to Mr. Beauchamp Tower’s experiments including an experimental determination of the viscosity of the olive oil, Philos. Trans. R. Soc. London, A177, 157–234 (1886).

    Google Scholar 

  16. C. Shen, Use of the degenerated Reynolds equation in solving the microchannel flow problem, Phys. Fluids, (to appear, 2004).

    Google Scholar 

  17. C. Shen, D. B. Tian, C. Xie, J. Fan, Examination of LBM in simulation of the micro-channel flow in transitional regime, Proceedings of the 1st Intern. Conference on micro and mini-channels, ASME, 405–410 (2003); see also: C. Shen C, D. B. Tian, C. Xie, J. Fan, Examination of the LBM in simulation of microchannel flow in transitional regime, Microscale Thermophysical Engineering vol. 8, pp. 423–432 (2004).

    Google Scholar 

  18. C. Shen, Rarefied Gas Dynamics, Fundamentals, Simulations and Micro Flows, Springer Verlag, Berlin Heidelberg (2005).

    Google Scholar 

  19. J._C. Shin, C. M. Ho J. Q. Liu, Y. C. Tai, Monatomic and polyatomic gas flow through uniform microchannels, ASME-DSC 59, 197 (1996).

    Google Scholar 

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Birkhäuser Verlag

About this chapter

Cite this chapter

(2006). Rarefied Lubrication in Mems. In: Slow Rarefied Flows. Progress in Mathematical Physics, vol 41. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7537-X_7

Download citation

Publish with us

Policies and ethics

Search

Navigation