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Gas flows through constricted shallow micro-channels

  • A. GAT (a1), I. FRANKEL (a1) and D. WEIHS (a1)

Abstract

We study the viscous compressible flow through micro-channels of non-uniform cross-section. A lubrication approximation is applied to analyse the flow through shallow configurations whose gap width is small in comparison with the other characteristic dimensions. Focusing on channels with a symmetric constriction (or cavity) we obtain the solution to the problem by means of a Schwarz–Christoffel transformation. This analytic solution is verified by examining the convergence of numerical simulations with diminishing Reynolds number and gap width. Explicit closed-form expressions for the pressure-head and mass-flow-rate losses in terms of the geometrical parameters characterizing the constriction are presented and discussed in the context of experimental data existing in the literature.

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Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. Dover.
Arkilic, E. B., Schmidt, M. A. & Breuer, K. S. 1997 Gaseous slip flow in long microchannels. J. Microelectromech. Syst. 6, 167178.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
van den Berg, H. R., ten Seldam, C. A. & van der Gulik, P. S. 1993 Compressible laminar flow in a capillary. J. Fluid Mech. 246, 120.
Beskok, A., Karniadakis, G. E. & Trimmer, W. 1996 Rarefaction and compressibility effects in gas microflows. Trans. ASME: J. Fluids Engng 118, 448456.
Cercignani, C. 2000 Rarefied Gas Dynamics. Macmillan.
Chapman, S. & Cowling, T. G. 1970 The Mathematical Theory of Non-uniform Gases. Cambridge University Press.
Fan, Q., Xue, H. & Shu, C. 1999 DSMC simulations of gaseous flows in microchannels. In 5th ASME/JSME Joint Thermal Engineering Conference March 15-19 1999, San Diego, California.
Gad-el-Hak, M. 1999 The fluid mechanics of microdevices. Trans. ASME: J. Fluids Engng 121, 533.
Graur, I. A., Meolans, J. G. & Zeitoun, D. E. 2005 Analytical and numerical description for isothermal gas flow in microchannels. Microfluid Nanofluid 2, 6477.
Harley, J. C., Huang, Y., Bau, H. H. & Zemel, J. N. 1995 Gas flow in micro-channels. J. Fluid Mech 284, 257274.
Ho, C. M. & Tai, Y. C. 1996 Mems and its applications for flow control. Trans. ASME: J. Fluids Engng 118, 437447.
Ho, C. M. & Tai, Y. C. 1998 Micro-electro-mechanical-systems (MEMS) and fluid flows. Annu. Rev. Fluid Mech. 30, 579612.
Lee, W. Y., Wong, M. & Zohar, Y. 2001 Gas flow in microchannels with bends. J. Micromech. Microengng 11, 635644.
Lee, W. Y., Wong, M. & Zohar, Y. 2002 a Microchannels in series connected via a contraction/expansion section. J. Fluid Mech 459, 187206.
Lee, W. Y., Wong, M. & Zohar, Y. 2002 b Pressure loss in constriction microchannels. J. Microelectromech. Syst 11, 236244.
Liu, J. Q., Tai, Y. C. & Ho, C. M. 1995 MEMS for pressure distribution studies of gaseous flows in microchannels. In Proc. IEEE Micro-electromech. Syst, pp. 209––215.
Maxwell, J. C. 1879 On stresses in rarified gases arising from inequalities of temperature. Phil. Trans. R. Soc. Lond. 170.
Milne-Thomson, L. M. 1968 Theoretical Hydrodynamics. Macmillan.
Pong, K., Ho, C. & Tai, Y. 1994 Non-linear pressure distribution in uniform microchannels. ASME-FED vol. 197, pp. 51–56.
Prud'homme, R., Chapman, T. & Bowen, J. 1986 Laminar compressible flow in a tube. Appl. Sci. Res. 43, 6774.
Qin, F.-H., Sun, D.-J. & Yin, X.-Y. 2007 Perturbation analysis on gas flow in a straight microchannel. Phys. Fluids 19.
Sharipov, F. 1999 Non-isothermal gas flow through rectangular microchannels. J. Micromech. Microengng 9, 394401.
Sone, Y. 2002 Kinetic Theory and Fluid Dynamics. Birkhauser.
Tsai, C.-H., Chen, H.-T., Wang, Y.-N., Lin, C.-H. & Fu, L.-M. 2007 Capabilities and limitations of 2-dimensional and 3-dimensional numerical methods in modeling the fluid flow in sundden exapansion microchannels. Microfluid Nanofluid 3, 1318.
White, F. M. 1986 Fluid Mechanics, 2nd edn. McGraw-Hill.
Yao, Z.-H., He, F., Ding, Y.-T., Shen, M.-Y & Wang, X.-F. 2004 Low-speed gas flow subshocking phenomenon in a long-constant-area microchannel. AIAA J. 42, 15171521.
Yu, Z. T. F., Lee, Y.-K., Wong, M. & Zohar, Y. 2005 Fluid flows in microchannels with cavities. J. Microelectromech. Syst. 14, 13861398.
Zohar, Y., Lee, S. Y. K., Lee, W. Y., Jiang, L. & Tong, P. 2002 Subsonic gas flow in a straight and uniform microchannel. J. Fluid Mech. 472, 125151.
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Gas flows through constricted shallow micro-channels

  • A. GAT (a1), I. FRANKEL (a1) and D. WEIHS (a1)

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