Rarefaction and compressibility effects on steady or transient gas flows in microchannels

Proceedings of the Second International Conference on Microchannels and Minichannels (ICMM2004)

Volumn , Issue , 2004, Pages 13-24

  Colin, Stéphane ^a  

^a INSA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

AEROSPACE APPLICATIONS; APPROXIMATION THEORY; BOUNDARY CONDITIONS; MICROMETERS; PHASE EQUILIBRIA; THERMODYNAMIC STABILITY;

GAS MICROFLOWS; MICROSYSTEMS; THERMODYNAMIC EQUILIBRIUM;

FLOW OF FLUIDS;

EID: 4544365487     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/icmm2004-2316     Document Type: Conference Paper

References (61)

1. Arkilic, E. B. and Breuer, K. S., Gaseous flow in small channels, AIAA Paper, vol. 93-3270, pp. 1-7, 1993.
2. Arkilic. E. B., Breuer, K. S., and Schmidt. M. A., Mass flow and tangential momentum accommodation in silicon micromachined channels, J. Fluid Mech., vol. 437, pp. 29-43, 2001.
3. Aubert, C. and Colin, S., High-order boundary conditions for gaseous flows in rectangular microchannels. Microscale Thermophys. Eng., vol. 5, no. 1, pp. 41-54, 2001.
4. Aubert, C., Colin, S., and Caen. R., Unsteady gaseous flows in tapered microchannels, in First International Conference on Modeling and Simulation of Microsystems, Semiconductors, Sensors and Actuators (MSM98), vol. 1. Santa Clara Marriot: Computational Publications, pp. 486-491, 1998.
5. Beskok, A. and Karniadakis, G. E., A model for flows in channels, pipes, and ducts at micro and nano scales, Microscale Thermophys. Eng., vol. 3, no. 1, pp. 43-77, 1999.
6. Bestman, A. R., Ikonwa. I. O., and Mbelegodu, I. U., Transient slip flow, Int. J. Energy Res., vol. 19, no. 3, pp. 275-277, 1995.
7. Bhatnagar, P., Gross, E., and Krook, K., A model for collision processes in gasses. Physics Review, vol. 94, pp. 511-524, 1954.
8. Bird, G. A., Molecular gas dynamics and the direct simulation of gas flows. Oxford: Clarendon Press, 1998.
9. Bird, G., Monte Carlo simulation of gas flows, Annu. Rev. Fluid Mech., vol 10, pp. 11-31, 1978.
10. Caen, R., Mas, I., and Colin, S., Ecoulements non permanents dans les microcanaux : réponse fréquentielle des microtubes pneumatiques, C. R. Acad. Sci., Ser. II b, vol. 323, pp. 805-812, 1996.
11. Cercignani, C., Illner. R., and Pulvirenti, M., The mathematical theory of dilute gases, vol. 106. New-York: Springer-Verlag, 1994.
12. Chapman, S. and Cowling, T. G., The mathematical theory of non-uniform gases. Cambridge: University Press, 1952.
13. Chen, C. S., Lee, S. M., and Sheu, J. D., Numerical analysis of gas flow in microchannels, Numer. Heat Transf., A, vol. 33, pp. 749-762, 1998.
14. Chen. S. and Doolen, G., Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech., vol. 30, pp. 329, 1998.
15. Colin, S., Anduze, M., and Caen, R., A pneumatic frequency generator for experimental analysis of unsteady microflows. in Micro-Electro-Mechanical Systems (MEMS) -1998-, vol. DSC-66, ASME, pp. 231-239, 1998.
16. Colin, S., Aubert, C., and Caen, R., Unsteady gaseous flows in rectangular microchannels: frequency response of one or two pneumatic lines connected in series. European Journal of Mechanics - B/Fluids, vol. 17, no. 1, pp. 79-104, 1998.
17. Colin, S., Elizarova. T. G., Sheretov, Y. V., Lengrand, J.-C., and Camon, H., Micro-écoulements gazeux : validation expérimentale de modèles QHD et de NavierStokes avec conditions aux limites de glissement, in 16ème Congrès Français de Mécanique, CDROM. Nice, 2003.
18. Colin, S., Lalonde, P., and Caen, R., Validation of a second-order slip flow model in rectangular microchannels, Heat Transfer Eng., vol. 25, no. 3. pp. 23-30, 2004.
19. Deissler, R. G., An analysis of second-order slip flow and temperature-jump boundary conditions for rarefied gases. Int. J. Heat Mass Transfer, vol. 7, pp. 681-694, 1964.
20. Ebert. W. A. and Sparrow, E. M., Slip flow in rectangular and annular ducts, J. Basic Eng., vol. 87, pp. 1018-1024, 1965.
21. Elizarova, T. G. and Sheretov, Y. V., Analyse du problème de l'ecoulement gazeux dans les microcanaux par les équations quasi hydrodynamiques, La Houille Blanche, no. 5. pp. 66-72.2003.
22. Elizavora, T. G. and Sheretov, Y. V., Theroretical and numerical investigation of quasi-gasdynamic and quasihydrodynamic equations, Comput. Math. Math. Phys., vol. 41. no. 2, pp. 219-234, 2001.
23. Fan, J. and Shen. C., Statisticall simulation of low-speed unidirectional flows in transition regime, in Rarefied Gas Dynamics, vol. 2. R. Brnm, R. Campargue, R. Gatignol, and J.-C. Lengrand, Eds.: Cépaduès Editions, pp. 245-252, 1999.
24. Gad-el-Hak, M., The fluid mechanics of microdevices - The Freeman Scholar Lecture, J. Fluids Eng., vol. 121, pp. 5-33, 1999.
25. Grad, H., On the kinetic theory of rarefied gases, Comm. Pure Appl. Math., vol. 2, pp. 331-407, 1949.
26. Harley. J. C., Huang, Y., Bau, H. H., and Zemel, J. N., Gas flow in micro-channels. J. Fluid Mech., vol. 284, pp. 257-274, 1995.
27. Hash, D. and Hassan. H., Two-dimensional coupling issues of hybrid DSMC/Navier-Stokes solvers, Physical Review E. vol. 55. pp. 6333-6336, 1997.
28. Hobson, J. P., Accommodation pumping - A new principle for low pressure, Journal of Vacuum Science and Technology, vol. 7. no. 2, pp. 301-357, 1970.
29. Hobson. J. P., Analysis of accommodation pumps, Journal of Vacuum Science and Technology, vol. 8, no. 1, pp. 290-293, 1971.
30. Hobson, J. P., Physical factors influencing accommodation pumps. Journal of Vacuum Science and Technology, vol. 9. no. 1, pp. 252-256, 1972.
31. Hudson. M. L. and Bartel. T. J., DSMC simulation of thermal transpiration and accommodation pumps, in Rarefied Gas Dynamics, vol. 1. R. Brun, R. Campargue. R. Gatignol, and J.-C. Lengrand, Eds.: Cépadués Editions, pp. 719-726, 1999.
32. Jie, D., Diao, X., Cheong. K. B., and Yong, L. K., Navier-Stokes simulations of gas flow in micro devices. J. Micromech. Microeng., vol. 10. no. 3. pp. 372-379, 2000.
33. Karniadakis, G. E. and Beskok. A., Microflows: fundamentals and simulation. New York: Springer-Verlag, 2002.
34. Kennard, E. H., Kinetic theory of gases, 1st ed. New York: McGraw-Hill Book Company., 1938.
35. Lalonde. P., Etude expérimentale d'écoulements gazeux dans les microsystèmes à fluides. PhD Thesis. Toulouse: Institut National des Sciences Appliquées. 2001.
36. Lengrand, J.-C., Chap. 2 : microécoulements gazeux, in Microfluidique, S. Colin. Ed.: Hermès Science Publications. 2004.
37. Liu. J., Tai. Y.-C., and Ho, C.-M., MEMS for pressure distribution studies of gaseous flows in microchannels. in 8th Ann. Int. Workshop MEMS. An Investigation of Micro Structures, Sensors, Actuators, Machines, and Systems. Amsterdam: IEEE. pp. 209-215, 1995.
38. Loyalka, S. K. and Hamoodi, S. A., Poiseuille flow of a rarefied gas in a cylindrical tube : solution of linearized Boltzmann equation, Phys. Fluids A, vol. 2, no. 11. November, pp. 2061-2065, 1990.
39. Maurer. J., labeling, P., Joseph. P., and Willaime. H., Second-order slip laws in microchannels for helium and nitrogen, Phys. Fluids, vol. 15, no. 9, pp. 2613-2621, 2003.
40. Mavriplis, C., Ann, J. C., and Goulard, R., Heat transfer and flowfields in short microchannels using direct simulation Monte Carlo, J. Thermophys. Heat Transf., vol. 11. no. 4, pp. 489-496, 1997.
41. Maxwell, J. C., On stresses in rarefied gases arising from inequalities of temperature. Philosophical Transactions of the Royal Society, vol. 170, pp. 231-256, 1879.
42. Mitsuya. Y., Modified Reynolds equation for ultra-thin film gas lubrication using 1.5-order slip-flow model and considering surface accommodation coefficient. J. Tribal., vol. 115, pp. 289-294, 1993.
43. Morini, G. L. and Spiga, M., Slip flow in rectangular microtubes, Microscale Thermophys. Eng., vol. 2. no. 4, pp. 273-282, 1998.
44. Muntz. E. P. and Vargo, S. E., Microscale vacuum pumps, in The MEMS Handbook, M. Gad-el-Hak, Ed. New York: CRC Press, pp. 29.1-29.28, 2002.
45. Muntz, E. P., Rarefied gas dynamics, Annu. Rev. Fluid Mech., vol. 21. pp. 387-417, 1989.
46. Norberg, P., Ackelid, U., Lundstrom, I., and Petersson, L. G., On the transient gas flow through catalytically active micromachined channels, J. Appl. Phys., vol. 81, no. 5, pp. 2094-2100, 1997.
47. Oran, E. S., OH, C. K., and Cybyk, B. Z., Direct Simulation Monte Carlo: recent advances and applications. Annu. Rev. Fluid Mech., vol. 30. pp. 403-441, 1998.
48. Pan, L. S., Liu, G. R and Lam, K. Y., Determination of slip coefficient for rarefied gas flows using direct simulation Monte Carlo, J. Micromech. Microeng., vol. 9. no. 1, pp. 89-96, 1999.
49. Pan. L. S., Ng. T. Y., Xu. D., and Lam, K. Y., Molecular block model direct simulation Monte Carlo method for low velocity microgas flows, J. Micromech. Microeng., vol. 11, no. 3, pp. 181-188, 2001.
50. Piekos, E. S. and Breuer. K. S., Numerical modeling of micromechanical devices using the direct simulation Monte Carlo method, J. Fluids Eng., vol. 118. pp. 464-469, 1996.
51. Roveda, R., Goldstein. D., and Varghese, P., Hybrid Euler/particle approach for continuum/rarefied flows. J. Spacecraft and Rockets, vol. 35, no. 3. pp. 258-265, 1998.
52. Sharipov. F. and Seleznev, V., Data on internal rarefied gas flows. J. Phys. Chem. Ref. Data, vol. 27, no. 3, pp. 657-706, 1998.
53. Shih. J. C., Ho, C.-M., Liu. J.. and Tai, Y.-C., Monatomic and polyatomic gas flow through uniform microchannels. vol. DSC-59. New York: ASME, pp. 197-203, 1996.
54. Sreekanth. A. K.. Slip flow through long circular tubes, in 6th International Symposium on Rarefied Gas Dynamics, L. Trilling and H. Y. Wachman, Eds. New York: Academic Press, pp. 667-680, 1969.
55. Stefanov, S. and Cercignani, C., Monte Carlo simulation of a channel flow of a rarefied gas, Eur. J. Mech., B/Fluids, vol. 13, no. 1, pp. 93-114, 1994.
56. Vargo, S. E. and Muntz, E. P., An evaluation of a multiple-stage micromechanical Knudsen compressor and vacuum pump, in Proceedings of the 20th Rarefied Gas Dynamics Conference. Beijing, pp. 995-1000, 1997.
57. Vargo, S. E. and Muntz. E. P., Comparison of experiment and prediction for transitional flow in a single-stage micromechanical Knudsen compressor, in Rarefied Gas Dynamics, vol. 1, R. Brun, R. Campargue, R. Gatignol, and J.-C. Lengrand, Eds.: Cépaduès Editions, pp. 711-718, 1999.
58. Vargo, S. E., Muntz, E. P., Shiflert, G. R., and Tang, W. C., Knudsen compressor as a micro- and macroscale vacuum pump without moving parts or fluids, Journal of Vacuum Science Technology A, vol. 17, no. 4, pp. 2308-2313, 1999.
59. Wu, J.-S. and Tseng, K.-C., Analysis of micro-scale gas flows with pressure boundaries using direct simulation Monte Carlo method, Computers & Fluids, vol. 30, no. 6, pp. 711-735, 2001.
60. Xue, H. and Fan, Q., A new analytic solution of the Navier-Stokes equations for microchannel flow, Microscale Thermophys. Eng., vol. 4, no. 2, pp. 125-143, 2000.
61. Young, R. M., Analysis of a micromachine based vacuum pump on a chip actuated by the thermal transpiration effect, Journal of Vacuum Science Technology B, vol. 17, no. 2, pp. 280-287, 1999.