Comptes Rendus
no. 5
Effets de raréfaction dans les micro-écoulements gazeux

Présenté par : Guy Laval

Stéphane Colin1  ; Lucien Baldas1
1 Laboratoire de génie mécanique de Toulouse, INSA, 135, avenue de Rangueil, 31077 Toulouse cedex 4, France
Comptes Rendus. Physique, Volume 5 (2004) no. 5, pp. 521-530.

L'étude des écoulements de gaz dans les microsystèmes nécessite la prise en compte des effets de raréfaction. Après avoir présenté les échelles de longueur caractéristiques des micro-écoulements gazeux et défini les différents régimes d'écoulement rencontrés, nous exposons les méthodes analytiques de calcul du régime d'écoulement glissant, le plus fréquemment rencontré dans les microsystèmes fluidiques. Les différentes méthodes de résolution numérique des micro-écoulements gazeux sont ensuite passées en revue, avec une attention particulière pour la simulation directe de Monte Carlo. La dernière partie est consacrée à quelques applications spécifiques de micropompage d'origine thermique liées à la raréfaction des écoulements.

Studying gaseous flows in microsystems requires that rarefaction effects be taken into account. The significant length scales for gaseous microflows and the encountered flow regimes are presented. The analytical methods for the modeling of the slip flow regime, frequent in microfluidic applications, are detailed. Numerical methods for the simulation of micro gaseous flows are also examined, with emphasis on the Direct Simulation Monte Carlo method. Finally, some specific applications of thermal micropumping based on rarefaction effects are presented.

Publié le :
DOI : 10.1016/j.crhy.2004.04.005
Mot clés : Raréfaction, Microfluidique, Nombre de Knudsen, Écoulement glissant, Micropompage thermique
Keywords: Rarefaction, Microfluidics, Knudsen number, Slip flow, Thermal micropumping
Stéphane Colin 1 ; Lucien Baldas 1

1 Laboratoire de génie mécanique de Toulouse, INSA, 135, avenue de Rangueil, 31077 Toulouse cedex 4, France 
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Stéphane Colin; Lucien Baldas. Effets de raréfaction dans les micro-écoulements gazeux. Comptes Rendus. Physique, Volume 5 (2004) no. 5, pp. 521-530. doi : 10.1016/j.crhy.2004.04.005. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2004.04.005/

[1] G.E. Karniadakis; A. Beskok Microflows: Fundamentals and Simulation, Springer-Verlag, New York, 2002

[2] G.A. Bird Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon Press, Oxford, 1998

[3] M. Gad-el-Hak The fluid mechanics of microdevices – The Freeman Scholar Lecture, J. Fluids Engrg., Volume 121 (1999), pp. 5-33

[4] J.-C. Lengrand Chapter 2 : microécoulements gazeux (S. Colin, ed.), Microfluidique , Hermès Science, 2004

[5] E.H. Kennard Kinetic Theory of Gases, McGraw-Hill, New York, 1938

[6] W.A. Ebert; E.M. Sparrow Slip flow in rectangular and annular ducts, J. Basic Engrg., Volume 87 (1965), pp. 1018-1024

[7] G.L. Morini; M. Spiga Slip flow in rectangular microtubes, Microscale Thermophys. Eng., Volume 2 (1998) no. 4, pp. 273-282

[8] E.B. Arkilic; K.S. Breuer; M.A. Schmidt Mass flow and tangential momentum accommodation in silicon micromachined channels, J. Fluid Mech., Volume 437 (2001), pp. 29-43

[9] J.C. Harley; Y. Huang; H.H. Bau; J.N. Zemel Gas flow in micro-channels, J. Fluid Mech., Volume 284 (1995), pp. 257-274

[10] J.C. Shih, C.-M. Ho, J. Liu, Y.-C. Tai, Monatomic and polyatomic gas flow through uniform microchannels, vol. DSC-59, ASME, New York,

[11] J. Liu; Y.-C. Tai; C.-M. Ho MEMS for pressure distribution studies of gaseous flows in microchannels, An Investigation of Micro Structures, Sensors, Actuators, Machines, and Systems, 8th Ann. Int. Workshop MEMS, IEEE, Amsterdam, 1995, pp. 209-215

[12] A.K. Sreekanth Slip flow through long circular tubes (L. Trilling; H.Y. Wachman, eds.), 6th International Symposium on Rarefied Gas Dynamics, Academic Press, New York, 1969, pp. 667-680

[13] E.S. Piekos; K.S. Breuer Numerical modeling of micromechanical devices using the direct simulation Monte Carlo method, J. Fluids Engrg., Volume 118 (1996), pp. 464-469

[14] S. Chapman; T.G. Cowling The Mathematical Theory of Non-Uniform Gases, University Press, Cambridge, 1952

[15] R.G. Deissler An analysis of second-order slip flow and temperature-jump boundary conditions for rarefied gases, Int. J. Heat Mass Transfer, Volume 7 (1964), pp. 681-694

[16] P. Lalonde, Etude expérimentale d'écoulements gazeux dans les microsystèmes à fluides, Institut National des Sciences Appliquées de Toulouse, Thèse de Doctorat, Toulouse. 2001

[17] C. Aubert; S. Colin High-order boundary conditions for gaseous flows in rectangular microchannels, Microscale Thermophys. Eng., Volume 5 (2001) no. 1, pp. 41-54

[18] J. Maurer; P. Tabeling; P. Joseph; H. Willaime Second-order slip laws in microchannels for helium and nitrogen, Phys. Fluids, Volume 15 (2003) no. 9, pp. 2613-2621

[19] S. Colin; P. Lalonde; R. Caen Validation of a second-order slip flow model in rectangular microchannels, Heat Transfer Engrg., Volume 25 (2004) no. 3, pp. 23-30

[20] A. Beskok; G.E. Karniadakis A model for flows in channels, pipes, and ducts at micro and nano scales, Microscale Thermophys. Eng., Volume 3 (1999) no. 1, pp. 43-77

[21] H. Xue; Q. Fan A new analytic solution of the Navier–Stokes equations for microchannel flow, Microscale Thermophys. Eng., Volume 4 (2000) no. 2, pp. 125-143

[22] D. Jie; X. Diao; K.B. Cheong; L.K. Yong Navier–Stokes simulations of gas flow in micro devices, J. Micromech. Microengrg., Volume 10 (2000) no. 3, pp. 372-379

[23] T.G. Elizavora; Y.V. Sheretov Theroretical and numerical investigation of quasi-gasdynamic and quasi-hydrodynamic equations, Comput. Math. Math. Phys., Volume 41 (2001) no. 2, pp. 219-234

[24] T.G. Elizarova; Y.V. Sheretov Analyse du problème de l'écoulement gazeux dans les microcanaux par les équations quasi hydrodynamiques, Microfluidique. Micro-écoulements liquides et gazeux : phénomènes physiques et applications, SHF, 2002, pp. 309-318

[25] S. Colin, T.G. Elizarova, Y.V. Sheretov, J.-C. Lengrand, H. Camon, Micro-écoulements gazeux : validation expérimentale de modèles QHD et de Navier–Stokes avec conditions aux limites de glissement, in : 16ème Congrès Français de Mécanique, Actes sur CD ROM, Nice, 2003

[26] H. Grad On the kinetic theory of rarefied gases, Comm. Pure Appl. Math., Volume 2 (1949), pp. 331-407

[27] F. Sharipov; V. Seleznev Data on internal rarefied gas flows, J. Phys. Chem. Ref. Data, Volume 27 (1998) no. 3, pp. 657-706

[28] P. Bhatnagar; E. Gross; K. Krook A model for collision processes in gasses, Phys. Rev., Volume 94 (1954), pp. 511-524

[29] C. Cercignani; R. Illner; M. Pulvirenti, The Mathematical Theory of Dilute Gases, vol. 106, Springer-Verlag, New-York, 1994

[30] E.P. Muntz Rarefied gas dynamics, Annu. Rev. Fluid Mech., Volume 21 (1989), pp. 387-417

[31] H. Cheng; G. Emmanuel Perpectives on hypersonic nonequilibrium flow, AIAA J., Volume 33 (1995), pp. 385-400

[32] G. Bird Monte Carlo simulation of gas flows, Annu. Rev. Fluid Mech., Volume 10 (1978), pp. 11-31

[33] E.S. Oran; C.K. Oh; B.Z. Cybyk Direct Simulation Monte Carlo: recent advances and applications, Annu. Rev. Fluid Mech., Volume 30 (1998), pp. 403-441

[34] C. Mavriplis; J.C. Ahn; R. Goulard Heat transfer and flowfields in short microchannels using direct simulation Monte Carlo, J. Thermophys. Heat Transfer, Volume 11 (1997) no. 4, pp. 489-496

[35] L.S. Pan; G.R. Liu; K.Y. Lam Determination of slip coefficient for rarefied gas flows using direct simulation Monte Carlo, J. Micromech. Microengrg., Volume 9 (1999) no. 1, pp. 89-96

[36] S. Stefanov; C. Cercignani Monte Carlo simulation of a channel flow of a rarefied gas, Eur. J. Mech. B Fluids, Volume 13 (1994) no. 1, pp. 93-114

[37] J.-S. Wu; K.-C. Tseng Analysis of micro-scale gas flows with pressure boundaries using direct simulation Monte Carlo method, Comput. & Fluids, Volume 30 (2001) no. 6, pp. 711-735

[38] M.L. Hudson; T.J. Bartel DSMC simulation of thermal transpiration and accommodation pumps (R. Brun; R. Campargue; R. Gatignol; J.-C. Lengrand, eds.), Rarefied Gas Dynamics, vol. 1, Cépaduès, 1999, pp. 719-726

[39] C.S. Chen; S.M. Lee; J.D. Sheu Numerical analysis of gas flow in microchannels, Numer. Heat Transfer A, Volume 33 (1998), pp. 749-762

[40] J. Fan; C. Shen Statistical simulation of low-speed unidirectional flows in transition regime (R. Brun; R. Campargue; R. Gatignol; J.-C. Lengrand, eds.), Rarefied Gas Dynamics, vol. 2, Cépaduès, 1999, pp. 245-252

[41] L.S. Pan; T.Y. Ng; D. Xu; K.Y. Lam Molecular block model direct simulation Monte Carlo method for low velocity microgas flows, J. Micromech. Microengrg., Volume 11 (2001) no. 3, pp. 181-188

[42] R. Roveda; D. Goldstein; P. Varghese Hybrid Euler/particle approach for continuum/rarefied flows, J. Spacecraft and Rockets, Volume 35 (1998) no. 3, pp. 258-265

[43] D. Hash; H. Hassan Two-dimensional coupling issues of hybrid DSMC/Navier–Stokes solvers, Phys. Rev. E, Volume 55 (1997), pp. 6333-6336

[44] S. Chen; G. Doolen Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech., Volume 30 (1998), p. 329

[45] E.P. Muntz; S.E. Vargo Microscale vacuum pumps (M. Gad-el-Hak, ed.), The MEMS Handbook, CRC Press, New York, 2002, p. 29.1-29.28

[46] S.E. Vargo; E.P. Muntz An evaluation of a multiple-stage micromechanical Knudsen compressor and vacuum pump, Proceedings of the 20th Rarefied Gas Dynamics Conference, Beijing, 1997, pp. 995-1000

[47] S.K. Loyalka; S.A. Hamoodi Poiseuille flow of a rarefied gas in a cylindrical tube: solution of linearized Boltzmann equation, Phys. Fluids A, Volume 2 (1990) no. 11, pp. 2061-2065

[48] S.E. Vargo; E.P. Muntz Comparison of experiment and prediction for transitional flow in a single-stage micromechanical Knudsen compressor (R. Brun; R. Campargue; R. Gatignol; J.-C. Lengrand, eds.), Rarefied Gas Dynamics, vol. 1, Cépaduès, 1999, pp. 711-718

[49] S.E. Vargo; E.P. Muntz; G.R. Shiflett; W.C. Tang Knudsen compressor as a micro- and macroscale vacuum pump without moving parts or fluids, J. Vac. Sci. Technol. A, Volume 17 (1999) no. 4, pp. 2308-2313

[50] R.M. Young Analysis of a micromachine based vacuum pump on a chip actuated by the thermal transpiration effect, J. Vac. Sci. Technol. B, Volume 17 (1999) no. 2, pp. 280-287

[51] J.P. Hobson Accommodation pumping – a new principle for low pressure, J. Vac. Sci. Technol., Volume 7 (1970) no. 2, pp. 301-357

[52] J.P. Hobson Analysis of accommodation pumps, J. Vac. Sci. Technol., Volume 8 (1971) no. 1, pp. 290-293

[53] J.P. Hobson Physical factors influencing accommodation pumps, J. Vac. Sci. Technol., Volume 9 (1972) no. 1, pp. 252-256

[54] Y. Mitsuya Modified Reynolds equation for ultra-thin film gas lubrication using 1,5-order slip-flow model and considering surface accommodation coefficient, J. Tribol., Volume 115 (1993), pp. 289-294

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