Database for flows of binary gas mixtures through a plane microchannel. (English) Zbl 1154.76048

Summary: We consider a binary mixture of rarefied gases between two parallel plates. The Poiseuille flow, thermal transpiration (flow caused by a temperature gradient of the plates) and concentration-driven flow (flow caused by a gradient of concentration of the component species) are analyzed on the basis of the linearized model Boltzmann equation with the diffuse reflection boundary condition. The analyses are first performed for mixtures of virtual gases composed of the hard-sphere or Maxwell molecules, and the results are compared with those of the original Boltzmann equation. Then, the analyses for noble gases (He-Ne, He-Ar and Ne-Ar) are performed assuming more realistic molecular models (the inverse power-law potential and Lennard-Jones 12,6 models). By use of the results, flux databases covering the entire ranges of the Knudsen number and of the concentration and a wide range of temperature are constructed. The databases are prepared for the use in the fluid-dynamic model for mixtures in a stationary nonisothermal microchannel derived in [S. Takata, H. Sugimoto and S. Kosuge, ibid. 26, No. 2, 155–181 (2007; Zbl 1124.76048)], but can also be incorporated in the generalized Reynolds equation [S. Fukui and R. Kaneko, J. Tribol. 110, 253–262 (1988)] in the gas film lubrication theory. The databases constructed can be downloaded freely from Electronic Annex 2 in the online version of this article.


76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)


Zbl 1124.76048
Full Text: DOI


[1] Fukui, S.; Kaneko, R., Analysis of ultra-thin gas film lubrication based on linearized Boltzmann equation including thermal creep flow, J. tribol., 110, 253-262, (1988)
[2] Shen, C., Use of the degenerated Reynolds equation in solving the microchannel flow problem, Phys. fluids, 17, 046101, (2005) · Zbl 1187.76479
[3] Takata, S.; Sugimoto, H.; Kosuge, S., Gas separation by means of the Knudsen compressor, Eur. J. mech. B/fluids, 26, 155-181, (2007) · Zbl 1124.76048
[4] Knudsen, M., Eine revision gleichgewichtsbedingung der gase. thermische molekularströmung, Ann. phys. (Leipzig), 31, 205-229, (1910) · JFM 41.0876.02
[5] Pham-Van-Diep, G.; Keeley, P.; Muntz, E.P.; Weaver, D.P., A micromechanical Knudsen compressor, (), 715-721
[6] Sone, Y.; Waniguchi, Y.; Aoki, K., One-way flow of a rarefied gas induced in a channel with a periodic temperature distribution, Phys. fluids, 8, 2227-2235, (1996) · Zbl 1027.76650
[7] Cercignani, C.; Lampis, M.; Lorenzani, S., Plane poiseuille – couette problem in micro-electro-mechanical systems applications with gas-rarefaction effects, Phys. fluids, 18, 087102, (2006) · Zbl 1262.76087
[8] Maxwell, J.C., On stresses in rarefied gases arising from inequalities of temperature, Philos. trans. roy. soc., 170, 231-256, (1879) · JFM 11.0777.01
[9] Sone, Y., Kinetic theory and fluid dynamics, (2002), Birkhäuser Boston · Zbl 1021.76002
[10] Ohwada, T.; Sone, Y.; Aoki, K., Numerical analysis of the Poiseuille and thermal transpiration flows between two parallel plates on the basis of the Boltzmann equation for hard-sphere molecules, Phys. fluids A, Phys. fluids A, 2, 639-2049, (1990), Erratum: · Zbl 0696.76092
[11] Sharipov, F.; Seleznev, V., Data on internal rarefied gas flows, J. phys. chem. ref. data, 27, 657-706, (1998)
[12] Chernyak, V.G.; Kalinin, V.V.; Suetin, P.E., The kinetic phenomena in nonisothermal motion of a binary gas through a plane channel, Int. J. heat mass transfer, 27, 1189-1196, (1984) · Zbl 0546.76122
[13] Onishi, Y., On the behaviour of a slightly rarefied gas mixture over plane boundaries, Z. angew. math. phys., 37, 573-596, (1986) · Zbl 0603.76078
[14] Huang, C.M.; Tompson, R.V.; Ghosh, T.K.; Ivchenko, I.N.; Loyalka, S.K., Measurements of thermal creep in binary gas mixtures, Phys. fluids, 11, 1662-1672, (1999) · Zbl 1147.76418
[15] Sharipov, F.; Kalempa, D., Gaseous mixture flow through a long tube at arbitrary Knudsen numbers, J. vac. sci. technol. A, 20, 814-822, (2002)
[16] Naris, S.; Valougeorgis, D.; Kalempa, D.; Sharipov, F., Gaseous mixture flow between two parallel plates in the whole range of the gas rarefaction, Physica A, 336, 294-318, (2004)
[17] Siewert, C.E.; Valougeorgis, D., The mccormack model: channel flow of a binary gas mixture driven by temperature, pressure and density gradients, Eur. J. mech. B/fluids, 23, 645-664, (2004) · Zbl 1060.76631
[18] Naris, S.; Valougeorgis, D.; Kalempa, D.; Sharipov, F., Flow of gaseous mixtures through rectangular microchannels driven by pressure, temperature, and concentration gradients, Phys. fluids, 17, 100607, (2005) · Zbl 1187.76378
[19] Kosuge, S.; Sato, K.; Takata, S.; Aoki, K., Flows of a binary mixture of rarefied gases between two parallel plates, (), 150-155
[20] McCormack, F.J., Construction of linearized kinetic models for gaseous mixtures and molecular gases, Phys. fluids, 16, 2095-2105, (1973) · Zbl 0274.76054
[21] Chapman, S.; Cowling, T.G., The mathematical theory of non-uniform gases, (1990), Cambridge University Press Cambridge · Zbl 0098.39702
[22] Cercignani, C.; Sharipov, F., Gaseous mixture slit flow at intermediate Knudsen numbers, Phys. fluids A, 4, 1283-1289, (1992) · Zbl 0767.76064
[23] Chu, C.K., Kinetic-theoretic description of the formation of a shock wave, Phys. fluids, 8, 12-22, (1965)
[24] Sone, Y., Asymptotic theory of flow of rarefied gas over a smooth boundary I, (), 243-253
[25] Sone, Y., Asymptotic theory of flow of rarefied gas over a smooth boundary II, (), 737-749
[26] Takata, S.; Aoki, K., The ghost effect in the continuum limit for a vapor – gas mixture around condensed phases: asymptotic analysis of the Boltzmann equation, Transp. theory stat. phys., Transp. theory stat. phys., 31, 289-237, (2002), Erratum: · Zbl 1106.82359
[27] Aoki, K.; Bardos, C.; Takata, S., Knudsen layer for gas mixtures, J. stat. phys., 112, 629-655, (2003) · Zbl 1124.82314
[28] Cercignani, C., Plane Poiseuille flow and Knudsen minimum effect, (), 92-101
[29] Cercignani, C., Plane Poiseuille flow according to the method of elementary solutions, J. math. anal. appl., 12, 254-262, (1965)
[30] Niimi, H., Thermal creep flow of rarefied gas between two parallel plates, J. phys. soc. jpn., 30, 572-574, (1971)
[31] Abramowitz, M.; Stegun, I.A., Handbook of mathematical functions, (1968), Dover New York
[32] Takata, S.; Yasuda, S.; Kosuge, S.; Aoki, K., Numerical analysis of thermal-slip and diffusion-slip flows of a binary mixture of hard-sphere molecular gases, Phys. fluids, 15, 3745-3766, (2003) · Zbl 1186.76516
[33] Gasquet, C.; Witomski, P., Fourier analysis and applications, (1999), Springer-Verlag New York · Zbl 0931.94001
[34] Cercignani, C., The Boltzmann equation and its applications, (1988), Springer-Verlag New York · Zbl 0646.76001
[35] Sharipov, F., Onsager – casimir reciprocity relations for open gaseous systems at arbitrary rarefaction. III. theory and its application for gaseous mixtures, Physica A, 209, 457-476, (1994)
[36] Ohwada, T.; Sone, Y.; Aoki, K., Numerical analysis of the shear and thermal creep flows of a rarefied gas over a plane wall on the basis of the linearized Boltzmann equation for hard-sphere molecules, Phys. fluids A, 1, 1588-1599, (1989) · Zbl 0695.76032
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