Gas separation by means of the Knudsen compressor. (English) Zbl 1124.76048

Summary: We investigate the possibility of making use of Knudsen compressor as a gas separator. Starting from the description at the microscopic level on the basis of kinetic theory of gases, we derive a fluid-dynamical model describing the behaviour of the mixture in Knudsen compressor. Then, by the use of this model, we numerically demonstrate that the Knudsen compressor works certainly as a gas separator. The separation performance is shown to reach a practical level by increasing the number of elemental units in the device. The numerical simulation is carried out for various molecular models, not only for fundamental models as hard-sphere and Maxwell molecules, but also for more realistic models such as the inverse power-law potential and Lennard-Jones models, assuming the McCormack model equation at the microscopic level. The results show that the modelling by the celebrated Maxwell molecule (or the BGK-type) model equation fails to capture the phenomenon of gas separation in the device. This presents a remarkable contrast to the capability of other fundamental model, the hard-sphere molecule, even though this model exaggerates the phenomenon to some extent.


76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
Full Text: DOI


[1] 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
[2] Knudsen, M., Eine revision gleichgewichtsbedingung der gase. thermische molekularströmung, Ann. phys. (Leipzig), 31, 205-229, (1910) · JFM 41.0876.02
[3] Kennard, E.H., Kinetic theory of gases, (1938), McGraw-Hill New York
[4] Pham-Van-Diep, G.; Keeley, P.; Muntz, E.P.; Weaver, D.P., A micromechanical Knudsen compressor, (), 715-721
[5] 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
[6] Vargo, S.E.; Muntz, E.P., An evaluation of a multiple-stage micromechanical Knudsen compressor and vacuum pump, (), 995-1000
[7] Hudson, M.L.; Bartel, T.J., DSMC simulation of thermal transpiration and accommodation pumps, (), 719-726
[8] Young, M.; Han, Y.L.; Muntz, E.P.; Shiflett, G.; Ketsdever, A.; Green, A., Thermal transpiration in microsphere membranes, (), 743-751
[9] Han, Y.L.; Young, M.; Muntz, E.P.; Shiflett, G., Knudsen compressor performance at low pressures, (), 162-167
[10] Young, M.; Han, Y.L.; Muntz, E.P.; Shiflett, G., Characterization and optimization of a radiantly driven multi-stage Knudsen compressor, (), 174-179
[11] Sone, Y.; Sato, K., Demonstration of a one-way flow of a rarefied gas induced through a pipe without average pressure and temperature gradients, Phys. fluids, 12, 1864-1868, (2000) · Zbl 1184.76522
[12] Aoki, K.; Sone, Y.; Takata, S.; Takahashi, K.; Bird, G.A., One-way flow of a rarefied gas induced in a circular pipe with a periodic temperature distribution, (), 940-947
[13] Sone, Y.; Fukuda, T.; Hokazono, T.; Sugimoto, H., Experiment on a one-way flow of a rarefied gas through a straight circular pipe without average temperature and pressure gradients, (), 948-955
[14] Sone, Y.; Sugimoto, H., Knudsen compressor, J. vac. soc. jpn., 45, 138-141, (2002)
[15] Sone, Y.; Sugimoto, H., Vacuum pump without a moving part and its performance, (), 1041-1048
[16] Aoki, K.; Degond, P., Homogenization of a flow in a periodic channel of small section, Multiscale model. simul., 1, 304-334, (2003) · Zbl 1107.76060
[17] Sugimoto, H.; Sone, Y., Vacuum pump without a moving part driven by thermal edge flow, (), 168-173
[18] K. Aoki, P. Degond, S. Takata, Fluid-dynamic models for Knudsen compressors, in preparation · Zbl 1182.76027
[19] Sone, Y., Kinetic theory and fluid dynamics, (2002), Birkhäuser Boston · Zbl 1021.76002
[20] Aoki, K.; Sone, Y.; Masukawa, N., A rarefied gas flow induced by a temperature field, (), 35-41
[21] Sone, Y.; Yoshimoto, M., Demonstration of a rarefied gas flow induced near the edge of a uniformly heated plate, Phys. fluids, 9, 3530-3534, (1997)
[22] Kosuge, S.; Sato, K.; Takata, S.; Aoki, K., Flows of a binary mixture of rarefied gases between two parallel plates, (), 150-155
[23] Sharipov, F.; Kalempa, D., Gaseous mixture flow through a long tube at arbitrary Knudsen numbers, J. vac. sci. technol. A, 20, 814-822, (2002)
[24] M. Kayashima, Device for the transport and compression of gases by the use of the porous media, Patent JP. 1513106, B (in Japanese) · Zbl 0911.57015
[25] 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)
[26] Sharipov, F., Rarefied gas flow through a long tube at any temperature ratio, J. vac. sci. technol. A, 14, 2627-2635, (1996)
[27] Shen, C., Use of the degenerated Reynolds equation in solving the microchannel flow problem, Phys. fluids, 17, 046101, (2005) · Zbl 1187.76479
[28] Cercignani, C.; Lampis, M.; Lorenzani, S., Flow of a rarefied gas between parallel and almost parallel plates, (), 719-724
[29] Y. Sone, Molecular Gas Dynamics, Birkhäuser, Boston, in press
[30] von Karman, T., From low-speed aerodynamics to astronautics, (1963), Pergamon Press Oxford
[31] Charrier, P.; Dubroca, B., Asymptotic transport models for heat and mass transfer in reactive porous media, Multiscale model. simul., 2, 124-157, (2003) · Zbl 1078.76068
[32] Aoki, K.; Bardos, C.; Takata, S., Knudsen layer for gas mixtures, J. stat. phys., 112, 629-655, (2003) · Zbl 1124.82314
[33] Cercignani, C., Plane Poiseuille flow and Knudsen minimum effect, (), 92-101
[34] Cercignani, C., Plane Poiseuille flow according to the method of elementary solutions, J. math. anal. appl., 12, 254-262, (1965)
[35] Niimi, H., Thermal creep flow of rarefied gas between two parallel plates, J. phys. soc. jpn., 30, 572-574, (1971)
[36] Börgers, C.; Greengard, C.; Thomann, E., The diffusion limit of free molecular flow in thin plane channels, SIAM J. appl. math., 52, 1057-1075, (1992) · Zbl 0761.76089
[37] Golse, F., Anomalous diffusion limit for the Knudsen gas, Asymptotic anal., 17, 1-12, (1998) · Zbl 0974.76073
[38] Babovsky, H., On Knudsen flows within thin tubes, J. stat. phys., 44, 865-878, (1986) · Zbl 0629.76079
[39] Babovsky, H.; Bardos, C.; Platkowski, T., Diffusion approximation for a Knudsen gas in a thin domain with accommodation on the boundary, Asymptotic anal., 3, 265-289, (1991) · Zbl 0850.76599
[40] Bird, G.A., Molecular gas dynamics, (1976), Oxford University Press Oxford
[41] Bird, G.A., Molecular gas dynamics and the direct simulation of gas flows, (1994), Oxford University Press Oxford
[42] 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
[43] McCormack, F.J., Construction of linearized kinetic models for gaseous mixtures and molecular gases, Phys. fluids, 16, 2095-2105, (1973) · Zbl 0274.76054
[44] Hamel, B.B., Kinetic model for binary gas mixtures, Phys. fluids, 8, 418-425, (1965)
[45] Chapman, S.; Cowling, T.G., The mathematical theory of non-uniform gases, (1995), Cambridge University Press Cambridge · Zbl 0098.39702
[46] Bird, R.B.; Stewart, W.E.; Lightfoot, E.N., Transport phenomena, (1960), John Wiley & Sons New York
[47] Vincenti, W.G.; Kruger, C.H., Introduction to physical gas dynamics, (1965), John Wiley & Sons New York
[48] Cercignani, C., Rarefied gas dynamics, from basic concepts to actual calculations, (2000), Cambridge University Press Cambridge · Zbl 0961.76002
[49] Sone, Y., Asymptotic theory of flow of rarefied gas over a smooth boundary I, (), 243-253
[50] Sone, Y., Asymptotic theory of a steady flow of a rarefied gas past bodies for small Knudsen numbers, (), 19-31
[51] Cercignani, C.; Sharipov, F., Gaseous mixture slit flow at intermediate Knudsen numbers, Phys. fluids A, 4, 1283-1289, (1992) · Zbl 0767.76064
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.