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Thermal transpiration flow through a single rectangular channel

Published online by Cambridge University Press:  10 April 2014

Hiroki Yamaguchi ,
Marcos Rojas-Cárdenas ,
Pierre Perrier ,
Irina Graur  and
Tomohide Niimi
Hiroki Yamaguchi*
Affiliation:
Department of Micro-Nano Systems Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya, Aichi 464-8603, Japan
Marcos Rojas-Cárdenas
Affiliation:
IUSTI, UMR 7343, CNRS, Aix-Marseille University, 13013 Marseille, France
Pierre Perrier
Affiliation:
IUSTI, UMR 7343, CNRS, Aix-Marseille University, 13013 Marseille, France
Irina Graur
Affiliation:
IUSTI, UMR 7343, CNRS, Aix-Marseille University, 13013 Marseille, France
Tomohide Niimi
Affiliation:
Department of Micro-Nano Systems Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya, Aichi 464-8603, Japan
*
†Email address for correspondence: hiroki@nagoya-u.jp
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Abstract

A thermal transpiration flow through a single rectangular micro-channel was studied experimentally for various gas species, including all rare gases, in order to investigate the influence of gas species on the flow properties. The final equilibrium flow characteristics and relaxation time of the pressure variation were evaluated as functions of the rarefaction parameter. The thermal molecular pressure difference was well fitted by the log-normal distribution function, and its magnitude was found to be strongly dependent on the gas species: a larger pressure difference was obtained for molecules of smaller diameter. However, for the thermal molecular pressure ratio and the thermal molecular pressure exponent, which are dimensionless quantities, the dependence on the gas species was negligible. The relaxation time of the pressure variation was well normalized by the characteristic time of the system. The influence of the geometry was evaluated by comparing the present results, obtained for the case of a rectangular channel, with already published data obtained for the case of a circular cross-section tube. The comparison showed that these two geometrical configurations influence the fluid flow in equal manner, if appropriate geometrical parameters are used for their representation.

JFM classification

Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics Micro-/Nano-fluid dynamics: Non-continuum effects Rarefied Gas Flow: Rarefied Gas Flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 744 , 10 April 2014 , pp. 169 - 182
Copyright
© 2014 Cambridge University Press 

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References

Arkilic, E. B., Breuer, K. S. & Schmidt, M. A. 2001 Mass flow and tangential momentum accommodation in silicon micromachined channels. J. Fluid Mech. 437, 29–43.CrossRefGoogle Scholar
Bird, G. A. 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press.CrossRefGoogle Scholar
Ewart, T., Perrier, P., Graur, I. A. & Méolans, J. G. 2007 Mass flow rate measurements in a microchannel, from hydrodynamic to near free molecular regimes. J. Fluid Mech. 584, 337–356.CrossRefGoogle Scholar
Gupta, N. K., An, S. & Gianchandani, Y. B. 2012 A Si-micromachined 48-stage Knudsen pump for on-chip vacuum. J. Micromech. Microengng 22, 105026.CrossRefGoogle Scholar
Hadj Nacer, M., Graur, I., Perrier, P., Méolans, J. G. & Wuest, M. 2014 Gas flow through microtubes with different internal surface coatings. J. Vac. Sci. Technol. A 32, 021601.CrossRefGoogle Scholar
Knudsen, M. 1910a Eine Revision der Gleichgewichtsbedingung der Gase. Thermische Molekularströmung. Ann. Phys. 336, 205–229.CrossRefGoogle Scholar
Knudsen, M. 1910b Thermischer Molekulardruck der Gase in Röhren. Ann. Phys. 338, 1435–1448.CrossRefGoogle Scholar
Liu, J., Gupta, N. K., Wise, K. D., Gianchandani, Y. B. & Fan, X. 2011 Demonstration of motionless Knudsen pump based micro-gas chromatography featuring micro-fabricated columns and on-column detectors. Lab on a Chip 11, 3487–3492.CrossRefGoogle ScholarPubMed
Maxwell, J. C. 1879 On stresses in rarefied gases arising from inequalities of temperature. Phil. Trans. R. Soc. Lond. 170, 231–256.Google Scholar
Perrier, P., Graur, I. A., Ewart, T. & Méolans, J. G. 2011 Mass flow rate measurements in microtubes: from hydrodynamic to near free molecular regime. Phys. Fluids 23, 042004.CrossRefGoogle Scholar
Porodnov, B. T., Kulev, A. N. & Tuchevetov, F. T. 1978 Thermal transpiration in a circular capillary with a small temperature difference. J. Fluid Mech. 88, 609–622.CrossRefGoogle Scholar
Reynolds, O. 1879 On certain dimensional properties of matter in the gaseous state. Parts I and II. Phil. Trans. R. Soc. Lond. 170, 727–845.Google Scholar
Rojas-Cárdenas, M., Graur, I., Perrier, P. & Méolans, J. G. 2011 Thermal transpiration flow: a circular cross-section microtube submitted to a temperature gradient. Phys. Fluids 23, 031702.CrossRefGoogle Scholar
Rojas-Cárdenas, M., Graur, I., Perrier, P. & Méolans, J. G. 2012 An experimental and numerical study of the final zero-flow thermal transpiration stage. J. Therm. Sci. Technol. 7, 437–452.CrossRefGoogle Scholar
Rojas-Cárdenas, M., Graur, I., Perrier, P. & Méolans, J. G. 2013 Time-dependent experimental analysis of a termal transpiration rarefied gas flow. Phys. Fluids 25, 072001.CrossRefGoogle Scholar
Sugimoto, H. & Hibino, M. 2012 Numerical analysis on gas separator with thermal transpiration in micro channels. In Rarefied Gas Dynamics (ed. Mareschal, M. & Santos, A.), AIP Conf. Proc., vol. 1501, pp. 794–801. American Institute of Physics.Google Scholar
Takaishi, T. & Sensui, Y. 1963 Thermal transpiration effect of hydrogen, rare gases and methane. Trans. Faraday Soc. 59, 2503–2514.CrossRefGoogle Scholar
Vargo, S. E. & Muntz, E. P. 2001 Initial results from the first MEMS fabricated thermal transpiration-driven vacuum pump. In Rarefied Gas Dynamics (ed. Bartel, T. J. & Gallis, M. A.), AIP Conf. Proc., vol. 585, pp. 502–509. American Institute of Physics.Google Scholar
Yamaguchi, H., Hanawa, T., Yamamoto, O., Matsuda, Y., Egami, Y. & Niimi, T. 2011 Experimental measurement on tangential momentum accommodation coefficient in a single microtube. Microfluid. Nanofluid. 11, 57–64.CrossRefGoogle Scholar