An Experimental and Numerical Study of the Final Zero-Flow Thermal Transpiration Stage

By just applying a temperature difference to a micro-system filled with rarefied gas, it is possible to engender a displacement or a compression of the gas in the temperature gradient direction. This is the Thermal Transpiration phenomenon. In the present work, thermal transpiration has been studied both through an experimental approach, which exploits an original measuring system, and through a numerical approach, which is modeled on the basis of the Shakhov model kinetic equation. In both studies, a circular cross section glass micro-tube is submitted to a temperature gradient. The obtained results for Helium, such as the thermal molecular pressure difference, the thermal molecular pressure ratio and the thermal molecular pressure exponent at the final zero-flow stage, are analyzed in the case of a tube submitted to a temperature difference of 51 K. Finally, the obtained thermal molecular pressure ratio results are also compared to the semi-empirical formulas of Liang (1951) and Takaishi and Sensui (1963). These semi-empirical formulas are still in use nowadays to introduce correction factors for pressure measurements done when the pressure gauge functions at different temperatures in respect to the temperature of the operating gas. For the here working pressure conditions and the used tube dimensions the gas rarefaction conditions go from near free molecular to slip regime.

[1]  J. Maxwell,et al.  On Stresses in Rarified Gases Arising from Inequalities of Temperature , 2022 .

[2]  Irina Graur,et al.  Gas flow through an elliptical tube over the whole range of the gas rarefaction , 2008 .

[3]  T. Storvick,et al.  Thermal transpiration and mechanocaloric effect. IV. Flow of a polyatomic gas in a cylindrical tube , 1982 .

[4]  Yoshio Sone,et al.  Molecular Gas Dynamics: Theory, Techniques, and Applications , 2006 .

[5]  N. Hadacek,et al.  Pressure drop for a rarefied-gas flow through a tube with a thermal gradient at low temperature , 2001 .

[6]  B. Annis,et al.  Thermal Creep in Gases , 1972 .

[7]  H. Sugimoto,et al.  Vacuum Pump without a Moving Part and its Performance , 2003 .

[8]  E. M. Shakhov.  Generalization of the Krook kinetic relaxation equation , 1968 .

[9]  William Crookes,et al.  XV. On attraction and repulsion resulting from radiation , 1874, Philosophical Transactions of the Royal Society of London.

[10]  S. Liang.  Some Measurements of Thermal Transpiration , 1951 .

[11]  S. K. Loyalka,et al.  Some numerical results for the BGK model: Thermal creep and viscous slip problems with arbitrary accomodation at the surface , 1975 .

[12]  M. Knudsen,et al.  Eine Revision der Gleichgewichtsbedingung der Gase. Thermische Molekularströmung , 1909 .

[13]  B. T. Porodnov,et al.  Thermal transpiration in a circular capillary with a small temperature difference , 1978, Journal of Fluid Mechanics.

[14]  T. Storvick,et al.  Kinetic theory of thermal transpiration and mechanocaloric effect. V. Flow of polyatomic gases in a cylindrical tube with arbitrary accommodation at the surface , 1984 .

[15]  E. P. Muntz,et al.  Knudsen compressor as a micro- and macroscale vacuum pump without moving parts or fluids , 1999 .

[16]  H. Sugimoto,et al.  Experiment on a one-way flow of a rarefied gas through a straight circular pipe without average temperature and pressure gradients , 2000 .

[17]  A. Chew,et al.  Measurement of thermal transpiration across an array of parallel capillaries using a differential capacitance manometer , 1999 .

[18]  F. Sharipov,et al.  Non-isothermal flow of rarefied gas through a long pipe with elliptic cross section , 2009 .

[19]  H. Sugimoto,et al.  Vacuum Pump without a Moving Part Driven by Thermal Edge Flow , 2005 .

[20]  S. Loyalka,et al.  Thermal Creep Slip with Arbitrary Accommodation at the Surface , 1971 .

[21]  Irina Graur,et al.  Thermal transpiration flow: A circular cross-section microtube submitted to a temperature gradient , 2011 .

[22]  Y. Gianchandani,et al.  Thermal transpiration in zeolites: A mechanism for motionless gas pumps , 2008 .

[23]  J. Los,et al.  Measurements of thermomolecular pressure differences on argon and nitrogen , 1952 .

[24]  T. Takaishi,et al.  Thermal transpiration effect of hydrogen, rare gases and methane , 1963 .

[25]  F. Tompkins,et al.  Thermal transpiration: application of Liang's equation , 1957 .

[26]  M. Knudsen.  Die Gesetze der Molekularstrmung und der inneren Reibungsstrmung der Gase durch Rhren , 1909 .

[27]  T. Storvick,et al.  Thermal transpiration: A comparison of experiment and theory , 1978 .

[28]  T. Ghosh,et al.  Measurements of thermal creep in binary gas mixtures , 1999 .

[29]  J. P. Hobson,et al.  A Study of Thermal Transpiration Using Ultrahigh-Vacuum Techniques , 1965 .

[30]  A. Chew,et al.  Thermal transpiration of helium and nitrogen in 50-μm bore silica capillaries , 2000 .

[31]  A Passian,et al.  Thermal transpiration at the microscale: a Crookes cantilever. , 2003, Physical review letters.