Measurements of tangential momentum accommodation coefficient for various gases in plane microchannel
Phys. Fluids 21, 102004 (2009); doi:10.1063/1.3253696
Published 30 October 2009
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Mass flow rate measurements in a single silicon microchannel were carried out for various gases in isothermal steady flows. The results obtained from hydrodynamic to near free molecular regime by using a powerful experimental platform allowed us to deduce interesting information, notably about the reflection/accommodation process at the wall. In the 0–0.3 Knudsen range, a continuum analytic approach was derived from the NS equations, associated with first or second order slip boundary conditions. Identifying the experimental mass flow rate curves to the theoretical ones the tangential momentum accommodation coefficient (TMAC) of various gases was extracted. Over the full Knudsen range [0–30] the experimental results were compared with theoretical values calculated from the kinetic approaches: using variable accommodation coefficient values as fitting parameter, the theoretical curves were fitted to the experimental ones. Whatever the Knudsen range and whatever the theoretical approach, the TMAC values are found decreasing when the molecular weights of the gas increase (as long as the different gases are compared using the same approach). Moreover, the values of the various accommodation coefficients are rather close to one another but sufficiently smaller than unity indicating that the full accommodation modeling is not satisfactory to describe the gas/wall interaction.
©2009 American Institute of Physics
| History: | Received 3 March 2009; accepted 18 September 2009; published 30 October 2009 |
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REFERENCES (29)
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- S. Colin, P. Lalonde, and R. Caen, “Validation of a second-order slip flow model in a rectangular microchannel,”
Heat Transf Eng. 25, 23 (2004) . - E. B. Arkilic, K. S. Breuer, and M. A. Schmidt, “Mass flow and tangential momentum accomodation in silicon micromachined channels,”
J. Fluid Mech. 437, 29 (2001) . - J. Maurer, P. Tabeling, P. Joseph, and H. Willaime, “Second-order slip laws in microchannels for helium and nitrogen,” Phys. Fluids 15, 2613 (2003).
- T. Ewart, P. Perrier, I. A. Graur, and J. G. Méolans, “Mass flow rate measurements in gas micro flows,”
Exp. Fluids 41, 487 (2006) . - T. Ewart, P. Perrier, I. A. Graur, and J. G. Méolans, “Mass flow rate measurements in microchannel, from hydrodynamic to near free molecular regimes,”
J. Fluid Mech. 584, 337 (2007) . - G. Karniadakis and A. Beskok, Microflows: Fundamentals and Simulation (Springer, New York, 2002).
- Y. Sone, Kinetic Theory and Fluid Mechanics (Birkhäuser, Boston, 2002).
- T. Ewart, P. Perrier, I. A. Graur, and J. G. Méolans, “Tangential momentum accomodation in microtube,”
Microfluid. Nanofluid. 3, 689 (2007) . - S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge University Press, Cambridge, 1952).
- C. Cercignani, Mathematical Methods in Kinetic Theory, 2nd Ed. (Plenum, New York, 1990).
- J. C. Maxwell, “On stress in rarefied gases arising from inequalities of temperature,” Philos. Trans. R. Soc. London, Ser. B 170, 231 (1878).
- F. Sharipov and V. Seleznev, “Data on internal rarefied gas flows,”
J. Phys. Chem. Ref. Data 27, 657 (1998) . - C. Cercignani and A. Daneri, “Flow of a rarefied gas between two parallel plates,”
J. Appl. Phys. 34, 3509 (1963) . - S. K. Loyalka, “Kinetic theory of thermal transpiration and mechanocaloric effects II,” J. Chem. Phys. 63, 4054 (1975).
- T. Ohwada, Y. Sone, and K. Aoki, “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 1, 2042 (1989).
- S. K. Loyalka, T. S. Stvorik, and H. S. Park, “Poiseulle flow and thermal creep flow in long, rectangular channels in the molecular and transition flow regimes,”
J. Vac. Sci. Technol. 13, 1188 (1976) . - F. Sharipov, “Rarefied gas flow through a long rectangular channel,”
J. Vac. Sci. Technol. A 17, 3062 (1999) . - F. Sharipov, “Non-isothermal gas flow through rectangular microchannels,”
J. Micromech. Microeng. 9, 394 (1999) . - S. K. Loyalka, N. Petrellis, and S. T. Stvorick, “Some numerical results for the bgk model: Thermal creep and viscous slip problems with arbitrary accommodation of the surface,”
Phys. Fluids 18, 1094 (1975) . - I. A. Graur, J. G. Méolans, and D. E. Zeitoun, “Analytical and numerical description for isothermal gas flows in microchannels,”
Microfluid. Nanofluid. 2, 64 (2006) . - M. N. Kogan, Rarefied Gas Dynamics (Plenum, New York, 1969).
- F. Sharipov, “Data on the velocity slip and temperature jump coefficients,” in Thermal and Mechanical Simulation and Experiments in Micro-Electronics and Micro-Systems, Proc. 5th Int. Conf. EuroSimE, edited by L. J. Ernst, G. Q. Zhang, P. Rodgers, and O. de Saint Leger (Shaker, Belgium, 2004), pp. 243–249.
- A. Agrawal and S. V. Prabhu, “Survey on measurement of tangential momentum accommodation coefficient,”
J. Vac. Sci. Technol. A 26, 634 (2008) . - T. Gronych, R. Ulman, L. Peksa, and P. Repa, “Measurements of the relative momentum accommodation coefficient for different gases with a viscosity vacuum gauge,”
Vacuum 73, 275 (2004) . - P. E. Suetin, B. T. Porodnov, V. G. Chernayk, and S. F. Borisov, “Poiseuille flow at arbitrary Knudsen number and tangential momentum accommodation,”
J. Fluid Mech. 60, 581 (1973) . - O. V. Sazhin, S. F. Borisov, and F. Sharipov, “Accommodation coefficient of tangential momentum on atomically clean and contaminated surfaces,”
J. Vac. Sci. Technol. A 19, 2499 (2001) . - B. T. Porodnov, P. E. Suetin, S. F. Borisov, and V. D. Akinshin, “Experimental investigation of rarefied gas flow in different channels,”
J. Fluid Mech. 64, 417 (1974) . - T. Ewart, “Etude des écoulements gazeux isothermes en microconduits: Du régime hydrodynamique au proche régime molćulaire libre,” Ph.D. thesis, Provence Ubiversity, 2007 (in French).
- P. Perrier, “Instrumentation et physisique expérimentale appliquées à la spectrométrie de masse et aux écoulemets gazeux,” Habilitating Thesis, Provence University, 2008 (in French).







