Journal of Fluid Mechanics

Papers

Mass flow rate measurements in a microchannel, from hydrodynamic to near free molecular regimes

TIMOTHÉE EWARTa1, PIERRE PERRIERa1, IRINA A. GRAURa1 and J. GILBERT MÉOLANSa1

a1 Université de Provence – Ecole Polytechnique Universitaire de Marseille, Département de Mécanique Energétique – UMR CNRS 6595, 5 rue Enrico Fermi, 13453 Marseille cedex 13, France timothee.ewart@polytech.univ-mrs.fr

Abstract

Helium mass flow rates in a microchannel were measured, for a wide Knudsen-number range, in isothermal steady conditions. The flow Knudsen numbers, considered here, cover the range from continuum slip regime to the near free molecular regime. We used a single-channel system involved in an experimental platform more powerful than those previously used. The experimental errors and uncertainties were accurately investigated and estimated. In the continuum slip regime, it was found that the first-order approach is pertinent for Knudsen number between 0.03 and 0.3. Moreover, the slip coefficient was deduced by comparing the experiments with the theoretical first-order slip continuum approach. For Knudsen number between 0.03 and 0.7, a polynomial second-power form is proposed for the mass flow rate expression. Otherwise, the experimental results on the mass flow rate were compared with theoretical values calculated from kinetic approaches over the 0.03–50 Knudsen number range, and an overall agreement appears through the comparison. It was also found, when the Knudsen number increased, that the wall influence on measurement occurred first through the accommodation process in the transition regime followed by the wall influence through the aspect ratio in the free molecular regime.

(Received July 18 2006)

(Revised March 10 2007)

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