Débit gazeux dans un microcanal : une formule utilisable du régime continu au régime moléculaire libre

Mass-Flow Rate in a Microchannel : a Formula Valid from Continuum to Free-Molecular Regimes

¹ CNRS/ICARE, 1C avenue de la recherche scientifique, 45071 Orléans Cedex 2, France
² Institute for Mathematical Modeling, Russian Acad. of Sciences, Miusskaya sq. 4a, 125047 Moscow, Russia

Auteur de correspondance : telizar@yahoo.com

Abstract

One considers the flow of a gas through a 2D or axisymmetric microchannel. The objective is to find an expression of the mass-flow rate as a function of pressures at both channel ends, gas properties and gas-surface interaction. Previous expressions are reminded that take into account rarefaction effects through terms of 1st and 2nd order in Knudsen number, added to the Poiseuille formula. The paper emphasizes on the correct evaluation of the additional terms, as concerns viscosity law, wall accommodation, definition of mean free path and physical interpretation of velocity slip. Then the expression of the flow rate in the free molecular regime is presented, based on a numerical simulation at molecular level. Qualitative differences with the previous approach are evidenced : the flow rate is proportional to the difference of end pressures, rather than to the difference of squared pressures. Finally, an interpolation formula is proposed for the intermediate (transitional) regime. It fits with both previous approaches and does not require any additional adjustment.