ICMM2005-75257 RECENT RESULTS OF RAREFIED GAS DYNAMICS AND THEIR APPLICATIONS IN MICROFLOWS

ABSTRACT Since the size of microsystems is close to the molecular mean free path, the gas rarefaction must be taken into account in modelling of microflows. However, the transition regime represents many difficulties for practical calculations because the Boltzmann equation must be applied. This approach requires great computational efforts and many engineers prefer to substitute such calculations by some estimations, which lead to quite incorrect results in many cases. At the same time, many rigorous results for the transition regime already obtained from the Boltzmann equation can be easily used in practical calculations. A brief survey of many recent books on microflows showed that all of then give just elementary information about the kinetic theory of gases, while the results on the transition flows of gases obtained during the few last decades are omitted. The aim of the present work is to review the recent results of rarefied gas dynamics and to give several examples of their applications in microchannels. NOMENCLATURE a tube radius and channel height b channel width f distribution function G P Poiseuille flow G T thermal creep k Boltzmann constant L channel lengtḣ M mass flow rate m molecular mass n number density P pressure Q collision integral r position vector R(v ; v) scattering kernel T temperature u bulk velocity v molecular velocity v m most probable molecular velocity α n energy accommodation coefficient α t momentum accommodation coefficient δ rarefaction parameter µ viscosity ξ P pressure gradient ξ T temperature gradient ρ mass density Σ cross section σ P viscous slip coefficient σ T thermal slip coefficient Main definitions The main parameter determining rarefied gas flows is the gas rarefaction defined a

General approach to transient flows of rarefied gases through long capillaries

International audienceAn approach to model a transient flow of rarefied gas through a long capillary based on numerical data for flow rate previously obtained from the linearized and stationary kinetic equation was proposed. As an example, non-steady flow through a long circular tube connecting two reservoirs is considered. Pressures in the reservoirs and flow rates in the inlet and outlet are obtained as a function of time. It is shown that the behaviors of these quantities vary by changing the gas rarefaction from the free-molecular regime to hydrodynamic one. The typical time to reach the equilibrium state is calculated. (c) 2013 Elsevier Ltd. All rights reserved