Rarefied gas flow through a channel of finite length into a vacuum
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TATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS
Rarefied Gas Flow through a Channel of Finite Length into a Vacuum1 O. Sazhin Ural State University, Yekaterinburg, 620083 Russia email: [email protected] Received April 7, 2009
Abstract—A rarefied gas flow through a finitelength channel into a vacuum is studied by the direct simula tion Monte Carlo method. The mass flow rate through the channel is calculated over the wide range of gas rarefactions. The analysis of the flow field, both within the channel and in upstream and downstream con tainers, is presented. PACS numbers: 47.60.Dx, 47.61.Fg DOI: 10.1134/S1063776109100161 1
1. INTRODUCTION In recent years, the direction in rarefied gas dynamics related to the analysis of micro and nanof luidic systems is being developed [1]. In contrast to the traditional approach, where gas movement is studied on a macroscopic size, the abovementioned direction is a field of rarefied gas dynamics where gas movement is studied on a micro and nanoscale. Practical appli cation of the results of this research can be in the development and creation of devices such as micro and nanoseparators, micropumps, microshutters, microgyroscopes, micro and nanosatellites, and other micro and nanoelectroraechanical systems (MEMS/NEMS). The flow of gas in MEMS/NEMS, depending on the device size and gas pressure, can be viscous, transitional, or free molecular. Incidentally, the free molecular flow in nanodevices can be observed even at normal atmospheric pressure. In studying the internal flow of rarefied gas, special attention is paid to the capillaries of various geometric shapes and sizes. A rather large number of theoretical works is dedicated to the rarefied gas flow, caused by a small pressure difference, through straight capillaries of infinite length [2, 3]. In this case, the gas concentra tion and temperature change linearly along the capil lary axis, and hence linearized models of the integral differential Boltzmann equation is successfully used for flow calculation. In particular, in one of the pio neering works [4], the mass flow rate of gas through a straight infinitely long channel (capillary with a rect angular cross section) was calculated in a wide range of gas rarefaction. An important outcome of this study is the discovery of the socalled Knudsen minimum (or Knudsen paradox)—a minimum of the flow rate through a channel in the transitional regime. Subse 1
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quently, a minimum of the gas flow rate through a channel was also confirmed experimentally [5]. Rarefied gas flow through finitelength capillaries presents a much more complex task. In the case of a small pressure difference, the gas flow through a chan nel is calculated in [6] using the BGK model of the Boltzmann equation. From this work, in particular, it follows that the position of the Knudsen minimum depends on the length of the channel. In the case of a finitelength capillary and a large pressure difference, as in the case of gas flow into a vacuum, the
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