A comprehensive review on micro- and nano-scale gas flow effects: Slip-jump phenomena, Knudsen paradox, thermally-driven flows, and Knudsen pumps

A rarefied gas in a long straight pipe with a periodic structure consisting of alternately arranged narrow and wide pipes and with periodic temperature distribution, which is known as the Knudsen compressor (or pump), is considered. Under the assumption that the pipe is much thinner than the period, a diffusion model that describes the pressure distribution and mass flux of the gas in each pipe element is derived, together with the connection conditions at the junctions of the narrow and wide pipes, from the kinetic system composed of the Boltzmann equation and its boundary condition on the pipe wall. Then, on the basis of the diffusion model and the connection conditions, a global diffusion model for the entire pipe is constructed by means of homogenization. The present work is a formal extension to the case of the Boltzmann equation of the previous work [K. Aoki and P. Degond, Multiscale Model. Simul. 1, 304 (2003)], where a simplified version of the Bhatnagar–Gross–Krook (BGK) collision model is used. Some numerical results based on the original BGK model are also presented both for the global diffusion model and for the local diffusion model with the connection conditions at the junctions.

/pdf/diffusion-models-for-knudsen-compressors-3cn6oifqky.pdf

Diffusion models for Knudsen compressors

A model pumping system without a moving part, which makes use of thermal transpiration and is operated with its ends at an equal temperature, is constructed. The system consists of ten units, each of which is a pipe of length 30 mm and inner diameter 15 mm with a simple inner structure and a heater. Its performance is examined under various conditions. For example, it reduces the pressure of a reservoir of 8 × 103 cm3 to a half in 300 sec when the other exit of the system is kept a constant pressure at 10 or 20 Pa and the temperature at the heater is by about 150 K higher than the temperatures at the two ends of the system.

Vacuum Pump without a Moving Part and its Performance

By just applying a temperature difference to a micro-system filled with rarefied gas, it is possible to engender a displacement or a compression of the gas in the temperature gradient direction. This is the Thermal Transpiration phenomenon. In the present work, thermal transpiration has been studied both through an experimental approach, which exploits an original measuring system, and through a numerical approach, which is modeled on the basis of the Shakhov model kinetic equation. In both studies, a circular cross section glass micro-tube is submitted to a temperature gradient. The obtained results for Helium, such as the thermal molecular pressure difference, the thermal molecular pressure ratio and the thermal molecular pressure exponent at the final zero-flow stage, are analyzed in the case of a tube submitted to a temperature difference of 51 K. Finally, the obtained thermal molecular pressure ratio results are also compared to the semi-empirical formulas of Liang (1951) and Takaishi and Sensui (1963). These semi-empirical formulas are still in use nowadays to introduce correction factors for pressure measurements done when the pressure gauge functions at different temperatures in respect to the temperature of the operating gas. For the here working pressure conditions and the used tube dimensions the gas rarefaction conditions go from near free molecular to slip regime.

An Experimental and Numerical Study of the Final Zero-Flow Thermal Transpiration Stage

It is demonstrated experimentally that a one-way flow of a slightly rarefied gas is induced in a circular straight pipe of a uniform diameter with its two ends being kept at an equal temperature and pressure by heating the middle part along the pipe and by putting up a shelf or shelves inside of a half part of the pipe on one side of the heater. The experiment is done in a small vacuum chamber of a glass bell jar, and the flow is detected by a small windmill. A one-way flow is induced from the part of the pipe with a shelf or shelves to that without it or them. The mechanism of the flow is explained by the difference of dependence on the cross sectional area between the thermal transpiration and Poiseuille flow.

/pdf/experiment-on-a-one-way-flow-of-a-rarefied-gas-through-a-33co4xi5vm.pdf

Experiment on a One-Way Flow of a Rarefied Gas Through a Straight Circular Pipe Without Average Temperature and Pressure Gradients

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Experiment on a One-Way Flow of a Rarefied Gas Through a Straight Circular Pipe Without Average Temperature and Pressure Gradients