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Description
Thermal creep, or thermal transpiration, is a gas-transport phenomenon occurring in the presence of a temperature gradient: gas molecules migrate from the colder side to the hotter one. First identified by Reynolds and later analyzed by Maxwell and Knudsen, this effect has recently attracted renewed attention as it becomes important at small scale. The miniaturization of mechanical components in MEMS devices lead to the development of Knudsen pumps - gas pumps without moving parts that operate without vibration and exhibit long operational lifetimes. Such pumps typically rely on arrays of microchannels with heterogeneous geometries, which can be interpreted as porous media analogous to the Capillary Bundle Model.
In this work, we investigate experimentally the gas transport through a bundle of 3600 circular capillaries (a=2.95µm, L=5cm) under rarefied conditions spanning the slip-flow to transitional regimes. The bundle of capillaries is settled between two tanks of constant volumes, which are maintained at constant, but different temperatures. These two tanks are also connected by the large diameter tube with a solenoidal valve. After the pressures are equilibrated in the system, the solenoidal valve is closed and a test gas starts to flow from a cold tank to the hot one. The direct gas mass flow measurement is challenging at these scales, gas transfer is obtained from the fit of the time evolution of the reservoir pressures.
The observed flow dynamics exhibit two characteristic stages: (i) An initial thermal creep flow, i.e. from the cold reservoir toward the hot reservoir, generating a pressure difference between the tanks. (ii) A subsequent pressure - driven Poiseuille flow that counteracts the thermal creep, establishing a new steady state.
The pressure in each tank and the pressure difference between the tanks, as well as the temperatures in each tank are recorded over time. The fit of the pressure difference between the tank in forme $\Delta p=TPD(1-exp(-(t-t_0)/\tau)))$ allows to obtain two parameters, the characteristic time, $\tau$, and the final pressure difference, the Thermo-molecular Pressure Difference (TPD). The mass flow rate through the capillaries is also derived.
Experiments were performed using three pure gases, He, Ar, and CO₂, and the results are compared with the theoretical model proposed previously . Additionally, the effective permeability of the capillary bundle is derived to support the optimization of the experimental setup and future studies involving rectangular microchannels and realistic porous materials.
| Country | France |
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