# Measurements and modeling of the gas flow in a microchannel: influence of aspect ratios, surface nature, and roughnesses

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## Abstract

This article extends in various directions of our previous studies related to gas flow in long rectangular cross-section microchannels. In the present article, the mass flow rate of various gases through microchannels with different aspect ratios, and various surface coatings (Au and SiO\(_2\)) and surface roughnesses (from 0.9 to 12 nm) is measured under isothermal conditions. Previously, we developed a method to calculate the mass flow rate through rectangular microchannels that allows taking into account the real dimensions of the rectangular channel cross-section. In the present article, this method was applied to extract the velocity slip and tangential momentum accommodation coefficients in the frame of the Maxwell diffuse-specular scattering kernel. An extension of the previous approach is also proposed in the present paper. This extension allows considering the possible difference in properties (roughness or material) between the vertical and horizontal channel walls by introducing different accommodation coefficients for each wall. By applying the new method, we can extract a single accommodation coefficient for all the channel walls under the assumption of homogeneous material and roughness and two different accommodation coefficients for the horizontal and vertical walls in the case when the two walls have different properties (roughness or material).

## Notes

### Acknowledgements

We wish to acknowledge the support of MIMENTO platform of technology and especially FEMTO-ST Laboratory (http://www.femto-st.fr) for the microsystem fabrication and the measurement of the microchannel dimensions. This research received funding from the European Community’s Seventh Framework Program (ITN FP7/2007-2013) under Grant Agreement Number 215504.

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