The importance of mean free path in determining gas micro flow behaviour

Nishanth Dongari, Yonghao Zhang, Jason Reese

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Abstract

We investigate whether a power-law form of probability distribution function better describes the free paths of dilute gas molecules in a confined system. An effective molecular mean free path model is derived, which allows the mean free path to vary close to bounding surfaces. Our model is compared with molecular dynamics simulation data, and also other classical mean free path models. As gas transport properties can be related to the mean free path through kinetic theory, the Navier-Stokes constitutive relations are then modified and applied to various benchmark test cases. Results for isothermal pressure-driven Poiseuille flows in micro-channels are reported, and we compare our results with conventional hydrodynamic models, solutions of the Boltzmann equation, and experimental data. Our new approach provides good results for mean free path and cross-sectional flow velocity profiles up to Knudsen numbers around 1, and for integral flow parameters such as flow rate and friction factor up to Knudsen number of 10. We discuss some limitations of our power-law model, and point to the way forward for further development.
Original languageEnglish
Title of host publicationProceedings of the 8th International Conference on Nanochannels, Microchannels and Minichannels 2010
Subtitle of host publicationparts a & b
Place of PublicationNew York
Pages481-490
Number of pages10
Publication statusPublished - 2011

Keywords

  • knudsen layer
  • molecules
  • models
  • transition regime
  • thermal transpiration
  • importance
  • mean free path
  • determine
  • gas micro flow behaviour

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    Dongari, N., Zhang, Y., & Reese, J. (2011). The importance of mean free path in determining gas micro flow behaviour. In Proceedings of the 8th International Conference on Nanochannels, Microchannels and Minichannels 2010: parts a & b (pp. 481-490).