The importance of mean free path in determining gas 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
Pages481-490
Number of pages9
DOIs
Publication statusPublished - 1 Aug 2010
Event8th International Conference on Nanochannels, Microchannels and Minichannels - Montréal, , Canada
Duration: 1 Aug 20105 Aug 2010

Conference

Conference8th International Conference on Nanochannels, Microchannels and Minichannels
CountryCanada
CityMontréal,
Period1/08/105/08/10

Keywords

  • thermal transpiration
  • molecules
  • models
  • transition regime
  • knudsen layer

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    Dongari, N., Zhang, Y., & Reese, J. (2010). The importance of mean free path in determining gas flow behaviour. 481-490. Paper presented at 8th International Conference on Nanochannels, Microchannels and Minichannels, Montréal, , Canada. https://doi.org/10.1115/FEDSM-ICNMM2010-30743