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

Nishanth Dongari, Yonghao Zhang, Jason Reese

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

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.
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

Fingerprint

mean free path
Gases
gases
Knudsen flow
flow velocity
gas transport
friction factor
Kinetic theory
cross flow
Boltzmann equation
probability distribution functions
data simulation
kinetic theory
laminar flow
Flow velocity
Transport properties
Probability distributions
Distribution functions
Molecular dynamics
Hydrodynamics

Keywords

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

Cite this

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). New York.
Dongari, Nishanth ; Zhang, Yonghao ; Reese, Jason. / The importance of mean free path in determining gas micro flow behaviour. Proceedings of the 8th International Conference on Nanochannels, Microchannels and Minichannels 2010: parts a & b. New York, 2011. pp. 481-490
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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. New York, pp. 481-490.

The importance of mean free path in determining gas micro flow behaviour. / Dongari, Nishanth; Zhang, Yonghao; Reese, Jason.

Proceedings of the 8th International Conference on Nanochannels, Microchannels and Minichannels 2010: parts a & b. New York, 2011. p. 481-490.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

TY - GEN

T1 - The importance of mean free path in determining gas micro flow behaviour

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AU - Zhang, Yonghao

AU - Reese, Jason

PY - 2011

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N2 - 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.

AB - 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.

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KW - thermal transpiration

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Dongari N, Zhang Y, Reese J. 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. New York. 2011. p. 481-490