The importance of mean free path in determining gas flow behaviour

Nishanth Dongari, Yonghao Zhang, Jason Reese

Research output: Contribution to conferencePaper

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

Conference

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

Fingerprint

Gas Flow
Flow of gases
Path
Knudsen number
Power Law
Kinetic theory
Boltzmann equation
Gases
Poiseuille Flow
Hydrodynamic Model
Flow velocity
Microchannel
Transport properties
Probability Distribution Function
Probability distributions
Constitutive Relations
Transport Properties
Kinetic Theory
Distribution functions
Molecular dynamics

Keywords

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

Cite this

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
Dongari, Nishanth ; Zhang, Yonghao ; Reese, Jason. / The importance of mean free path in determining gas flow behaviour. Paper presented at 8th International Conference on Nanochannels, Microchannels and Minichannels, Montréal, , Canada.9 p.
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Dongari, N, Zhang, Y & Reese, J 2010, 'The importance of mean free path in determining gas flow behaviour' Paper presented at 8th International Conference on Nanochannels, Microchannels and Minichannels, Montréal, , Canada, 1/08/10 - 5/08/10, pp. 481-490. https://doi.org/10.1115/FEDSM-ICNMM2010-30743

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

2010. 481-490 Paper presented at 8th International Conference on Nanochannels, Microchannels and Minichannels, Montréal, , Canada.

Research output: Contribution to conferencePaper

TY - CONF

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

AU - Dongari, Nishanth

AU - Zhang, Yonghao

AU - Reese, Jason

PY - 2010/8/1

Y1 - 2010/8/1

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

KW - thermal transpiration

KW - molecules

KW - models

KW - transition regime

KW - knudsen layer

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