## Abstract

We investigate a power-law form for the probability distribution function of free paths of dilute gas molecules in a confined region. A geometry-dependent effective molecular mean free path (MFP) model is then derived for a planar wall

confinement, by taking into account the boundary limiting effects on the molecular paths. The power-law based effective MFP is validated against molecular dynamics simulation data and compared with exponential effective MFP models. The Navier-Stokes constitutive relations are then modified according to the kinetic theory of gases i.e. transport properties can be described in terms of the free paths which the molecules describe between collisions. Results for isothermal pressure-driven Poiseuille gas flows in micro-channels are reported, and we compare results with conventional hydrodynamic models, solutions of the Boltzmann equation and experimental data.

confinement, by taking into account the boundary limiting effects on the molecular paths. The power-law based effective MFP is validated against molecular dynamics simulation data and compared with exponential effective MFP models. The Navier-Stokes constitutive relations are then modified according to the kinetic theory of gases i.e. transport properties can be described in terms of the free paths which the molecules describe between collisions. Results for isothermal pressure-driven Poiseuille gas flows in micro-channels are reported, and we compare results with conventional hydrodynamic models, solutions of the Boltzmann equation and experimental data.

Original language | English |
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Title of host publication | Rarefied Gas Dynamics |

Editors | D.A Levin, I.J Wysong, A.L Garcia, H Abarbanel |

Publisher | Springer |

Pages | 724-729 |

Number of pages | 6 |

Volume | 1333 |

Edition | 1st |

ISBN (Print) | 978-0-7354-0889-0 |

DOIs | |

Publication status | Published - 28 Jun 2011 |

Event | 27th International Symposium on Rarefied Gas Dynamics - Pacific Grove, Claifornia, United States Duration: 10 Jul 2010 → 15 Jul 2010 |

### Publication series

Name | AIP Conference Proceedings |
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Publisher | Springer |

Volume | 1333 |

ISSN (Print) | 0094-243X |

### Conference

Conference | 27th International Symposium on Rarefied Gas Dynamics |
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Country | United States |

City | Pacific Grove, Claifornia, |

Period | 10/07/10 → 15/07/10 |

## Keywords

- microscale gas flows
- Knudsen layer
- molecular mean free path
- slip ﬂows