### Abstract

We present an analytical model predicting the experimentally observed gas mass flow rate in rectangular micro channels over slip and transition regimes without the use of any fitting parameter. Previously, Sone [1] reported a class of

pure continuum regime flows that requires terms of Burnett order in constitutive equations of shear stress to be predicted appropriately. The corrective terms to the conventional Navier-Stokes equation were named the ghost effect. We demonstrate in this paper similarity between Sone ghost effect model and newly so-called ‘volume diffusion hydrodynamic model’. A generic analytical solution to gas mass flow rate in a rectangular micro channel is then obtained. It is shown that the volume diffusion hydrodynamics allows to accurately predict the gas mass flow rate up to Knudsen number of 5. This can be achieved without necessitating the use of any adjustable parameters in boundary conditions or parametric scaling laws for constitutive relations. The present model predicts the non-linear variation of pressure profile along the axial direction and also captures the change in curvature with increase in rarefaction.

pure continuum regime flows that requires terms of Burnett order in constitutive equations of shear stress to be predicted appropriately. The corrective terms to the conventional Navier-Stokes equation were named the ghost effect. We demonstrate in this paper similarity between Sone ghost effect model and newly so-called ‘volume diffusion hydrodynamic model’. A generic analytical solution to gas mass flow rate in a rectangular micro channel is then obtained. It is shown that the volume diffusion hydrodynamics allows to accurately predict the gas mass flow rate up to Knudsen number of 5. This can be achieved without necessitating the use of any adjustable parameters in boundary conditions or parametric scaling laws for constitutive relations. The present model predicts the non-linear variation of pressure profile along the axial direction and also captures the change in curvature with increase in rarefaction.

Original language | English |
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Pages | 720-726 |

Number of pages | 7 |

Publication status | Published - 9 Jul 2012 |

Event | 28th International Symposium on Rarefied Gas Dynamics - Zaragosa, Spain Duration: 9 Jul 2012 → 13 Jul 2012 |

### Conference

Conference | 28th International Symposium on Rarefied Gas Dynamics |
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Country | Spain |

City | Zaragosa |

Period | 9/07/12 → 13/07/12 |

### Keywords

- mass diffusion
- volume diffusion hydrodynamics
- microchannel gas flow
- Knudsen paradox
- pressure distribution
- slip flows

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## Cite this

Dadzie, K., & Dongari, N. (2012).

*Transition regime analytical solution to gas mass flow rate in a rectangular micro channel*. 720-726. Paper presented at 28th International Symposium on Rarefied Gas Dynamics, Zaragosa, Spain.