### Abstract

The force-driven Poiseuille flow of dense gases between two parallel plates is investigated through the numerical solution of the generalized Enskog equation for two-dimensional hard discs. We focus on the competing effects of the mean free path (Formula presented.), the channel width (Formula presented.) and the disc diameter (Formula presented.). For elastic collisions between hard discs, the normalized mass flow rate in the hydrodynamic limit increases with (Formula presented.) for a fixed Knudsen number (defined as (Formula presented.)), but is always smaller than that predicted by the Boltzmann equation. Also, for a fixed (Formula presented.), the mass flow rate in the hydrodynamic flow regime is not a monotonically decreasing function of (Formula presented.) but has a maximum when the solid fraction is approximately 0.3. Under ultra-tight confinement, the famous Knudsen minimum disappears, and the mass flow rate increases with (Formula presented.), and is larger than that predicted by the Boltzmann equation in the free-molecular flow regime; for a fixed (Formula presented.), the smaller (Formula presented.) is, the larger the mass flow rate. In the transitional flow regime, however, the variation of the mass flow rate with (Formula presented.) is not monotonic for a fixed (Formula presented.): the minimum mass flow rate occurs at (Formula presented.). For inelastic collisions, the energy dissipation between the hard discs always enhances the mass flow rate. Anomalous slip velocity is also found, which decreases with increasing Knudsen number. The mechanism for these exotic behaviours is analysed.

Language | English |
---|---|

Pages | 252-266 |

Number of pages | 15 |

Journal | Journal of Fluid Mechanics |

Volume | 794 |

Early online date | 30 Mar 2016 |

DOIs | |

Publication status | Published - 1 May 2016 |

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### Keywords

- granular media
- micro-/nano-fluid dynamics
- non-continuum effects

### Cite this

*Journal of Fluid Mechanics*,

*794*, 252-266. https://doi.org/10.1017/jfm.2016.173

}

*Journal of Fluid Mechanics*, vol. 794, pp. 252-266. https://doi.org/10.1017/jfm.2016.173

**Non-equilibrium dynamics of dense gas under tight confinement.** / Wu, Lei; Liu, Haihu; Reese, Jason M.; Zhang, Yonghao.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Non-equilibrium dynamics of dense gas under tight confinement

AU - Wu, Lei

AU - Liu, Haihu

AU - Reese, Jason M.

AU - Zhang, Yonghao

PY - 2016/5/1

Y1 - 2016/5/1

N2 - The force-driven Poiseuille flow of dense gases between two parallel plates is investigated through the numerical solution of the generalized Enskog equation for two-dimensional hard discs. We focus on the competing effects of the mean free path (Formula presented.), the channel width (Formula presented.) and the disc diameter (Formula presented.). For elastic collisions between hard discs, the normalized mass flow rate in the hydrodynamic limit increases with (Formula presented.) for a fixed Knudsen number (defined as (Formula presented.)), but is always smaller than that predicted by the Boltzmann equation. Also, for a fixed (Formula presented.), the mass flow rate in the hydrodynamic flow regime is not a monotonically decreasing function of (Formula presented.) but has a maximum when the solid fraction is approximately 0.3. Under ultra-tight confinement, the famous Knudsen minimum disappears, and the mass flow rate increases with (Formula presented.), and is larger than that predicted by the Boltzmann equation in the free-molecular flow regime; for a fixed (Formula presented.), the smaller (Formula presented.) is, the larger the mass flow rate. In the transitional flow regime, however, the variation of the mass flow rate with (Formula presented.) is not monotonic for a fixed (Formula presented.): the minimum mass flow rate occurs at (Formula presented.). For inelastic collisions, the energy dissipation between the hard discs always enhances the mass flow rate. Anomalous slip velocity is also found, which decreases with increasing Knudsen number. The mechanism for these exotic behaviours is analysed.

AB - The force-driven Poiseuille flow of dense gases between two parallel plates is investigated through the numerical solution of the generalized Enskog equation for two-dimensional hard discs. We focus on the competing effects of the mean free path (Formula presented.), the channel width (Formula presented.) and the disc diameter (Formula presented.). For elastic collisions between hard discs, the normalized mass flow rate in the hydrodynamic limit increases with (Formula presented.) for a fixed Knudsen number (defined as (Formula presented.)), but is always smaller than that predicted by the Boltzmann equation. Also, for a fixed (Formula presented.), the mass flow rate in the hydrodynamic flow regime is not a monotonically decreasing function of (Formula presented.) but has a maximum when the solid fraction is approximately 0.3. Under ultra-tight confinement, the famous Knudsen minimum disappears, and the mass flow rate increases with (Formula presented.), and is larger than that predicted by the Boltzmann equation in the free-molecular flow regime; for a fixed (Formula presented.), the smaller (Formula presented.) is, the larger the mass flow rate. In the transitional flow regime, however, the variation of the mass flow rate with (Formula presented.) is not monotonic for a fixed (Formula presented.): the minimum mass flow rate occurs at (Formula presented.). For inelastic collisions, the energy dissipation between the hard discs always enhances the mass flow rate. Anomalous slip velocity is also found, which decreases with increasing Knudsen number. The mechanism for these exotic behaviours is analysed.

KW - granular media

KW - micro-/nano-fluid dynamics

KW - non-continuum effects

UR - http://www.scopus.com/inward/record.url?scp=84961951113&partnerID=8YFLogxK

U2 - 10.1017/jfm.2016.173

DO - 10.1017/jfm.2016.173

M3 - Article

VL - 794

SP - 252

EP - 266

JO - Journal of Fluid Mechanics

T2 - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -