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 λ, the channel width L, and the disc diameter σ. For elastic collisions between hard discs, the normalised mass flow rate in the hydrodynamic limit increases with L/σ for a fixed Knudsen number (defined as Kn = λ/L), but is always smaller than that predicted by the Boltzmann equation. Also, for a fixed L/σ, the mass flow rate in the hydrodynamic flow regime is not a monotonically decreasing function of Kn but has a maximum when the solid fraction is about 0.3. Under ultra-tight confinement the famous Knudsen minimum disappears, and the mass flow rate increases with Kn, and is larger than that predicted by the Boltzmann equation in the free-molecular flow regime; for a fixed Kn, the smaller the L/σ, the larger the mass flow rate. In the transitional flow regime, however, the variation of the mass flow rate with L/σ is not monotonic for a fixed Kn: the minimum mass flow rate occurs at L/σ ≈ 2 ∼ 3. 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 behaviour is analysed.
|Number of pages||15|
|Journal||Journal of Fluid Mechanics|
|Early online date||30 Mar 2016|
|Publication status||E-pub ahead of print - 30 Mar 2016|
- Poiseuille flow
- dense gases
- nonequilibrium dynamics