Rarefaction effects in dilute granular Poiseuille flow: Knudsen minimum and temperature bimodality

The gravity-driven flow of smooth inelastic hard-disks through a channel, analog of granular Poiseuille flow, is analysed using event-driven simulations. We find that the variation of the mass-flow rate ($Q$) with Knudsen number ($Kn$) can be non-monotonic in the elastic limit (i.e.~the restitution coefficient $e_n\to 1$) in channels with very smooth walls. The {\it Knudsen minimum effect} (i.e.~the minimum flow rate occurring at $Kn\sim O(1)$ for the Poiseuille flow of a molecular gas) is found to be absent in a granular gas with $e_n\leq 0.99$, irrespective of wall roughness. Another rarefaction phenomenon, the {\it bimodality} of the temperature profile, with a local minimum at the channel centerline and two symmetric maxima ($T_{\max}$) away from the centerline, is studied. We show that the inelastic dissipation is responsible for the onset of temperature bimodality [i.e.~the excess temperature, $\triangle T= (T_{\max}/T_{\min}-1)\neq 0$] near the continuum limit ($Kn\sim 0$), but the rarefaction being its origin (as in molecular gas) holds beyond $Kn\sim O(0.1)$. The competition between dissipation and rarefaction seems to be responsible for the observed dependence of both mass-flow rate and temperature bimodality on $Kn$ and $e_n$. [Alam etal. 2015, JFM (revised)].