The Knudsen Paradox in Micro-Channel Poiseuille Flows with a Symmetric Particle
The Knudsen paradox-the non-monotonous variation of mass-flow rate with the Knudsen number-is a unique and well-established signature of micro-channel rarefied flows. A particle which is not of insignificant size in relation to the duct geometry can significantly alter the flow behavior when introduced in such a system. In this work, we investigate the effects of a stationary particle on a micro-channel Poiseuille flow, from continuum to free-molecular conditions, using the direct simulation Monte-Carlo (DSMC) method. We establish a hydrodynamic basis for such an investigation by evaluating the flow around the particle and study the blockage effect on the Knudsen paradox. Our results show that with the presence of a particle this paradoxical behavior is altered. The effect is more significant as the particle becomes large and results from a shift towards relatively more ballistic molecular motion at shorter geometrical distances. The need to account for combinations of local and non-local transport effects in modeling reactive gas-solid flows in confined geometries at the nano-scale and in nanofabrication of model pore systems is discussed in relation to these results.