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Abstract
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.
Highlights
A sub-micron sized particle when transported in a micro-channel can significantly alter the rarefied behavior of the carrier gas
Note that Qnorm is independent of the local pressure gradient, but depends mainly on the channel height represented in terms of a rarefaction parameter δm [41] given by:
We present a direct simulation Monte-Carlo (DSMC) investigation of the effect of a stationary particle on the Knudsen paradox observed in micro-channel Poiseuille flows
Summary
A sub-micron sized particle when transported in a micro-channel can significantly alter the rarefied behavior of the carrier gas These effects emerge partly because the dispersed particle serves as an extra momentum source or sink in the system and partly due to the blockage induced by the particle, which further affects the effective hydrodynamic length of the bounding duct. The paradox was first studied experimentally and theoretically by Knudsen [3] in experiments of Poiseuille flow driven by the identical pressure drop in channels with varying widths The observation of this minimum was attributed, by Pollard and Present [4], to the imbalance between two counteracting molecular effects–the obstruction of long diffusion paths due to molecular collisions, leading to a net decrease in Q on the one hand and the development of drift transport leading to an increase in Q on the other hand. As the pressure crosses this threshold (λ < a), drift transport increases (towards the Poiseuille form) leading to an increase in Q
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