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Updated: Apr 7, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Predicting the Knudsen paradox in long capillaries by decomposing the flow into ballistic and collision parts
Giorgos Tatsios1, Stefan K Stefanov2, Dimitris Valougeorgis1
1Department of Mechanical Engineering, University of Thessaly, Volos, Greece.
Abstract:
The well-known Knudsen paradox observed in pressure driven rarefied gas flows through long capillaries is quantitatively explored by decomposing the particle distribution function into its ballistic and collision parts. The classical channel, tube, and duct Poiseuille flows are considered. The solution is obtained by a typical direct simulation Monte Carlo algorithm supplemented by a suitable particle decomposition indexation process. It is computationally confirmed that in the free-molecular and early transition regimes the reduction rate of the ballistic flow is larger than the increase rate of the collision flow deducing the Knudsen minimum of the overall flow. This description interprets in a precise, quantitative manner the appearance of the Knudsen minimum and verifies previously reported qualitative physical arguments.
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