Knudsen force

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Knudsen force is the force experienced by two surfaces at two different temperatures that are separated by a distance comparable to a mean free path of the molecules of the ambient medium. [1]

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The Knudsen paradox has been observed in experiments of channel flow with varying channel width or equivalently different pressures. If the normalized mass flux through the channel is plotted over the Knudsen number based on the channel width a distinct minimum is observed around . This is a paradoxical behaviour because, based on the Navier–Stokes equations, one would expect the mass flux to decrease with increasing the Knudsen number. The minimum can be understood intuitively by considering the two extreme cases of very small and very large Knudsen number. For very small Kn the viscosity vanishes and a fully developed steady state channel flow shows infinite flux. On the other hand, the particles stop interacting for large Knudsen numbers. Because of the constant acceleration due to the external force, the steady state again will show infinite flux.

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References

  1. Passian, A.; Wig, A.; Meriaudeau, F.; Ferrell, T. L.; Thundat, T. (23 August 2002). "Knudsen forces on microcantilevers". Journal of Applied Physics. The Smithsonian/NASA Astrophysics Data System. 92 (10): 6326–6333. Bibcode:2002JAP....92.6326P. doi:10.1063/1.1515108. Archived from the original on 10 July 2012. Retrieved 14 December 2010.