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A precise upper limit for the correctness of the Navier-Stokes theory with respect to the kinetic theory


The condition of positive normal pressures must hold for all solutions in the kinetic theory, but is violated by the Navier-Stokes equations for sufficiently high distortions. A dimensionless measure of this discrepancy is furnished by the tension number. In order for all pressures to be positive, it is necessary and sufficient that the tension number be less than 1. If this condition is violated, the normal-stress effects of the kinetic and Navier-Stokes theories are of opposite sign.

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This work was done with the partial support of a grant of the US National Science Foundation to the Johns Hopkins University.

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Truesdell, C. A precise upper limit for the correctness of the Navier-Stokes theory with respect to the kinetic theory. J Stat Phys 1, 313–318 (1969).

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Key words

  • kinetic theory of gases
  • Navier-Stokes theory of fluids
  • tension number
  • truncation number
  • Knudsen number
  • normal-stress effects