PMID: 11909035Mar 23, 2002Paper

Nonlinear viscosity derived by means of Grad's moment method

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Byung Chan Eu

Abstract

In this paper we examine the stress tensor component evolution equations recently derived by Uribe and Garcia-Colin [Phys. Rev. E 60, 4052 (1999)] for unidirectional flow at uniform temperature under the assumption/approximation of vanishing transversal velocity gradients. By removing this assumption/approximation we derive the stress tensor evolution equation from the Boltzmann equation within the framework of the Grad moment expansion for the case of uniform temperature (the same condition as theirs). Specializing the evolution equation to the case of steady unidirectional flow in a square channel, we obtain a set of steady state evolution equations for the components of the stress tensor. Because the transversal velocity gradients are not assumed to vanish in this paper in contrast to their paper, the present result is more general than theirs. Its special case corresponding to the one-dimensional flow considered by Uribe and Garcia-Colin is at variance with theirs because of a missing term in their stress evolution equation for the xy component. The nonlinear viscosity formulas are also different. A general remark is given with regard to the relation of dimensionalities of hydrodynamic equations and the kinetic equation und...Continue Reading

References

Dec 2, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·A Santos
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·F J Uribe, L S García-Colín

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Citations

Jun 6, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Andrés Santos

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