Journal of Statistical Physics

, Volume 18, Issue 3, pp 237–270 | Cite as

Kinetic theory of nonlinear viscous flow in two and three dimensions

  • M. H. Ernst
  • B. Cichocki
  • J. R. Dorfman
  • J. Sharma
  • H. van Beijeren
Articles

Abstract

On the basis of a nonlinear kinetic equation for a moderately dense system of hard spheres and disks it is shown that shear and normal stresses in a steady-state, uniform shear flow contain singular contributions of the form ¦X¦3/2 for hard spheres, or ¦X¦ log ¦X¦ for hard disks. HereX is proportional to the velocity gradient in the shear flow. The origin of these terms is closely related to the hydrodynamic tails t−d/2 in the current-current correlation functions. These results also imply that a nonlinear shear viscosity exists in two-dimensional systems. An extensive discussion is given on the range ofX values where the present theory can be applied, and numerical estimates of the effects are given for typical circumstances in laboratory and computer experiments.

Key words

Kinetic theory nonlinear transport properties uniform steady-state shear flow non-Newtonian fluid properties hydrodynamic long-time tails 

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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • M. H. Ernst
    • 1
  • B. Cichocki
    • 1
  • J. R. Dorfman
    • 2
    • 3
  • J. Sharma
    • 2
    • 3
  • H. van Beijeren
    • 4
  1. 1.Instituut voor Theoretische Fysica der Rijksuniversiteit UtrechtThe Netherlands
  2. 2.Institute for Physical Science and TechnologyUniversity of MarylandCollege Park
  3. 3.Department of Physics and AstronomyUniversity of MarylandCollege Park
  4. 4.Institut für Theoretische PhysikRWTHAachenWest Germany

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