Rapid Granular Flows: Kinetics and Hydrodynamics

  • Isaac Goldhirsch
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


The kinetics of a monodisperse collection of spherical particles whose collisions are characterized by a fixed coefficient of normal restitution is analyzed in one, two and three dimensions, the major goal being the derivation of hydrodynamic equations of motion and boundary conditions. A generalized Chapman-Enskog expansion serves to extract such equations from the Boltzmann equation, appropriately modified to account for inelastic collisions. Among the results obtained is an explanation of the anisotropic pressure (“normal stress differences”) in granular gases as a Burnett effect. Boundary conditions are developed by employing a novel (systematic) method which is relevant to both inelastic particles and molecules. The limitations of the Chapman-Enskog approach applied to granular gases are discussed as are the limitations of the hydrodynamic equations. A biased outlook on future developments is presented.


Boltzmann Equation Knudsen Number Hydrodynamic Equation Granular Flow Normal Stress Difference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Isaac Goldhirsch
    • 1
  1. 1.Department of Fluid Mechanics and Heat Transfer, Faculty of EngineeringTel-Aviv UniversityRamat-Aviv, Tel-AvivIsrael

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