The hydrodynamics of inelastic granular systems

Jeremy Schofield and Irwin Oppenheim

Physica A: Statistical Mechanics and its Applications, 1993, vol. 196, issue 2, 209-240

Abstract: The hydrodynamic equations for a system of inelastic granular particles are derived from first principles of statistical mechanical theory by applying projection operator techniques. An effective Liouvillian operator for the granular distribution function is derived by exploiting the fact that each granular particle has many interacting internal degrees of freedom which remain at equilibrium at a temperature T and provide a sink for the translational relative momenta of the inelastic granular system. The nonlinear hydrodynamic equations for the granular system are obtained following projection operator techniques developed by Levine and Oppenheim. The resulting equations are similar to the ordinary hydrodynamic equations but contain additional terms due to the fact that translational energy is not conserved in collisions between the granular particles. The solutions to the linearized equations are also analyzed in different regimes comparing the additional terms due to the inelasticity of collisions with the magnitude of the gradients of the system.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:196:y:1993:i:2:p:209-240

DOI: 10.1016/0378-4371(93)90601-Y

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