THE HYDRODYNAMICS OF INELASTIC GRANULAR SYSTEMS

The hydrodynamic equations for a system of inelastic granular particle s are derived from first principles of statistical mechanical theory b y applying projection operator techniques. An effective Liouvillian op erator for the granular distribution function is derived by exploiting the fact that each granular particle has many interacting internal de grees of freedom which remain at equilibrium at a temperature T and pr ovide a sink for the translational relative momenta of the inelastic g ranular 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 o rdinary 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.