Multi-scale kinetic description of granular clusters: invariance, balance, and temperature

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Abstract

We discuss a multi-scale continuum representation of bodies made of several mass particles flowing independently each other. From an invariance procedure and a nonstandard balance of inertial actions, we derive the balance equations introduced in earlier work directly in pointwise form, essentially on the basis of physical plausibility. In this way, we analyze their foundations. Then, we propose a Boltzmann-type equation for the distribution of kinetic energies within control volumes in space and indicate how such a distribution allows us to propose a definition of (granular) temperature along processes far from equilibrium.

Keywords

Continuum thermodynamics Multi-scale models Invariance Kinetic theory Granular matter 
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Notes

Acknowledgements

This work has been developed within the programs of the research group in ‘Theoretical Mechanics’ of the ‘Centro di Ricerca Matematica Ennio De Giorgi’ of the Scuola Normale Superiore in Pisa. The support of GNFM-INDAM is acknowledged.

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Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di PisaRomeItaly
  2. 2.DICeAUniversità di FirenzeFlorenceItaly

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