Statistical Mechanics of jamming and segregation in granular media

TL;DR

This paper applies Edwards' statistical mechanics to granular media using lattice models, deriving a phase diagram that links jamming to a fluid-glassy phase transition and exploring segregation phenomena.

Contribution

It analytically demonstrates the validity of Edwards' approach in granular media and connects jamming to a phase transition, also analyzing segregation mechanisms.

Findings

Jamming corresponds to a fluid-glassy phase transition.

Edwards' statistical mechanics accurately describes granular media behavior.

Segregation arises from phase transitions and gravity effects.

Abstract

In the framework of schematic hard spheres lattice models we discuss Edwards' Statistical Mechanics approach to granular media. As this approach appears to hold here to a very good approximation, by analytical calculations of Edwards' partition function at a mean field level we derive the system phase diagram and show that ``jamming'' corresponds to a phase transition from a ``fluid'' to a ``glassy'' phase, observed when crystallization is avoided. The nature of such a ``glassy'' phase turns out to be the same found in mean field models for glass formers. In the same context, we also briefly discuss mixing/segregation phenomena of binary mixtures: the presence of fluid-crystal phase transitions drives segregation as a form of phase separation and, within a given phase, gravity can also induce a kind of ``vertical'' segregation, usually not associated to phase transitions.