Size segregation in granular media induced by phase transition

TL;DR

This paper develops a mean field statistical mechanics model to explain size segregation in granular media, revealing a thermodynamic phase transition driven by depletion forces, supported by numerical simulations.

Contribution

Introduces a new thermodynamic mechanism for size segregation in granular mixtures using a mean field theory and lattice model, identifying a phase transition influenced by small grains.

Findings

Discovery of a crossover from Brazil nut to reverse Brazil nut effect.

Identification of a phase transition driven by depletion forces.

Confirmation of theoretical predictions through numerical simulations.

Abstract

In order to study analytically the nature of the size segregation in granular mixtures, we introduce a mean field theory in the framework of a statistical mechanics approach, based on Edwards' original ideas. For simplicity we apply the theory to a lattice model for hard sphere binary mixture under gravity, and we find a new purely thermodynamic mechanism which gives rise to the size segregation phenomenon. By varying the number of small grains and the mass ratio, we find a crossover from Brasil nut to reverse Brasil nut effect, which becomes a true phase transition when the number of small grains is larger then a critical value. We suggest that this transition is induced by the effective attraction between large grains due to the presence of small ones (depletion force). Finally the theoretical results are confirmed by numerical simulations of the 3d system under taps.