Segregation in fluidized versus tapped packs

TL;DR

This paper compares two statistical mechanics models for binary granular mixtures under external driving, analyzing size segregation phenomena and predicting differences in Brazil nut effect behaviors at varying shaking amplitudes.

Contribution

It analytically solves a lattice model to compare two approaches, revealing their similarities and differences in size segregation predictions under different shaking conditions.

Findings

Models agree at low shaking amplitudes

Predictions differ for Brazil nut to reverse Brazil nut crossover

Differences could be experimentally observed

Abstract

We compare the predictions of two different statistical mechanics approaches, corresponding to different physical measurements, proposed to describe binary granular mixtures subjected to some external driving (continuous shaking or tap dynamics). In particular we analytically solve at a mean field level the partition function of a simple hard sphere lattice model under gravity and we focus on the phenomenon of size segregation. We find that the two approaches lead to similar results and seem to coincide in the limit of very low shaking amplitude. However they give different predictions of the crossovers from Brazil nut effect to reverse Brazil nut effect with respect to the shaking amplitude, which could be detected experimentally.