Volume fluctuations and geometrical constraints in granular packs

TL;DR

This study investigates the structural organization of large granular sphere packings using a novel tetrahedral correlation analysis, revealing a two-phase system balancing free volume sharing and geometrical constraints.

Contribution

Introduces a new tetrahedral correlation technique to analyze granular packings and models the structure as two distinct phases constrained by geometry and stability.

Findings

Exponential volume distribution of tetrahedra matches theoretical predictions.

System exhibits a two-phase structure balancing free volume and constraints.

Heterogeneity maximizes entropy while maintaining mechanical stability.

Abstract

Structural organization and correlations are studied in very large packings of equally sized acrylic spheres, reconstructed in three-dimensions by means of X-ray computed tomography. A novel technique, devised to analyze correlations among more than two spheres, shows that the structural organization can be conveniently studied in terms of a space-filling packing of irregular tetrahedra. The study of the volume distribution of such tetrahedra reveals an exponential decay in the region of large volumes; a behavior that is in very good quantitative agreement with theoretical prediction. I argue that the system's structure can be described as constituted of two phases: 1) an `unconstrained' phase which freely shares the volume; 2) a `constrained' phase which assumes configurations accordingly with the geometrical constraints imposed by the condition of non-overlapping between spheres and mechanical stability. The granular system exploits heterogeneity maximizing freedom and entropy while constraining mechanical stability.