[Paper Review] États de compacité maximale pour les mélanges binaires de grains sphériques : étude par simulation numérique

Jean-Noël Roux, François Chevoir+1 more|arXiv (Cornell University)|Jan 22, 2009

Material Dynamics and Properties21 references3 citations

TL;DR

This study uses discrete element method (DEM) simulations to investigate maximally compacted disordered states in binary mixtures of spherical grains with a diameter ratio of 3. It defines maximal packing density as mechanically stable, isotropically compressed configurations and finds that prolonged initial agitation increases compaction and induces partial crystallization (same-sized particles) or size segregation (binary mixtures), with maximal compaction achieved only in rapid assembly scenarios. The work establishes a practical definition of random close packing for granular systems under mechanical equilibrium conditions.

ABSTRACT

Disordered assemblies with maximum packing fraction are studied by discrete element numerical simulation for monodisperse or bidisperse spherical particles, the diameter ratio being set at three. A maximum packing fraction value corresponds to an equilibrium state under isotropic loading of rigid frictionless particles. A statistical study of size effects enables one to evaluate, in the limit of large systems, the maximum packing fractions of both monodisperse assemblies, for which the conventional value 0.639 is retrieved, and bidisperse ones, for two distinct values of the coarse particle volume fraction. An enduring initial assembling step in which agitated grains interact through collisions induces an increase in the final packing fraction due to crystalline order nucleation for a monodisperse system or to a gradual segregation for a binary mixture. Albeit slow and moderate in a number of practical situations, this effect leads to a definition of the random close packing state, as the one obtained with frictionless rigid grains under an isotropic pressure in the limit of fast assembling processes. A few potential extensions to this preliminary study are suggested.

Motivation & Objective

• To define a practical, mechanically consistent criterion for maximal random packing in disordered granular assemblies.
• To investigate the influence of initial agitation duration on final packing density and structural order in binary mixtures of spherical grains with a 3:1 diameter ratio.
• To quantify the maximal packing density for monodisperse and bidisperse systems under isotropic compression.
• To assess the role of system size and statistical fluctuations in determining reliable values of maximal packing density.
• To identify the conditions under which disordered, maximally compacted states emerge in granular systems, especially in the context of practical material preparation.

Proposed method

• Discrete Element Method (DEM) is used to simulate isotropic compression of rigid, non-frictional spherical particles.
• Particles are subjected to isotropic pressure to reach mechanically stable, equilibrium configurations, defining the maximal packing state.
• Simulations are conducted for monodisperse systems and binary mixtures with volume fractions of large particles at p = 0.5 and p = 0.7.
• The initial phase involves particle agitation via collisions to mimic real-world deposition processes.
• System size is varied to assess finite-size effects and statistical fluctuations in packing density.
• Structural order is monitored using local order parameters to detect crystallization or segregation.

Experimental results

Research questions

• RQ1 What defines a mechanically stable, disordered state of maximal packing in granular assemblies?
• RQ2 How does the duration of initial agitation affect the final packing density and structural order in binary spherical mixtures?
• RQ3 What is the maximal packing density for monodisperse and bidisperse systems with a 3:1 diameter ratio under isotropic compression?
• RQ4 To what extent does prolonged agitation lead to partial crystallization or size segregation in these systems?
• RQ5 What is the limiting value of maximal packing density in the thermodynamic limit, and how is it influenced by preparation protocol?

Key findings

• For monodisperse systems, the maximal packing density converges to the classical value of 0.639 in the large-system limit.
• In binary mixtures with p = 0.5 and p = 0.7, distinct maximal packing densities are observed, reflecting the influence of composition on compaction.
• Prolonged initial agitation leads to a gradual increase in packing density, accompanied by the nucleation of local crystalline order in monodisperse systems.
• In binary mixtures, extended agitation induces progressive size segregation, with larger particles migrating to the surface.
• The study confirms that maximal packing density should be defined as the state achieved under rapid, isotropic compression, not after prolonged equilibration.
• Statistical fluctuations between independent simulations are observed, but converge toward stable values with increasing system size.