[Paper Review] Modes of wall induced granular crystallisation in vibrational packing

Weijing Dai, J. Reimann+3 more|arXiv (Cornell University)|May 21, 2018

Granular flow and fluidized beds3 citations

TL;DR

This study investigates wall-induced granular crystallisation in vibrated cylindrical containers using molecular dynamics simulations of mono-disperse spheres. By analyzing bond orientation order parameters, it reveals that crystallisation initiates epitaxially from wall-adjacent templates, with distinct structural outcomes at cylindrical and planar walls, providing a microscopic basis for understanding structural dynamics in granular matter.

ABSTRACT

Granular crystallisation is an important phenomenon whereby ordered packing structures form in granular matter under vibration. However, compared with the well-developed principles of crystallisation at the atomic scale, crystallisation in granular matter remains relatively poorly understood. To investigate this behaviour further and bridge the fields of granular matter and materials science, we simulated mono-disperse spheres confined in cylindrical containers to study their structural dynamics during vibration. By applying adequate vibration, disorder-to-order transitions were induced. Such transitions were characterised at the particle scale through bond orientation order parameters. As a result, emergent crystallisation was indicated by the enhancement of the local order of individual particles and the number of ordered particles. The observed heterogeneous crystallisation was characterised by the evolution of the spatial distributions via coarse-graining the order index. Crystalline regimes epitaxially grew from templates formed near the container walls during vibration, here termed the wall effect. By varying the geometrical dimensions of cylindrical containers, the obtained crystallised structures were found to differ at the cylindrical wall zone and the planar bottom wall zone. The formed packing structures were quantitatively compared to X-ray tomography results using again these order parameters. The findings here provide a microscopic perspective for developing laws governing structural dynamics in granular matter.

Motivation & Objective

• To understand the mechanisms of granular crystallisation under vibration, particularly the role of container walls.
• To bridge gaps between atomic-scale crystallisation principles and granular matter dynamics.
• To investigate how container geometry influences the spatial distribution and evolution of crystalline order.
• To validate simulation results against X-ray tomography data using quantitative order parameters.
• To develop a microscopic framework for laws governing structural dynamics in disordered granular systems.

Proposed method

• Simulated mono-disperse spherical particles in cylindrical containers under controlled vibrational excitation.
• Employed bond orientation order parameters to quantify local particle-level structural order.
• Used coarse-graining of the order index to characterize spatial heterogeneity in crystallisation patterns.
• Analyzed crystallisation initiation from wall-adjacent regions as templates for epitaxial growth.
• Compared simulated packing structures with experimental X-ray tomography data using identical order parameters.
• Varied cylindrical container dimensions to assess geometric effects on final crystalline structures.

Experimental results

Research questions

• RQ1 How does the container wall influence the initiation and propagation of crystallisation in vibrated granular systems?
• RQ2 What are the distinct crystallisation modes at cylindrical versus planar wall boundaries?
• RQ3 To what extent do geometric variations in cylindrical containers alter the resulting granular packing structures?
• RQ4 How do simulated structural dynamics compare quantitatively with X-ray tomography measurements?
• RQ5 What role do local order parameters play in identifying and characterizing heterogeneous crystallisation?

Key findings

• Crystallisation initiates epitaxially from wall-adjacent regions, forming templates that guide ordered growth.
• The cylindrical wall zone exhibits different crystalline structures compared to the planar bottom wall zone due to geometric constraints.
• Bond orientation order parameters effectively quantify local structural order and track the disorder-to-order transition.
• The spatial distribution of order evolves heterogeneously, with crystalline domains growing from wall-adjacent nucleation sites.
• Simulated packing structures show strong quantitative agreement with X-ray tomography data when assessed using the same order parameters.
• Vibration-induced crystallisation is highly sensitive to container geometry, with distinct structural outcomes observed across different dimensions.