Slow granular flows: roles of polydispersity and cohesion Open Access
Illing, Pablo (Spring 2025)
Abstract
This work consists of two simulation projects and a experimental project, which
study the effect cohesive forces and polydispersity have on granular materials and on
granular flows.
The first computational project studies the compression and fracture of crystal
and glassy materials using 2D droplet arrays, and the effects of cohesive forces and
polydispersity. We use a bubble model to simulate droplets, with an attractive force,
which makes the bubbles adhere to each other and the walls. Droplets are first placed
in an hexagonal array. For monodisperse bubbles, this forms a crystalline aggregate,
polydisperse rafts resemble a glassy material. Once initialized, the droplet raft will
be compressed between two walls, with only one wall moving towards the other.
The array is compressed and eventually induced to rearrange. These rearrangements
occur via fractures, in which depletion bonds are broken between droplets. In crystal
arrays, fractures are preceded by a peak in the force exerted on the walls, which
drops once the fracture occurs. For small droplet arrays, a single fracture propagates
through the crystal in a single well-defined event. For larger rafts, multiple fractures
can nucleate at different locations and propagate nearly simultaneously, leading to
competing fractures. In polydisperse arrays, the addition of multiple droplet sizes
further disrupts the fracture events, showing differences between ideal crystalline
arrays, crystalline arrays with a small number of defects, and fully amorphous arrays.
The experimental project studied the 2D granular flow of highly polydisperse hard
disks in a non-conventional flow geometry. We use a variety of size distributions with
the largest particle being five time larger than the smallest. The experimental setup
uses plungers to push the particles in a back and forth fashion. We find the flow
behaves in a strikingly different manner compared to size distributions with lower
polydispersity that are commonly studied. We characterize the non-affine motion
and particle rearrangement, and find a qualitatively difference in the behavior of
smaller and larger particles. The smaller particles tend to have higher non-affine
motion, induced by the larger disks. Furthermore, we found that this local non-affine
behavior increases with increasing polydispersity.
For the third project we study the clogging of gravity driven cohesive particle
in a two dimensional hopper, using my simulations, and experimental data provided
by our collaborators at McMaster University. Using a similar model used in the first
computational project, with added gravitational forces, we simulate adhesive droplets
as they flow due to gravity through a hopper. We vary the size of the opening, as
well as the depletion and gravitational forces. We find that stronger depletion leads
to higher clogging probability. By taking into account the depletion and gravitational
forces, we can define a cohesive length scale, which effectively collapses all our sim-
ulation and experimental data onto a master curve. This indicates that for cohesive
granular materials, in addition to particle size, the cohesive length scale must also be
taken into account to describe the clogging.
Table of Contents
1 Introduction 1
1.1 Colloidal crystals and glasses . . . . . . . . . . . . . . . . . . . . . . . 6
1.2 Amorphous flow: Shearing of soft glassy materials . . . . . . . . . . . 9
1.3 Amorphous Flow: Hopper discharge and Clogging . . . . . . . . . . . 13
1.4 Dissertation Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2 Compression and fracture of ordered and disordered droplet rafts 18
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Computational methods . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.1 Simulation forces . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.2 Model parameters . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.3 Simulation timescales . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.4 Simulation goals . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3.1 Effective spring constant: two droplets . . . . . . . . . . . . . 30
2.3.2 Equivalent spring model for three droplets . . . . . . . . . . . 33
2.4 Computational results for large droplet arrays . . . . . . . . . . . . . 39
2.4.1 Equivalent spring model for nominally monodisperse crystals . 39
2.4.2 Bidisperse aggregates . . . . . . . . . . . . . . . . . . . . . . . 47
2.4.3 Competing fractures . . . . . . . . . . . . . . . . . . . . . . . 51
2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3 Amorphous flow of highly polydisperse disks 61
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.2 Experimental methods . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.2.1 Experimental procedure . . . . . . . . . . . . . . . . . . . . . 68
3.2.2 Particle size distributions . . . . . . . . . . . . . . . . . . . . . 68
3.2.3 Image analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.3.1 Mean Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.3.2 Non affine displacement and local particle rearrangement . . . 74
3.3.3 Time scale dependence . . . . . . . . . . . . . . . . . . . . . . 88
3.3.4 Strain clock . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4 Clogging of cohesive particles in a two-dimensional hopper 98
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.2.1 Computational methods . . . . . . . . . . . . . . . . . . . . . 100
4.2.2 Experimental methods . . . . . . . . . . . . . . . . . . . . . . 102
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5 Conclusions 117
Appendix A Effect of polydispersity on the rotation of hard disks 123
Bibliography 126
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