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Structure, Dynamics, and Forces of Jammed Systems

Desmond, Kenneth Wayne (2012)
Dissertation (196 pages)
Committee Chair / Thesis Adviser: Weeks, Eric
Committee Members: Berland, Keith ; Boettcher, Stefan ; Hentschel, George ; Goldman, Daniel (Georgia Institute of Technology);
Research Fields: Physics, General
Keywords: Packing; Colloids; Soft Matter; Disorder; Granular; Confinement; Flow
Program: Laney Graduate School, Physics
Permanent url: http://holden.library.emory.edu/ark:/25593/bnwwx

Abstract

The first system we study is a concentrated binary colloidal suspensions. We use con-
focal microscopy to directly observe particle motion within dense samples with packing
fractions ranging from 0.40-0.59. To study temporal fluctuations we use the dynamic sus-
ceptibility χ4, and find that the dynamical heterogeneity of the small and larger particles
are qualitatively similar with the smaller particles undergoing slightly larger fluctuations
relative to their size. The temporal fluctuations give rise to length scales and time scales
which grow as the jamming transition is approached, although the form of this growth is
ambiguous with respect to power-law or exponential growth.
The second system we study is random packing of disks and spheres within confined
geometries. Studies of random close packing have advanced our knowledge about the struc-
ture of systems such as liquids, glasses, emulsions, granular media, and amorphous solids.
When these systems are confined, their structural properties change. To understand these
changes we study random close packing in finite-sized confined systems, in both two and
three dimensions. The presence of confining walls significantly lowers the overall maximum
area fraction (or volume fraction in three dimensions). A simple model is presented which
quantifies the reduction in packing due to wall-induced structure. This wall-induced struc-
ture decays rapidly away from the wall, with characteristic length scales comparable to the
small particle diameter.
The final system we explore is a new quasi-two-dimensional model system we have
developed to probe the jamming transition. Our system consist of confining oil-in-water
emulsion droplets between two parallel plates, so that the droplets are squeezed into quasi-
two dimensional disks, analogous to granular photoelastic disks. These droplets have no
static friction and are highly deformable. To quantify the internal forces in our experiments,
we present an experimental protocol to determine the force law for droplets in contact. We
use our model system to characterize various critical scaling phenomena associated with the
jamming transition and the force chain network. We also flow our quasi-2D emulsions in
a flow geometry analogous to pure shear to better understand the microscopic events and
stress relaxations within jammed materials.

Table of Contents

1 Introduction

1.1 The Jamming Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Ideal Glass Transition and Using Colloids as an Experimental Model . . . . 5

1.3 Packing and the Influence of Boundaries . . . . . . . . . . . . . . . . . . . . . . . 9

1.4 The Ideal Jamming Transition at Zero Temperature . . . . . . . . . . . . . . . 12

1.5 Flow of Disordered Matter Near Jamming . . . . . . . . . . . . . . . . . . . . . . 15

2 Dynamic Heterogeneity in Colloidal Glasses

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2 Binary Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.3 Four-Point Susceptibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.4 Growing Length & Time Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.5 Theory and Expected Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.6 Comparing Results to Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3 Packing in Confined Geometries

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3 Results on 2D Packing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.4 Results on 3D Packing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.5 Modeling the Effects of Confinement on Volume Fraction . . . . . . . . . . . 52

3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4 Imaging and Image Analysis for 2D Experimental Model System

4.1 Imaging Droplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.2 Choosing an Oil Phase and Surfactant . . . . . . . . . . . . . . . . . . . . . . . 65

4.3 Stitching Images Together . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.4 Identifying Droplets and Their Center of Mass . . . . . . . . . . . . . . . . . . 68

4.5 Describing the Perimeter with a Continuous Function . . . . . . . . . . . . . 70

4.6 Radical Voronoi Tessellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.7 Identifying Contacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.8 Measuring Radius of Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.9 Mean 3D radius of curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5 Empirical Force Law for 2D Model System 85

5.1 Various Force Laws to be Tested . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.2 Adhesion Length lo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.3 Testing the Quality of an Assumed Force Law . . . . . . . . . . . . . . . . . . 90

5.4 Empirical Force Law for Same Size Droplets in Contact . . . . . . . . . . . 94

5.5 Empirical Force Law for Different Size Droplets in Contact . . . . . . . . . 100

5.6 Table of Fitting Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

6 Experimental Frictionless 2D Model of Jamming 107

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

6.2 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

6.3 Jamming Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

6.4 Critical Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

6.5 Pressure and Efective Force Law for Monodisperse Data . . . . . . . . . . 119

6.6 Force Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

6.7 Force Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

6.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

7 Spatial Cooperativity of Stress Relaxation Around Plastic Events in Quasi-

Static 2D Flow

7.1 Flow Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

7.2 Droplet-Droplet Forces and Viscous Forces . . . . . . . . . . . . . . . . . . . . 136

7.3 Determining When Plastic Events Occur . . . . . . . . . . . . . . . . . . . . . . 140

7.4 Stress Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

7.5 Evolution of Stress Around Plastic Event . . . . . . . . . . . . . . . . . . . . . 147

7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

8 Summary 152

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