Experimental investigations on the nonequilibrium dynamics of pattern formation in fluid and granular systems Open Access

Abstract

Patterns are quotidian in nature and occur on multiple length scales. Distinct multiscale patterns are generally a consequence of nonequilibrium dynamical processes associated with particular mechanical and hydrodynamic instabilities, which play a vital role in shaping the pattern geometry. In this thesis, I report experimental investigations on the pattern formation in a few examples of fluid and granular systems, and uncover the underlying mechanisms that give rise to those patterns.

Leidenfrost drops are known to experience star-shaped oscillations with little damping. However, the underlying mechanism remains unclear. Here I report that the hydrodynamic coupling between the rapid evaporated vapor flow and vapor-liquid interface excites the star-shaped oscillations, suggesting a purely hydrodynamic origin. In addition, I also give an analytical explanation for an oscillatory ``breathing mode'' found in small Leidenfrost drops.

Polygonal desiccation crack patterns are commonly observed in natural systems. However, it is unclear whether similar crack patterns spanning multiple length scales share the same underlying physics. I also report experimental investigation on polygonal cracks in drying suspensions of micron-sized particles. In cornstarch-water mixtures, multi-scale crack patterns were observed due to two distinct desiccation mechanisms. In addition, we find that the characteristic area of the polygonal cracks ($A_p$), and film thickness ($h$) obey a universal power law, $A_p=\alpha h^{4/3}$. Thus we provide a robust framework for understanding multiscale polygonal crack patterns.

Finally, I report experimental results on sedimentation of non-Brownian particles in viscous fluids, which is crucial in both nature and industrial processes. We observed an effective repulsion between particles with nonuniform density in both two-body and many-body systems, in contrast to particles with uniform density. This trend holds true in two and three dimensions. In addition, we also characterize the statistical properties of the sedimentation patterns of particles in three dimensions. Our results also shed light on the potential for controlling the uniformity of particle layers after sedimentation.

The patterns I report in this thesis represent typical examples in fluid and granular systems that are driven by nonequilibrium dynamics, and the underlying mechanisms we uncover are expected to enhance our understanding of how these seemingly simple patterns can arise in natural systems.

Table of Contents

Abstract Cover Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Cover Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

Citations to Previously Published Work . . . . . . . . . . . . . . . . . . . xi

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii

Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv

1 Introduction 1

1.1 Pattern formation in nature . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Patterns in fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Patterns in colloidal films . . . . . . . . . . . . . . . . . . . . . . . . 9

1.4 Patterns driven by sedimentation . . . . . . . . . . . . . . . . . . . . 12

2 Oscillations of Leidenfrost drops 18

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.3.1 The geometry of Leidenfrost drops on curved surfaces . . . . . 25

2.3.2 Breathing mode of small Leidenfrost drops . . . . . . . . . . . 30

2.3.3 Star-shaped oscillations of Leidenfrost water drops . . . . . . . 34

2.3.4 Pressure oscillations in the vapor layer . . . . . . . . . . . . . 36

2.3.5 Star-shaped oscillations of different liquids . . . . . . . . . . . 41

2.3.6 Origin of pressure oscillations in the vapor layer . . . . . . . . 47

2.3.7 Thermal effects . . . . . . . . . . . . . . . . . . . . . . . . . . 55

2.4 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3 Polygonal desiccation crack patterns 62

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.3.1 Multiscale cracks in cornstarch-water suspensions . . . . . . . 68

3.3.2 Critical condition for primary cracks . . . . . . . . . . . . . . 72

3.3.3 Cornstarch particle deswelling drives secondary cracks . . . . . 75

3.3.4 Primary cracks in different particle suspensions . . . . . . . . 78

3.3.5 Cornstarch-water suspensions in thin chambers . . . . . . . . 84

3.3.6 Universal scaling of multiscale polygonal cracks . . . . . . . . 86

3.3.7 Effective film thickness for cracks in thick cornstarch-water suspensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

3.4 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . 99

4 Sedimentation of non-Brownian particles 102

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

4.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

4.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 111

4.3.1 Effect of density distribution on sedimentation . . . . . . . . . 111

4.3.2 Sedimentation of multiple particles in quasi two dimensions . . 116

4.3.3 Sedimentation of multiple particles in three dimensions . . . . 119

4.4 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . 122

5 Summary 126

Bibliography 130

About this Dissertation

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School	Laney Graduate School
Department	Physics
Degree	Ph.D.
Submission	Dissertation
Language	English
Research Field	Physics, Condensed Matter
Keyword	soft matter nonequilibrium dynamics granular material fluid dynamics pattern formation
Committee Chair / Thesis Advisor	Justin Burton, Emory University
Committee Members	Connie Roth, Emory University Eric Weeks, Emory University Alberto Fernandez-Nieves, Georgia Institute of Technology Hayk Harutyunyan, Emory University

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