ISBN: 3-540-66701-6
TITLE: Pattern Formation in Granular Materials
AUTHOR: Ristow, Gerald H.
TOC:

1. Introduction 1
2. Some Experimental Phenomena of Granular Materials 5
2.1 Shear Flow 5
2.2 Dilatancy6
2.3 SolidFluid Transition 7 
2.4 Convection Rolls 8
2.5 Free-Surface Flow 9
2.6 Inclination Angle 10
2.7 Density and Stress Fluctuations 11
2.8 Commonly Used Materials 11
3. Vertical Shaking 13
3.1 Heap Formation 13
3.2 Convective Motion 17
3.3 Surface Patterns22
3.3.1 Surface Waves 23
3.3.2 Stationary Patterns 24
3.4 Compactification and Clustering 29
3.4.1 Compactification 30
3.4.2 Clustering 32
3.5 Segregation 32
4. Horizontal Shaking 37
4.1 SolidFluid Transition 37
4.2 Critical-Point Exponents 42
4.3 Crystallization 43
4.4 Convection Rolls 45
4.5 Surface Patterns 46
4.6 Lifting the Hysteresis by Gas Flow 48
4.7 Inverted Funnel Flow in Hoppers 49
5. Stratification 51
5.1 Experimental Findings 51
5.2 Discrete Models 57 
5.2.1 Model Based on Angle of Repose 57
5.2.2 Model Based on Energy Dissipation 58
5.3 Continuum Model 58
5.3.1 Model Description 58
5.3.2 Steady-State Profiles 60
5.3.3 Stability Analysis 61
5.3.4 Thin-Flow Regime 62
5.4 Dependence on Geometry 62
6. Conical Hopper 67
6.1 Segregation During Filling 67
6.2 Static Wall Stresses 68
6.3 Outflow Rate 68
6.3.1 Dependence on Orifice 69
6.3.2 Dependence on Silo Geometry 70
6.4 Flow Regions 71
6.5 Segregation During Outflow 73
6.6 Density Waves 74
6.7 Dynamic Wall Stresses 77
6.8 Silo Design to Decrease the Stress Fluctuations 79
7. Rotating Drum 81
7.1 Different Flow Regimes 81
7.1.1 Avalanches 82
7.1.2 Continuous Surface Flow 85
7.1.3 Centrifugal Regime 88
7.2 Segregation 90
7.2.1 Radial Size Segregation 91
7.2.2 Radial Density Segregation 96
7.2.3 Interplay of Size and Density Segregation 99
7.2.4 Friction-Induced Segregation 99
7.2.5 End-Longitudinal Segregation 101
7.2.6 Axial Segregation 102
7.3 Axial Band and Wave Dynamics 105
7.4 Competition of Mixing and Radial Segregation 107
7.5 Front Propagation and Radial Segregation 111
7.5.1 Experimental Setup and Studies 112
7.5.2 Approximation Through Diffusion Process 115
7.5.3 Concentration-Dependent Diffusion Coefficient 116
7.5.4 Calculation of Diffusion Coefficients 119
7.5.5 Front Propagation with and Without Segregation 123
8. Concluding Remarks and Outlook 125
A. Numerical Methods Used to Study Granular Materials 129 
A.1 Monte Carlo Method 129
A.2 Diffusing-Void Model 130
A.3 Method of Steepest Descent 130
A.4 Cellular Automata 131
A.5 Event-Driven Simulations 132
A.6 Time-Driven Simulations (Molecular Dynamics) 133
A.6.1 Time-Integration Scheme 133
A.6.2 Forces During Collisions 134
A.6.3 Numerical Stability 140
A.6.4 Comparison with Experiments 141
A.7 Summary 144
References 145
Index 159
END
