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Pattern Formation in Granular Materials : Springer Tracts in Modern Physics - Gerald H. Ristow

Pattern Formation in Granular Materials

Springer Tracts in Modern Physics

Hardcover Published: January 2000
ISBN: 9783540667018
Number Of Pages: 162

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Granular materials are an integral part of our everyday life. They are also the base material for most industrial processing techniques. The highly dissipative nature of the particle collisions means energy input is needed in order to mobilize the grains. This interplay of dissipation & excitation leads to a wide variety of pattern formation processes, which are addressed in this book. The reader is introduced to this wide field by, first, a description of the material properties of granular materials under different experimental conditions that are important in connection with the pattern formation dynamics &, second, by further details given later on in the description of the specific system.

Introductionp. 1
Some Experimental Phenomena of Granular Materialsp. 5
Shear Flowp. 5
Dilatancyp. 6
Solid-Fluid Transitionp. 7
Convection Rollsp. 8
Free-Surface Flowp. 9
Inclination Anglep. 10
Density and Stress Fluctuationsp. 11
Commonly Used Materialsp. 11
Vertical Shakingp. 13
Heap Formationp. 13
Convective Motionp. 17
Surface Patternsp. 22
Surface Wavesp. 23
Stationary Patternsp. 24
Compactification and Clusteringp. 29
Compactificationp. 30
Clusteringp. 32
Segregationp. 32
Horizontal Shakingp. 37
Solid-Fluid Transitionp. 37
Critical-Point Exponentsp. 42
Crystallizationp. 43
Convection Rollsp. 45
Surface Patternsp. 46
Lifting the Hysteresis by Gas Flowp. 48
Inverted Funnel Flow in Hoppersp. 49
Stratificationp. 51
Experimental Findingsp. 51
Discrete Modelsp. 57
Model Based on Angle of Reposep. 57
Model Based on Energy Dissipationp. 58
Continuum Modelp. 58
Model Descriptionp. 58
Steady-State Profilesp. 60
Stability Analysisp. 61
Thin-Flow Regimep. 62
Dependence on Geometryp. 62
Conical Hopperp. 67
Segregation During Fillingp. 67
Static Wall Stressesp. 68
Outflow Ratep. 68
Dependence on Orificep. 69
Dependence on Silo Geometryp. 70
Flow Regionsp. 71
Segregation During Outflowp. 73
Density Wavesp. 74
Dynamic Wall Stressesp. 77
Silo Design to Decrease the Stress Fluctuationsp. 79
Rotating Drump. 81
Different Flow Regimesp. 81
Avalanchesp. 82
Continuous Surface Flowp. 85
Centrifugal Regimep. 88
Segregationp. 90
Radial Size Segregationp. 91
Radial Density Segregationp. 96
Interplay of Size and Density Segregationp. 99
Friction-Induced Segregationp. 99
End-Longitudinal Segregationp. 101
Axial Segregationp. 102
Axial Band and Wave Dynamicsp. 105
Competition of Mixing and Radial Segregationp. 107
Front Propagation and Radial Segregationp. 111
Experimental Setup and Studiesp. 112
Approximation Through Diffusion Processp. 115
Concentration-Dependent Diffusion Coefficientp. 116
Calculation of Diffusion Coefficientsp. 119
Front Propagation with and Without Segregationp. 123
Concluding Remarks and Outlookp. 125
Numerical Methods Used to Study Granular Materialsp. 129
Monte Carlo Methodp. 129
Diffusing-Void Modelp. 130
Method of Steepest Descentp. 130
Cellular Automatap. 131
Event-Driven Simulationsp. 132
Time-Driven Simulations (Molecular Dynamics)p. 133
Time-Integration Schemep. 133
Forces During Collisionsp. 134
Numerical Stabilityp. 140
Comparison with Experimentsp. 141
Summaryp. 144
Referencesp. 145
Indexp. 159
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540667018
ISBN-10: 3540667016
Series: Springer Tracts in Modern Physics
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 162
Published: January 2000
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.12
Weight (kg): 0.43

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