Book contents
- Frontmatter
- Contents
- Preface
- Notation
- 1 Introduction
- 2 Theory for Slow Plane Flow
- 3 Flow through Hoppers
- 4 Flow through Wedge-Shaped Bunkers
- 5 Theory for Slow Three-Dimensional Flow
- 6 Flow through Axisymmetric Hoppers and Bunkers
- 7 Theory for Rapid Flow of Smooth, Inelastic Particles
- 8 Analysis of Rapid Flow in Simple Geometries
- 9 Theory for Rapid Flow of Rough, Inelastic Particles
- 10 Hybrid Theories
- Appendix A Operations with Vectors and Tensors
- Appendix B The Stress Tensor
- Appendix C Hyperbolic Partial Differential Equations of First Order
- Appendix D Jump Balances
- Appendix E Discontinuous Solutions of Hyperbolic Equations
- Appendix F Proof of the Coaxiality Condition
- Appendix G Material Frame Indifference
- Appendix H The Evaluation of Some Integrals
- Appendix I A Brief Introduction to Linear Stability Theory
- Appendix J Pseudo Scalars, Vectors, and Tensors
- Appendix K Answers to Selected Problems
- References
- Index
Preface
Published online by Cambridge University Press: 19 November 2009
- Frontmatter
- Contents
- Preface
- Notation
- 1 Introduction
- 2 Theory for Slow Plane Flow
- 3 Flow through Hoppers
- 4 Flow through Wedge-Shaped Bunkers
- 5 Theory for Slow Three-Dimensional Flow
- 6 Flow through Axisymmetric Hoppers and Bunkers
- 7 Theory for Rapid Flow of Smooth, Inelastic Particles
- 8 Analysis of Rapid Flow in Simple Geometries
- 9 Theory for Rapid Flow of Rough, Inelastic Particles
- 10 Hybrid Theories
- Appendix A Operations with Vectors and Tensors
- Appendix B The Stress Tensor
- Appendix C Hyperbolic Partial Differential Equations of First Order
- Appendix D Jump Balances
- Appendix E Discontinuous Solutions of Hyperbolic Equations
- Appendix F Proof of the Coaxiality Condition
- Appendix G Material Frame Indifference
- Appendix H The Evaluation of Some Integrals
- Appendix I A Brief Introduction to Linear Stability Theory
- Appendix J Pseudo Scalars, Vectors, and Tensors
- Appendix K Answers to Selected Problems
- References
- Index
Summary
The flow of granular materials such as sand, snow, coal, and catalyst particles is a common occurrence in natural and industrial settings. Unfortunately, the mechanics of these materials is not well understood. Experiments reveal complex and, at times, unexpected behavior, whereas existing theories are often tentative and do not represent the entire range of observed behavior. Nevertheless, significant advances have been made in the understanding of the mechanics of granular flows, and the time is ripe for an account of experimental observations and theoretical models pertaining to flow in relatively simple geometries.
The importance of understanding granular flows need not be overstated – a large fraction of the materials handled and processed in the chemical, metallurgical, pharmaceutical, and food-processing industries are granular in nature. The flow and transportation of these materials are often critical operations in these processes. In most cases, the design of processes and equipment is based largely on experience and empirical rules. An appreciation of the underlying principles may be helpful in developing better design and operating procedures.
Some of the early investigations of granular flow were motivated by the need to understand the deformation of soils subjected to external loads, such as large structures. The deformation rates in these processes are usually very small. Theoretical models for these slow flows have increased in sophistication and complexity over the years, borrowing concepts from metal plasticity and soil mechanics. A contrasting picture of granular flow has emerged over the last three decades. This is believed to be applicable to rapid flows, where the deformation rates are large.
- Type
- Chapter
- Information
- An Introduction to Granular Flow , pp. xiii - xivPublisher: Cambridge University PressPrint publication year: 2008