Sands, Powders, and Grains

Granular materials can be found in an enormous variety of places: from the powders used to make vitamin pills to the rings of Saturn, from beaches to grain elevators, and from pottery clay to interstellar dust. This text covers the basic properties of uniform granular materials, the mixing and segregation of heterogeneous materials (the famous "brazil-nut problem"), and numerical models.

This is an introduction to the physical principles underlying the behavior of materials consisting of grains. These can be found in an enormous variety of places, ranging from the powders used to make vitamin pills to the rings of Saturn, from beaches to grain elevators, and from pottery clay to interstellar dust. Granular materials have interested physicists from Coulomb to Faraday to Reynolds and Rayleigh, but only recently have mathematical and experimental methods been developed to analyze their properties in detail.
This introductory text develops the fundamental physics of the behavior of granular materials. It covers the basic properties of flow, friction, and fluidization of uniform granular materials; discusses mixing and segregation of heterogeneous materials (the famous "brazil-nut problem"); and concludes with an introduction to numerical models. The presentation begins with simple experiments and uses their results to build concepts and theorems about materials whose behavior is often quite counter-intuitive; presenting in a unified way the background needed to understand current work in the field. Developed for students at the University of Paris, the text will be suitable for advanced undergraduates and beginning graduates; while also being of interest to researchers and engineers just entering the field.

Granular materials can be found in an enormous variety of places: from the powders used to make vitamin pills to the rings of Saturn, from beaches to grain elevators, and from pottery clay to interstellar dust. This text covers the basic properties of uniform granular materials, the mixing and segregation of heterogeneous materials (the famous "brazil-nut problem"), and numerical models.

1. Introduction.- 1.1 Some Orders of Magnitude Defining the Problem.- 1.2 Economic Implications and Industrial Problems.- 1.3 Granular Materials and Geophysics.- 1.4 A Brief Historical Review.- 1.5 Prerequisites and Selected Bibliography.- 2. Interactions in Granular Media.- 2.1 A Single Particle and Its Environment.- 2.2 Interactions between Two Particles.- 2.3 A Single Particle on Top of a Granular Medium.- 2.4 Interactions Between Several Particles.- 3. Fluidization, Decompaction, and Fragmentation.- 3.1 The Static Properties of a Granular Pile.- 3.2 Dynamic Properties of a Granular Pile.- 4. Granular Media in a State of Flow.- 4.1 A Sand Pile in Equilibrium: The Angle of Repose.- 4.2 Avalanche Models.- 5. Mixing and Segregation.- 5.1 Introduction.- 5.2 Segregation by Vibration.- 5.3 Segregation by Shearing.- 5.4 Segregation in Oyama's Three-Dimensional Drum.- 6. Numerical Simulations.- 6.1 Introduction.- 6.2 Simulations of Collisions.- 6.3 Molecular Dynamics (MD) Simulations.- 6.4 Simulation of the Dynamics of Contacts.- 6.5 Monte Carlo (MC) Simulations.- 6.6 Sequential Model of a Pile.