A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact (the most common example would be friction when grains collide). The constituents that compose granular material are large enough such that they are not subject to thermal motion fluctuations. Thus, the lower size limit for grains in granular material is about 1 μm. On the upper size limit, the physics of granular materials may be applied to ice floes where the individual grains are icebergs and to asteroid belts of the Solar System with individual grains being asteroids. Some examples of granular materials are snow, nuts, coal, sand, rice, coffee, corn flakes, salt, and bearing balls. Research into granular materials is thus directly applicable and goes back at least to Charles-Augustin de Coulomb, whose law of friction was originally stated for granular materials. Granular materials are commercially important in applications as diverse as pharmaceutical industry, agriculture, and energy production. Powders are a special class of granular material due to their small particle size, which makes them more cohesive and more easily suspended in a gas. The soldier/physicist Brigadier Ralph Alger Bagnold was an early pioneer of the physics of granular matter and whose book The Physics of Blown Sand and Desert Dunes remains an important reference to this day. According to material scientist Patrick Richard, "Granular materials are ubiquitous in nature and are the second-most manipulated material in industry (the first one is water)". In some sense, granular materials do not constitute a single phase of matter but have characteristics reminiscent of solids, liquids, or gases depending on the average energy per grain. However, in each of these states, granular materials also exhibit properties that are unique. Granular materials also exhibit a wide range of pattern forming behaviors when excited (e.g. vibrated or allowed to flow). As such granular materials under excitation can be thought of as an example of a complex system. They also display fluid-based instabilities and phenomena such as Magnus effect.
Definitions Granular matter is a system composed of many macroscopic particles. Microscopic particles (atoms\molecules) are described (in classical mechanics) by all DOF of the system. Macroscopic particles are described only by DOF of the motion of each particle as a rigid body. In each particle are a lot of internal DOF. Consider inelastic collision between two particles - the energy from velocity as rigid body is transferred to microscopic internal DOF. We get "Dissipation" - irreversible heat generation. The result is that without external driving, eventually all particles will stop moving. In macroscopic particles thermal fluctuations are irrelevant. When a matter is dilute and dynamic (driven) then it is called granular gas and dissipation phenomenon dominates. When a matter is dense and static, then it is called granular solid and jamming phenomenon dominates. When the density is intermediate, then it is called granular liquid.
Static behaviors
Coulomb friction law Coulomb regarded internal forces between granular particles as a friction process, and proposed the friction law, that the force of friction of solid particles is proportional to the normal pressure between them and the static friction coefficient is greater than the kinetic friction coefficient. He studied the collapse of piles of sand and found empirically two critical angles: the maximal stable angle θ m {\displaystyle \theta _{m}} and the minimum angle of repose θ r {\displaystyle \theta _{r}} . When the sandpile slope reaches the maximum stable angle, the sand particles on the surface of the pile begin to fall. The process stops when the surface inclination angle is equal to the angle of repose. The difference between these two angles, Δ θ = θ m − θ r {\displaystyle \Delta \theta =\theta _{m}-\theta _{r}} , is the Bagnold angle, which is a measure of the hysteresis of granular materials. This phenomenon is due to the force chains: stress in a granular solid is not distributed uniformly but is conducted away along so-called force chains which are networks of grains resting on one another. Between these chains are regions of low stress whose grains are shielded for the effects of the grains above by vaulting and arching. When the shear stress reaches a certain value, the force chains can break and the particles at the end of the chains on the surface begin to slide. Then, new force chains form until the shear stress is less than the critical value, and so the sandpile maintains a constant angle of repose.
Janssen effect In 1895, H. A. Janssen discovered that in a vertical cylinder filled with particles, the pressure measured at the base of the cylinder does not depend on the height of the filling, unlike Newtonian fluids at rest which follow Stevin's law for hydrostatic pressure. Janssen suggested a simplified model with the following assumptions:
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