Granular material

[1] The constituents that compose granular material are large enough such that they are not subject to thermal motion fluctuations.

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.

[2] 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.

[4] 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.

[5] Granular materials also exhibit a wide range of pattern forming behaviors when excited (e.g. vibrated or allowed to flow).

Consider inelastic collision between two particles - the energy from velocity as rigid body is transferred to microscopic internal DOF.

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 sandpile slope reaches the maximum stable angle, the sand particles on the surface of the pile begin to fall.

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.

[7] 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.

Janssen suggested a simplified model with the following assumptions: 1) The vertical pressure,

sustains the vertical load at the contact with the wall; 4) The density of the material is constant over all depths.

The given pressure equation does not account for boundary conditions, such as the ratio between the particle size to the radius of the silo.

Since the internal stress of the material cannot be measured, Janssen's speculations have not been verified by any direct experiment.

The mechanical properties of assembly of mono-dispersed particles in 2D can be analyzed based on the representative elementary volume, with typical lengths,

Then stress on the boundary can be expressed as the concentrated force borne by individual particles.

, which describes the angle that if the tangential force falls within the friction cone the particles would still remain steady.

then the particles will begin sliding, resulting in changing the structure of the system and creating new force chains.

Unlike conventional gases, granular materials will tend to cluster and clump due to the dissipative nature of the collisions between grains.

This effect, known as the granular Maxwell's demon, does not violate any thermodynamics principles since energy is constantly being lost from the system in the process.

(Boltzmann Distribution) by taking its Laplace transform and calculate the generating function:

point was empirically found to resemble second-order transition: the bulk modulus shows a power law scaling with

[12][13] There are two main computational approaches to such simulations, time-stepped and event-driven, the former being the most efficient for a higher density of the material and the motions of a lower intensity, and the latter for a lower density of the material and the motions of a higher intensity.

When water or other liquids are cooled sufficiently slowly, randomly positioned molecules rearrange and solid crystals emerge and grow.

Unlike removing energy by cooling, crystallization in granular material is achieved by external driving.

[11] In contrast to molecular systems, the positions of the individual particles can be tracked in the experiment.

[14] Computer simulations for a system of spherical grains reveal that homogeneous crystallization emerges at a volume fraction

Examples of granular materials
Chain of transmission of stress forces in a granular medium
Jamming during discharge of granular material is due to arch formation (red spheres)
Sand dunes