![Granular matter examples](https://upload.wikimedia.org/wikipedia/commons/6/62/Granular_matter_examples.PNG)
A granular material is a conglomeration of discrete
solid
Solid is one of the State of matter#Four fundamental states, four fundamental states of matter (the others being liquid, gas, and Plasma (physics), plasma). The molecules in a solid are closely packed together and contain the least amount o ...
,
macroscopic
The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic.
Overview
When applied to physical phenomena a ...
particle
In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object which can be described by several physical property, physical or chemical property, chemical ...
s characterized by a loss of energy whenever the particles interact (the most common example would be
friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction:
*Dry friction is a force that opposes the relative lateral motion of t ...
when
grains
A grain is a small, hard, dry fruit (caryopsis) – with or without an attached hull layer – harvested for human or animal consumption. A grain crop is a grain-producing plant. The two main types of commercial grain crops are cereals and legumes ...
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
iceberg
An iceberg is a piece of freshwater ice more than 15 m long that has broken off a glacier or an ice shelf and is floating freely in open (salt) water. Smaller chunks of floating glacially-derived ice are called "growlers" or "bergy bits". The ...
s and to
asteroid belt
The asteroid belt is a torus-shaped region in the Solar System, located roughly between the orbits of the planets Jupiter and Mars. It contains a great many solid, irregularly shaped bodies, of many sizes, but much smaller than planets, called ...
s of the
Solar System
The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...
with individual grains being
asteroid
An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere.
...
s.
Some examples of granular materials are
snow
Snow comprises individual ice crystals that grow while suspended in the atmosphere—usually within clouds—and then fall, accumulating on the ground where they undergo further changes.
It consists of frozen crystalline water throughout ...
,
nuts,
coal
Coal is a combustible black or brownish-black sedimentary rock, formed as rock strata called coal seams. Coal is mostly carbon with variable amounts of other elements, chiefly hydrogen, sulfur, oxygen, and nitrogen.
Coal is formed when dea ...
,
sand
Sand is a granular material composed of finely divided mineral particles. Sand has various compositions but is defined by its grain size. Sand grains are smaller than gravel and coarser than silt. Sand can also refer to a textural class of s ...
,
rice
Rice is the seed of the grass species ''Oryza sativa'' (Asian rice) or less commonly ''Oryza glaberrima
''Oryza glaberrima'', commonly known as African rice, is one of the two domesticated rice species. It was first domesticated and grown i ...
,
coffee
Coffee is a drink prepared from roasted coffee beans. Darkly colored, bitter, and slightly acidic, coffee has a stimulant, stimulating effect on humans, primarily due to its caffeine content. It is the most popular hot drink in the world.
S ...
,
corn flakes
Corn flakes, or cornflakes, are a breakfast cereal made from toasting flakes of corn (maize). The cereal, originally made with wheat, was created by Will Kellogg in 1894 for patients at the Battle Creek Sanitarium where he worked with his bro ...
,
fertilizer
A fertilizer (American English) or fertiliser (British English; see spelling differences) is any material of natural or synthetic origin that is applied to soil or to plant tissues to supply plant nutrients. Fertilizers may be distinct from ...
, and
bearing balls. Research into granular materials is thus directly applicable and goes back at least to
Charles-Augustin de Coulomb
Charles-Augustin de Coulomb (; ; 14 June 1736 – 23 August 1806) was a French officer, engineer, and physicist. He is best known as the eponymous discoverer of what is now called Coulomb's law, the description of the electrostatic force of attrac ...
, whose
law of friction was originally stated for granular materials. Granular materials are commercially important in applications as diverse as
pharmaceutical
A medication (also called medicament, medicine, pharmaceutical drug, medicinal drug or simply drug) is a drug used to diagnose, cure, treat, or prevent disease. Drug therapy (pharmacotherapy) is an important part of the medical field and re ...
industry,
agriculture
Agriculture or farming is the practice of cultivating plants and livestock. Agriculture was the key development in the rise of sedentary human civilization, whereby farming of domesticated species created food surpluses that enabled people to ...
, and
energy production.
Powders
A powder is a dry, bulk solid composed of many very fine particles that may flow freely when shaken or tilted. Powders are a special sub-class of granular materials, although the terms ''powder'' and ''granular'' are sometimes used to distin ...
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
Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma).
A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or ...
.
The
soldier
A soldier is a person who is a member of an army. A soldier can be a conscripted or volunteer enlisted person, a non-commissioned officer, or an officer.
Etymology
The word ''soldier'' derives from the Middle English word , from Old French ...
/
physicist
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe.
Physicists generally are interested in the root or ultimate caus ...
Brigadier
Ralph Alger Bagnold
Brigadier Ralph Alger Bagnold, OBE, FRS, (3 April 1896 – 28 May 1990) was an English 20th-century desert explorer, geologist and soldier.
In 1932, he staged the first recorded East-to-West crossing of the Libyan Desert. His work in the ...
was an early pioneer of the physics of granular matter and whose book ''
The Physics of Blown Sand and Desert Dunes
''The Physics of Blown Sand and Desert Dunes'' (1941) is a science book, written by Ralph A. Bagnold. The book laid the foundations of the scientific investigation of the transport of sand by wind. It also discusses the formation and movement of ...
'' remains an important reference to this day. According to
material scientist
Material is a substance or mixture of substances that constitutes an object. Materials can be pure or impure, living or non-living matter. Materials can be classified on the basis of their physical and chemical properties, or on their geologi ...
Patrick Richard, "Granular materials are ubiquitous in
nature
Nature, in the broadest sense, is the physics, physical world or universe. "Nature" can refer to the phenomenon, phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. ...
and are the second-most manipulated material in industry (the first one is
water
Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a ...
)".
In some sense, granular materials do not constitute a single
phase of matter
In the physical sciences, a phase is a region of space (a thermodynamic system), throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, magnetiza ...
but have characteristics reminiscent of
solid
Solid is one of the State of matter#Four fundamental states, four fundamental states of matter (the others being liquid, gas, and Plasma (physics), plasma). The molecules in a solid are closely packed together and contain the least amount o ...
s,
liquid
A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, a ...
s, or
gas
Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma).
A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or ...
es 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
A complex system is a system composed of many components which may interact with each other. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication ...
. They also display fluid-based instabilities and phenomena such as
Magnus effect
The Magnus effect is an observable phenomenon commonly associated with a spinning object moving through a fluid. The path of the spinning object is deflected in a manner not present when the object is not spinning. The deflection can be expl ...
.
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 physics, a rigid body (also known as a rigid object) is a solid body in which deformation is zero or so small it can be neglected. The distance between any two given points on a rigid body remains constant in time regardless of external force ...
. 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
In thermodynamics, dissipation is the result of an irreversible process that takes place in homogeneous thermodynamic systems. In a dissipative process, energy ( internal, bulk flow kinetic, or system potential) transforms from an initial form to ...
” - irreversible heat generation. The result is that without external driving, eventually all particles will stop moving. In macroscopic particles
thermal fluctuations
In statistical mechanics, thermal fluctuations are random deviations of a system from its average state, that occur in a system at equilibrium.In statistical mechanics they are often simply referred to as fluctuations. All thermal fluctuations b ...
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
![Stress transmision](https://upload.wikimedia.org/wikipedia/commons/d/d2/Stress_transmision.svg)
Coulomb
The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI).
In the present version of the SI it is equal to the electric charge delivered by a 1 ampere constant current in 1 second and to elementary char ...
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
and the minimum
angle of repose . 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,
, is the Bagnold angle, which is a measure of the
hysteresis
Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of ...
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
In architecture, a vault (French ''voûte'', from Italian ''volta'') is a self-supporting arched form, usually of stone or brick, serving to cover a space with a ceiling or roof. As in building an arch, a temporary support is needed while rin ...
and
arch
An arch is a vertical curved structure that spans an elevated space and may or may not support the weight above it, or in case of a horizontal arch like an arch dam, the hydrostatic pressure against it.
Arches may be synonymous with vaul ...
ing. When the
shear stress
Shear stress, often denoted by (Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. ''Normal stress'', on the ot ...
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. Janssen suggested a simplified model with the following assumptions:
1) The vertical pressure,
, is constant in the horizontal plane;
2) The horizontal pressure,
, is proportional to the vertical pressure
, where
is constant in space;
3) The wall friction static coefficient
sustains the vertical load at the contact with the wall;
4) The density of the material is constant over all depths.
The pressure in the granular material is then described in a different law, which accounts for saturation: