Jamming (physics)
Encyclopedia
Jamming is the physical process by which some materials, such as granular material
s, glass
es, foam
s, and other complex fluids, become rigid with increasing density. The jamming transition has been proposed as a new type of phase transition
, with similarities to a glass transition
but very different from the formation of
crystalline solids.
While a glass transition occurs when the liquid state is cooled, the jamming transition happens when density is increased. This crowding of the constituent particles prevents them from exploring phase space
, making the aggregate material behave as a solid. The system may be able to unjam if the temperature is increased, or external stresses are applied.
The jamming phase diagram
relates the jamming transition to inverse density, stress
and temperature.
The density at which systems jam is determined by many factors, including the shape of their components, the deformability of the particles, frictional interparticle forces, and the degree of dispersity of the system. The overall shape of the jamming manifold may depend on the particular system. For example, a particularly interesting feature of the jamming transition is the difference between attractive and repulsive systems. Whether the jamming surface diverges for high enough densities or low temperatures is uncertain.
Simulations of jammed systems study particle configurations leading to jamming in both static systems and systems under shear. Under shear stress
, average cluster size may diverge after a finite amount of strain, leading to a jammed state. A particle configuration may exist in a jammed state with a stress required to “break” the force chains causing the jam.
A static sand pile is jammed under the force of gravity and no energy is being dissipated. Systems which are consuming energy are also sometimes described as being jammed. An example is traffic jams, where due to jamming the average velocity of cars on a road may drop sharply. Here the cars on a road may be thought of as a like a granular material
or a non-newtonian fluid
that is being pumped through a tube. There under certain conditions the effective viscosity
may rapidly increase, dramatically increasing the granular material
or fluid
s's resistance to flowing and so causing the velocity to drop or even come to a complete stop. In this analogy the cars are like the grains in a granular material
and if they are dense enough (i.e., closely enough spaced along the road) then interactions between the cars (as they must avoid each other to avoid crashing) cause jamming. A simple model of this behavior is the Nagel-Schreckenberg model
.
Granular material
A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact . The constituents that compose granular material must be large enough such that they are not subject to thermal motion fluctuations...
s, glass
Glass
Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...
es, foam
Foam
-Definition:A foam is a substance that is formed by trapping gas in a liquid or solid in a divided form, i.e. by forming gas regions inside liquid regions, leading to different kinds of dispersed media...
s, and other complex fluids, become rigid with increasing density. The jamming transition has been proposed as a new type of phase transition
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
, with similarities to a glass transition
Glass transition
The liquid-glass transition is the reversible transition in amorphous materials from a hard and relatively brittle state into a molten or rubber-like state. An amorphous solid that exhibits a glass transition is called a glass...
but very different from the formation of
crystalline solids.
While a glass transition occurs when the liquid state is cooled, the jamming transition happens when density is increased. This crowding of the constituent particles prevents them from exploring phase space
Phase space
In mathematics and physics, a phase space, introduced by Willard Gibbs in 1901, is a space in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the phase space...
, making the aggregate material behave as a solid. The system may be able to unjam if the temperature is increased, or external stresses are applied.
The jamming phase diagram
Phase diagram
A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions at which thermodynamically distinct phases can occur at equilibrium...
relates the jamming transition to inverse density, stress
and temperature.
The density at which systems jam is determined by many factors, including the shape of their components, the deformability of the particles, frictional interparticle forces, and the degree of dispersity of the system. The overall shape of the jamming manifold may depend on the particular system. For example, a particularly interesting feature of the jamming transition is the difference between attractive and repulsive systems. Whether the jamming surface diverges for high enough densities or low temperatures is uncertain.
Simulations of jammed systems study particle configurations leading to jamming in both static systems and systems under shear. Under shear stress
Shear stress
A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...
, average cluster size may diverge after a finite amount of strain, leading to a jammed state. A particle configuration may exist in a jammed state with a stress required to “break” the force chains causing the jam.
A static sand pile is jammed under the force of gravity and no energy is being dissipated. Systems which are consuming energy are also sometimes described as being jammed. An example is traffic jams, where due to jamming the average velocity of cars on a road may drop sharply. Here the cars on a road may be thought of as a like a granular material
Granular material
A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact . The constituents that compose granular material must be large enough such that they are not subject to thermal motion fluctuations...
or a non-newtonian fluid
Non-Newtonian fluid
A non-Newtonian fluid is a fluid whose flow properties differ in any way from those of Newtonian fluids. Most commonly the viscosity of non-Newtonian fluids is not independent of shear rate or shear rate history...
that is being pumped through a tube. There under certain conditions the effective viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...
may rapidly increase, dramatically increasing the granular material
Granular material
A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact . The constituents that compose granular material must be large enough such that they are not subject to thermal motion fluctuations...
or fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
s's resistance to flowing and so causing the velocity to drop or even come to a complete stop. In this analogy the cars are like the grains in a granular material
Granular material
A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact . The constituents that compose granular material must be large enough such that they are not subject to thermal motion fluctuations...
and if they are dense enough (i.e., closely enough spaced along the road) then interactions between the cars (as they must avoid each other to avoid crashing) cause jamming. A simple model of this behavior is the Nagel-Schreckenberg model
Nagel-Schreckenberg model
The Nagel-Schreckenberg model is a theoretical model for the simulation of freeway traffic. The model was developed in the early 90s by the German physicists Kai Nagel and Michael Schreckenberg...
.