Granular Matter

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Entry by Haifei Zhang, AP 225, Fall 2009

What is granular matter

Sand is a very common granular material.

A granular material is a collection of distinct macroscopic particles, such as sand in an hourglass or peanuts in a container. The evolution of the particles follows Newton's equations, with repulsive forces between particles that are non-zero only when there is a contact between particles. Although granular materials are very simple to describe they exhibit a tremendous amount of complex behavior, much of which has not yet been satisfactorily explained.

Distribution of events as a function of td and <ΔIb> for 10-kb dsDNA.

a,A 3-nm pore,2,674 events; b,a 10-nm pore,9,477 events.The bias voltage was 120mV. The colour scale represents event-fraction density normalized as a probability distribution so that the integral of the density over all td and <ΔIb> is equal to 1.

Characteristics

A granular material on an incline plane, from simulations by Silbert and coworkers (2002)

Granular material behave differently than solids, liquids, and gases which has led many to characterize granular materials as a new form of matter.

For example, if a granular material is heaped on an inclined plane, then the large scale state of the system depends on the angle of the plane. For large angles the granular material flows like a non-Newtonian liquid. For small angles the granular material will behave like a solid and remain stationary. The value of the critical angle between these phases depends on the preparation history, and the transition between the phases is a manifestation of the glass transition. As you can see, there is a lot of interesting and complex physics to be understood by studying just the large scale properties of a granular material in such a simple arrangement. As the composition becomes more complicated, the behavior becomes even richer.

From a small scale point of view, the characteristics that make granular materials interesting are inelastic collisions and the unimportance of temperature. Because collisions between particles are inelastic then the energy of a granular material is a dynamic quantity, and because the particles that make up a granular materials are macroscopic then temperature does not produce significant motion. Ultimately we would like to describe the properties of a granular material using statistical arguments, but since there is no well defined energy or temperature then conventional equilibrium statistical mechanics does not apply. A full understanding of granular materials will require an extension of statistical mechanics, which is of great fundamental interest. One central question concerning such a statistical theory is whether the robust yet fragile concept central to complexity in the HOT approach is apparent in a granular material, which is very simple compared to ecological and biological systems.

Applications

Granular materials play an important role in many of our industries, such as mining, agriculture, civil engineering and pharmaceutical manufacturing. They clearly are also important for geological processes where landslides and erosion and, on a larger scale, plate tectonics determine much of the morphology of the Earth. Practically everything that we eat started out in a granular form and all the clutter on our desks is often so close to the angle of repose that a small perturbation will create an avalanche onto the floor. We may still think that Hugo has overstepped the bounds of common sense when he likens the creation of worlds to the movement of simple grains of sand. However, by the end of our recent review article, we hope to have shown that there is enormous richness and complexity to granular motion. Even the possibility that Victor Hugo's metaphor (quoted at the very beginning of this web site) could have a literal meaning might no longer appear far fetched: first connections are emerging between granular dynamics and processes taking place on an astrophysical scale.

Finally, many of our industries rely on transporting and storing granular materials. These include the pharmaceutical industry which relies on the processing of powders and pills, agriculture and the food processing industry where seeds, grains and foodstuffs are transported and manipulated, as well as all construction-based industries. Additional manufacturing processes, e.g. in the automotive industry, rely on casting large metal parts in carefully packed beds of sand. Yet the technology for handling and controlling granular materials is poorly developed. Estimates show that we waste 60% of the capacity of many of our industrial plants due to problems related to the transport of these materials from part of the factory floor to another. Hence even a small improvement in our understanding of how granular media behave should have an profound impact for industry.

References

[1] http://en.wikipedia.org/wiki/Granular_material

[2] http://jfi.uchicago.edu/granular/introduction.html

[3] The physics of granular media‎, Haye Hinrichsen and Dietrich E. Wolf, (2004)