Random close pack

Random close pack

Random close packing (RCP) is an empirical parameter used to characterize the maximum volume fraction of solid objects obtained when they are packed randomly. For example, when a solid container is filled with grain, shaking the container will reduce the volume taken up by the objects, thus allowing more grain to be added to the container. In other words shaking increases the density of packed objects.

The volume fraction filled by the solid objects in random close pack is 0.64 for (monodisperse) spherical objects. This is significantly smaller than the maximum theoretical filling fraction of 0.74048 that results from hexagonal close pack (HCP - also known as Close-packing). This discrepancy demonstrates that the "randomness" of RCP is vital to the definition.

Definition

Random close packing does not have a precise geometric definition. It is defined statistically, and results are empirical. A container is randomly filled with objects, and then the container is shaken or tapped until the objects do not compact any further, at this point the packing state is RCP. The definition of packing fraction is,"The volume taken by number of particles in a given space of volume".In other words packing fraction defines the packing density.It has been shown that the filling fraction increases logarithmically with the number of taps until the saturation density is reached. Also, the saturation density increases as the tapping amplitude decreases. Thus RCP is the packing fraction given by the limit as the tapping amplitude goes to zero, and the limit as the number of taps goes to infinity.

Effect of Object Shape

The particle volume fraction at RCP depends on the objects being packed. If the objects are polydispersed then the volume fraction depends non-trivially on the size-distribution and can be arbitrarily close to 1. Still for (relatively) monodisperse objects the value for RCP depends on the object shape; for spheres it is (0.64), for M&M's candy it is (0.68).

Example

Products containing loose pack items are often labeled with this message: 'Contents May Settle During Shipping'. Usually during shipping, the container will be 'tapped' numerous times, which will increase the packing density.The message is added to assure the consumer that the container is full on a mass basis, even though the container appears slightly empty.

ee also

*Sphere packing
*Close-packing

References

*"Physics of Granular States." Science 255, 1524, 1992.
*"Improving the Density of Jammed Disordered Packings using Ellipsoids." Science, 303, 990-993, 2004.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • Random walk — A random walk, sometimes denoted RW, is a mathematical formalization of a trajectory that consists of taking successive random steps. The results of random walk analysis have been applied to computer science, physics, ecology, economics and a… …   Wikipedia

  • Magnetoresistive random access memory — Computer memory types Volatile RAM DRAM (e.g., DDR SDRAM) SRAM In development T RAM Z RAM TTRAM Historical Delay line memory Selectron tube Williams tube Non volatile …   Wikipedia

  • Sphere packing — In mathematics, sphere packing problems are problems concerning arrangements of non overlapping identical spheres which fill a space. Usually the space involved is three dimensional Euclidean space. However, sphere packing problems can be… …   Wikipedia

  • Glossary of cue sports terms — The following is a glossary of traditional English language terms used in the three overarching cue sports disciplines: carom (or carambole) billiards referring to the various carom games played on a billiard table without pockets; pool (pocket… …   Wikipedia

  • List of Sonic the Hedgehog comic book characters — This article lists the fictional characters in the Sonic the Hedgehog comic series. Contents 1 Cast creation and influence 2 Main characters 2.1 Antoine D Coolette 2.2 …   Wikipedia

  • Media and Publishing — ▪ 2007 Introduction The Frankfurt Book Fair enjoyed a record number of exhibitors, and the distribution of free newspapers surged. TV broadcasters experimented with ways of engaging their audience via the Internet; mobile TV grew; magazine… …   Universalium

  • Business and Industry Review — ▪ 1999 Introduction Overview        Annual Average Rates of Growth of Manufacturing Output, 1980 97, Table Pattern of Output, 1994 97, Table Index Numbers of Production, Employment, and Productivity in Manufacturing Industries, Table (For Annual… …   Universalium

  • Computers and Information Systems — ▪ 2009 Introduction Smartphone: The New Computer.       The market for the smartphone in reality a handheld computer for Web browsing, e mail, music, and video that was integrated with a cellular telephone continued to grow in 2008. According to… …   Universalium

  • Life Sciences — ▪ 2009 Introduction Zoology       In 2008 several zoological studies provided new insights into how species life history traits (such as the timing of reproduction or the length of life of adult individuals) are derived in part as responses to… …   Universalium

  • Heli Attack 2 — is an Internet game created by Squarecircleco. Players take the role of a soldier in a jungle type environment, and must take down as many helicopters, or helis , as possible before the player dies, using a wide array of weapons. Points gained… …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”