Random close pack
From Wikipedia, the free encyclopedia
Random close packing (RCP) is an empirical parameter used to characterize the maximum volume fraction of solid objects obtained by "packing" these objects in a "random" manner after settling. 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.
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.
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[edit] 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 it until the objects do not compact any further, at this point the packing state is RCP. 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.
[edit] Effect of Object Shape
The particle volume fraction at RCP depends on the objects being packed. If the objects are polydisperse it depends non-trivially on the size-distribution and can in principle 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).
[edit] 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.
[edit] See also
[edit] References
- "Physics of Granular States." Science 255, 1524, 1992.
- "Improving the Density of Jammed Disordered Packings using Ellipsoids." Science, 303, 990-993, 2004.
