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.


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