Sphere Packing

Introductions
1The packing of the isometrical spheres
1.1The loosest packing of the isometrical spheres
1.2The closest packing of the isometrical spheres
2The packing of unequal spheres
2.1 Arrange the big spheres loosest packing. Fill middle and small size spheres in voids
2.2 Arrange the big spheres closest packing. Fill middle and small size spheres in voids
3Tests of sphere packing
3.1 Tests of sub-loose and the loosest packing of isometrical spheres
3.2Tests of sub-loose, the loosest and the closest packing of unequal sphere
4Conclusions
References
 

Sphere Packing

Abstract:The computed results of the packing rate and the specific surface area for the loosest packing and the closest packing of the isometrical spheres are given in this paper. The results show that these two packing rates are all constant respectively. It is impracticable that packing rate is increased by means of decreasing sphere diameter. In cases of that big spheres are in loosest packing or closest packing and small spheres are filled in the voids between the big spheres, the increment of packing rate and the diameter ratio of small sphere to big sphere are given in this paper.
The test results of the loosest packing ratio, the sub-loose packing ratio and densest packing ratio are quoted in this paper in the cases of a kind of isometric spheres and two kinds of isometric spheres. When the diameter ratio of small sphere to big sphere is equal of greater than some threshold value to each case, the packing rate is constant. When the diameter ratio is less than some threshold value, the packing rate can only be increased.
The computed and test results have important significance to instruct practical work.
Key Words: Sphere Packing, Loosest Packing, Closest Packing, Packing Rate, Voidage

Introductions

　　Spheres packing is refer to get the spheres and adjacent spheres together according to a certain way to contact each other.
　　There are two kinds of spheres packing: the packing of isometrical spheres and the packing of unequal size spheres.
　　The extreme cases of isometrical spheres packing have two kinds: the loosest packing and the closest packing.
　　Packing situation is shown by coordination number. Coordination number is defined as the number of the adjacent spheres contacted with a sphere. In the loosest packing, a sphere is contacted with other four spheres in the same floor, and contacted with each of the 1 sphere in up and down floors; therefore the coordination number is 6. In the closest packing, a sphere was contacted with other six spheres in the same floor, and contacted with each of the 3 spheres in up and down floor; therefore the coordination number is 12. Other situations are between the above two situations.