Mechanical Packing of Spherical Particles
01 Oct 1961-Journal of the American Ceramic Society (Blackwell Publishing Ltd)-Vol. 44, Iss: 10, pp 513-522
TL;DR: An idealized experimental study of particle packing was made as mentioned in this paper, where spherical metal shot of several discrete, narrow size ranges was efficiently packed in glass containers by mechanical vibration, and the significance and utility of this work to the ceramic and other industries was discussed.
Abstract: An idealized experimental study of particle packing was made. Spherical metal shot of several discrete, narrow size ranges was efficiently packed in glass containers by mechanical vibration. Packing arrangements and the dynamic process of packing were studied visually. One-size spheres packed in an orthorhombic arrangement with a density 62.5% of theoretical density. Forming of high-density multicomponent packings was shown to require at least a sevenfold difference between sphere sizes of the individual components. A quaternary packing with a density 95.1% of theoretical density was formed from spheres with diameter ratios 1:7:38:316 and volume compositions 6.1:10.2:23.0:60.7%, respectively. Such packings could be poured from their glass containers, thus proving that effective mechanical packing is simply an efficient arrangement of spheres of prescribed sizes and proportions. The significance and utility of this work to the ceramic and other industries is discussed.
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References
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TL;DR: In this article, the underlying principles of porosity and permeability of uniform spheres are investigated, and the relationships disclosed, important wherever orderly distribution of points or particles is involved, are especially treated as the underlying principle.
Abstract: Geometrically systematic arrangements of uniform spheres are searchingly investigated in Part I. The relationships disclosed, important wherever orderly distribution of points or particles is involved, are here especially treated as the underlying principles of porosity and permeability. Besides packings denned respectively as "chaotic," "haphazard," and "chance," six cases of simple, systematic packing are recognized; two are orientation variants, but four are independent arrangements and include the two hitherto described: "loosest" and "tightest." Striking symmetries appear, and close analogies to crystal structure, including twinned and tripled arrangements. The unit void of each case is thoroughly explored and illustrated, since in it lies the key to porosity and permeability. The stability of the several cases and their probabilities of being formed indicate that Case 6, tightest or rhombohedral, is most favored, and this is abundantly confirmed by experiment. The commonest natural packing, however,...
509 citations
470 citations
373 citations
TL;DR: In this paper, the porosity and permeability of ideal clastic materials were evaluated and compared with those of natural clastic sediments, including river and beach sand, in the problem of the distribution and localization of mineral deposits.
Abstract: The purpose of this study is threefold: to experimentally evaluate the factors controlling the porosity and permeability of ideal clastic materials; to determine the modifications produced in natural deposits by variations from the ideal; to apply the principles of permeability to the problem of the distribution and localization of mineral deposits in clastic sediments. The effect on porosity of absolute grain-size, variable grain-size, shape of grain, method of deposition, and compaction are experimentally determined for ideal materials and compared with those of river and beach sands and other clastic sediments. Various equations for permeability are discussed; and the controlling factors of temperature, hydraulic gradient, size and shape of grain, uniformity of grain-size, porosity, and stratification are experimentally evaluated for ideal materials, and the modifications caused by natural materials are delimited and discussed. Field observations on the effects of wave and river depositional processes ...
266 citations
TL;DR: In this paper, a theoretical analysis of the theoretical densest packing arrangement of spherical-shaped grains was carried out, showing that the use of very fine filler in the remaining voids will then reduce the voids theoretically to 3.9%.
Abstract: Spherical particles of equal size theoretically may be packed in five different ways, e.g. (1) cubical with a theoretical void space of 47.64%, (2) single-staggered or cubical-tetrahedral with a theoretical void space of 39.55%, (3) double-staggered with a theoretical void space of 30.20%, (4) pyramidal, and (5) tetrahedral; the void spaces in the latter two are identical, 25.95%.
Secondary, ternary, quaternary, and quinary spheres each set smaller than its predecessor, may be fitted into the voids in this last type of packing and the voids reduced theoretically to 14.9%.
The use of very fine filler in the remaining voids will then reduce the voids theoretically to 3.9%.
The use of particles of elliptical shape does not appear to reduce the porosity, but cylindrical-shaped particles, if properly arranged, would reduce the porosity below that possible with spheres.
The practical application of these theoretical methods of packing was studied, and the possibility of crushing ceramic materials to spherical shapes is discussed with particular emphasis on the higher-priced materials such as fused alumina, mullite (fused, synthetic, and natural), chromite, magnesite, forsterite, silicon carbide, and also silica, owing to the particular rounded character of natural sand grains.
Study of experimental work shows the possibility of approaching the theoretical densest packing arrangement by the use of spherical-shaped grains. Allowance must be made in some instances for the porosity of the grains themselves.
Surface areas can be calculated and the bonding mediums proportioned accordingly. Some commercial refractories investigated, which have relatively low porosity, seem to have taken advantage of a careful study of the laws of particle packing, both in the manner of packing of the grog grains and in the shape of the grains themselves.
104 citations