Packing of Spheres


IN connexion with Bernal's theory of liquids, Scott1 has determined the packing density of equal spheres by experiments with steel balls. In this laboratory we were interested in the dense random packing of beads of ion-exchange resins. Although particles of ion-exchange resins may vary in diameter from 1.3 mm. to 0.03 mm. or less, if the ratio of the diameters of the larger to the smaller beads in any batch exceeds 3 or 4, segregation may occur when the beads are backwashed or allowed to settle under water. If the ratio exceeded 6.5, it would be possible for the smallest spheres to fit into spaces between close-packed spheres of the largest diameter and so increase the packing density; but, if the problem is limited to the smaller ratios which occur in practice, only holes and not spaces can be filled by the smaller beads and the packing density should be 0.64–0.74.

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  1. 1

    Scott, G. D., Nature, 188, 908 (1960).

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PARRISH, J. Packing of Spheres. Nature 190, 800 (1961).

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