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Determination of the coordination number in disordered packings of equal spheres

A computation of the coordination number in a packing of equal spheres can be performed from the information obtained along a random line through the packing. It involves the distribution of the number per unit length of separators between intercepts of spheres with the line. The number of contacts per unit volume is derived from the slope of the distribution at the origin. The method is validated by computer experiments on four kinds of simulated ordered packings which are intercepted by a set of random lines (instead of a single one) in order to compensate biased results due to the small size of these packings: the comparison is then extended to a series of disordered dense packings of equal spheres. We present some possible applications of this study to stereological and physical problems.