Abstract
Two-component isotropic mixtures may be characterized by a correlation coefficient between sample compositions. Previous studies of this type have often been hard to use in those practical situations in which it is clear that sample composition depends on sample size. Alternatively the composition-distance relationship has not been fully preserved. Here it is shown that a more satisfactory characterization is obtained by basing a correlation coefficient upon elements of the mixture, an element being much smaller than the smallest constituent unit capable of independent movement and thus having the composition of one of the pure components. This correlation coefficient is independent of element size and may be used to provide a precise description of the statistical properties of the mixture. For example the variance of macroscopic circular and spherical samples may be deduced as may the correlation coefficient for linear macroscopic samples. The theory leads to a discussion of other work, of free space in particulate mixtures and of the necessary number of parameters required in the correlation coefficient. A practical result is that the variance of samples taken from a non-random isotropic mixture becomes inversely proportional to sample volume if the samples are sufficiently large, in contrast to work by Bourne and Landry.
Published Version
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