A General Expression for the Ordered-Packed Volume Fraction of Hard Spheres of Different Diameters

An expression is proposed to evaluate the ordered-packed volume fraction of hard spheres of unequal diameters in multicomponent mixtures. This value can be used with different mixing rules and with any one-component hard-sphere equation of state (EOS) meeting the correct close-packed limit. It is shown that the new method improves the results produced by conventional mixing rules for the individual radial distribution functions (RDFs) at contact value of hard-sphere mixtures. Particular attention is given to the case of the large diameter ratio especially when the larger spheres are at low concentration. Based on the observation that, in a binary mixture, the value of the RDF at contact value of the larger spheres approaches the value of the RDF at contact value of a one-component hard-sphere fluid, the proposed expression is used to correct the RDF at contact value of a pure hard-sphere fluid in the Santos et al. mixing rule. The EOS obtained by combining the Ghotbi−Vera one-component EOS with the correc...