Equation of state and correlation function contact values of a hard sphere mixture

Recently, there has been considerable activity in the study of the equation of state and correlation functions of a hard sphere mixture when the concentration of the large spheres is exceedingly small. This system is of considerable interest both as a simple prototype of an asymmetric mixture and as a simple but useful model of a colloidal suspension. We review our ad hoc formulae for the correlation function contact values and discuss the evidence, both pro and con, from exact and nearly exact theorems, computer simulations and experiment. Our conclusion is that our formulae are, on the whole, correct but the large sphere–large sphere correlation function contact value seems to need revision when the concentration of the large spheres is small but not exceedingly small. We propose a modest revision that preserves the seemingly correct aspects of our formula and this is in good agreement with the most recent simulations.