Pair correlation functions for a hard sphere mixture in the colloidal limit

Previously, we have proposed an approximation for the contact values of the radial distribution functions of a hard sphere mixture. For most situations, this approximation is similar to earlier approximations. However, our approximation is quite different in the colloidal limit, where one species is large in size but whose concentration is very dilute. We called this approximation the ad hoc approximation to emphasize that this new approximation was untested. In this paper, we seek to test this ad hoc approximation by computing, by means of a Monte Carlo simulation, the pair correlation functions for a binary hard sphere mixture. We are able to consider mixtures in which the large hard sphere is up to 10 times the size of the small hard sphere and concentrations of the large sphere as small as 1%. While not the colloidal limit, these results are informative. The ad hoc approximation is found to be in good agreement with the simulation results.