On the effective one-component description of highly asymmetric hard-sphere binary fluid mixtures

The phase diagram of a binary fluid mixture of highly asymmetric additive hard spheres is investigated. Demixing is analyzed from the exact low-density expansions of the thermodynamic properties of the mixture and compared with the fluid-fluid separation based on the effective one-component description. Differences in the results obtained from both approaches, which have been claimed to be equivalent, are pointed out and their possible origin is discussed. It is argued that to deal with these differences new theoretical approximations should be devised.