A new generalization of the Carnahan-Starling equation of state to additive mixtures of hard spheres

We introduce an expansion of the equation of state for additive hard-sphere mixtures in powers of the total packing fraction with coefficients which depend on a set of weighted densities used in scaled particle theory and fundamental measure theory. We demand that the mixture equation of state recovers the quasiexact Carnahan-Starling J. Chem. Phys. 51, 635 (1969)] result in the case of a one-component fluid and show from thermodynamic considerations and consistency with an exact scaled particle relation that the first and second orders of the expansion lead unambiguously to the Boublik-Mansoori-Carnahan-Starling-Leland J. Chem. Phys. 53, 471 (1970); J. Chem. Phys. 54, 1523 (1971)] equation and the extended Carnahan-Starling equation introduced by Santos et al. Mol. Phys. 96, 1 (1999)]. In the third order of the expansion, our approach allows us to define a new equation of state for hard-sphere mixtures which we find to be more accurate than the former equations when compared to available computer simulation data for binary and ternary mixtures. Using the new mixture equation of state, we calculate expressions for the surface tension and excess adsorption of the one-component fluid at a planar hard wall and compare its predictions to available simulation data.