Enhanced KR-Fundamental Measure Functional for Inhomogeneous Binary and Ternary Hard Sphere Mixtures

An enhanced KR-fundamental measure functional (FMF) is elaborated and employed to investigate binary and ternary hard sphere fluids near a planar hard wall or confined within two planar hard walls separated by certain interval. The present enhanced KR-FMF incorporates respectively, for aim of comparison, a recent 3rd-order expansion equation of state (EOS) and a BoublIk's extension of Kolafa's EOS for HS mixtures. It is indicated that the two versions of the EOS lead to, in the framework of the enhanced KR-FMF, similar density profiles, but the 3rd-order EOS is more consistent with an exact scaled particle theory (SPT) relation than the BK EOS. Extensive comparison between the enhanced KR-FMF-3rd-order EOS predictions and corresponding density profiles produced in different periods indicates the excellent performance of the present enhanced KR-FMF-3rd-order EOS in comparison with other available density functional approximations (DFAs). There are two anomalous situations from whose density profiles all DFAs studied deviate significantly; however, subsequent new computer simulation results for state conditions similar to the two anomalous situations are in very excellent agreement with the present enhanced KR-FMF-3rd-order EOS. The present paper indicates that (i) the validity of the ''naive'' substitution elaborated in the present paper and peculiar to the original KR-FMF is still in operation even if inhomogeneous mixtures are being dealt with; (ii) the high accuracy and self-consistency of the third order EOS seem to allow for application of the KR-FMF-third order EOS to more severe state conditions; and (iii) the ''naive'' substitution enables very easy the combination of the original KR-FMF with future's more accurate but potentially more complicated EOS of hard sphere mixtures. (general)