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

An enhanced KR-fundamental measure functional (FMF) is elaborated andemployed to investigate binary and ternary hard sphere fluids near a planarhard wall or confined within two planar hard walls separated by certaininterval. The present enhanced KR-FMF incorporates respectively, for aim ofcomparison, a recent 3rd-order expansion equation of state (EOS) and aBoublik'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 predictionsand corresponding density profiles produced in different periods indicatesthe excellent performance of the present enhanced KR-FMF-3rd-order EOS incomparison with other available density functional approximations (DFAs).There are two anomalous situations from whose density profiles all DFAsstudied deviate significantly; however, subsequent new computer simulationresults for state conditions similar to the two anomalous situations are invery excellent agreement with the present enhanced KR-FMF-3rd-order EOS. The present paper indicates that (i) the validity of the ``naive' substitutionelaborated in the present paper and peculiar to the original KR-FMF is stillin operation even if inhomogeneous mixtures are being dealt with; (ii) thehigh accuracy and self-consistency of the third order EOS seem to allow forapplication of the KR-FMF-third order EOS to more severe state conditions;and (iii) the ``naive' substitution enables very easy the combination of theoriginal KR-FMF with future's more accurate but potentially more complicatedEOS of hard sphere mixtures.