A new perturbative weighted density functional theory for an inhomogeneous hard-sphere fluid mixture

A new approach to the structure of the inhomogeneous fluid mixture is developed within the framework of density functional theory by expanding the Denton–Ashcroft weighted density-based expression for the first-order direct correlation function as a Taylor series in the weighted density inhomogeneity. The connection of this expansion with the conventional functional Taylor perturbative approach is investigated. A truncation of the proposed expansion coupled with the use of a scaled parameter to mimic the effect of the neglected higher-order contributions, determined self-consistently by forcing the wall theorem to be satisfied, is implemented. The theory is employed to predict the structure of a pure hard-sphere fluid as well as a hard-sphere mixture near a hard wall and the agreement with the available simulation results is found to be very good.