Preferential adsorption in a near-critical binary fluid mixture as analyzed in the framework of the non-random two-liquid model

We consider a binary fluid mixture, which lies in the one -phase region near the demixing critical point. Shortrange interactions between the mixture components and a solid surface in contact with the mixture can make the mixture composition inhomogeneous significantly near the surface. This inhomogeneity has been shown to cause various phenomena by using the renormalized local functional theory. In its free -energy density, the order -parameter field is coarse -grained without rescaled and only the most singular part is specified. In the present study, on the basis of the crossover theory, we introduce a square -gradient term to the freeenergy density of the extended non-random two -liquid model, which includes more than the most singular part. Thanks to similarity between the renormalized local functional theory and the crossover theory, the relationship between the two free -energy densities can be clarified. Supposing a mixture of nitroethane and 3-methylpentane and a mixture of 2,6-lutidine and water, we use the proposed free -energy density to calculate the inhomogeneous composition profile numerically. The free -energy density also enables us to calculate excess densities of entropy and enthalpy, unlike that of the renormalized local functional theory. We also find that the magnitude of the thermal force density, which is induced by a temperature gradient to cause flow in thermoosmosis, can depend on the calculation procedures significantly.