  When a binary liquid is confined by a strongly repulsive wall, the local
density is depleted near the wall and an interface similar to that between the
liquid and its vapor is formed. This analogy suggests that the composition of
the binary liquid near this interface should exhibit spatial modulation similar
to that near a liquid-vapor interface even if the interactions of the wall with
the two components of the liquid are the same. The Guggenheim adsorption
relation quantifies the concentrations of two components of a binary mixture
near a liquid-vapor interface and qualitatively states that the majority
(minority) component enriches the interface for negative (positive) mixing
energy if the surface tensions of the two components are not very different.
From molecular dynamics simulations of binary mixtures with different
compositions and interactions, we find that the Guggenheim relation is
qualitatively satisfied at wall-induced interfaces for systems with negative
mixing energy at all state points considered. For systems with positive mixing
energy, this relation is found to be qualitatively valid at low densities,
while it is violated at state points with high density where correlations in
the liquid are strong. This observation is validated by a calculation of the
density profiles of the two components of the mixture using density functional
theory with the Ramakrishnan-Yussouff free-energy functional. Possible reasons
for the violation of the Guggenheim relation are discussed.
