Born-Green-Yvon approach to the local densities of a fluid at interfaces

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Abstract
The local density of a nonuniform fluid is calculated from the first equation of the Born-Green-Yvon hierarchy by modeling the pair correlation function. For that purpose, the mean force term is divided into two parts, corresponding to the mutual repulsion of the fluid atoms and the their mutual attraction, respectively. In the repulsive force term the interaction is approximated by a hard-sphere interaction and the pair correlation function is taken locally as that of a homogeneous hard-sphere fluid at some average density determined by spatial coarse graining. In the attractive force term the particles are taken to be uncorrelated. The formalism is applied to (a) the free-liquid surface, (b) gas adsorption on a wall at low temperatures, and (c) a liquid in contact with a wall. In all cases good agreement with existing computer simulations is obtained. An interesting feature arises for the free-liquid surface, where the equation turns out to be an eigenvalue equation for the coexisting liquid density. For this case the surface tension is also calculated.