Hydrostatic equilibrium in fluid interfaces

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Abstract
The statistical mechanical expression for the pressure tensor is used to determine the density distribution in a fluid interface in hydrostatic equilibrium. The two principal assumptions in the model are, firstly, that an expansion of the pair distribution function in the interfacial gradient converges so rapidly that only the zero and first order terms are necessary to determine the density profile, and, secondly, that the radial distribution function for particles in an isochore plane can be obtained from the continuation of the bulk radial distribution function into interfacial densities. The resulting monotonic density functions agree well with otherwise obtained functions. It is tested whether the equation for hydrostatic equilibrium, in the present formulation gives, as it should do, the same interfacial density profiles as the first integrodifferential equation in the Born–Green–Yvon–Bogolyubov hierarchy.