On gradient theories of fluid interfacial stress and structure

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Abstract
The gradient approximations of the density profile equations obtained from momentum balance (the Yvon–Born–Green theory) and from minimization of the Helmholtz free energy (the van der Waals–Cahn–Hilliard theory) are compared. Tractable equations are obtained by approximating the pair correlation function as that of a homogeneous fluid at densities in the vicinity of the interacting pair. The theories are shown to be insensitive to the particular choice of such approximating pair correlation functions if the third force moments are composition and density independent. The YBG and the VDW–CH gradient approximations yield identical results for such approximating pair correlation functions if the first and third force moments are density and composition independent (in the case of a one‐component fluid, only density independence of the third force moment is required). Numerical results are presented for the interfacial properties of a one‐component square‐well fluid.