The surface tension and the bending rigidity of a planar liquid-vapor interface in the presence of vanishing gravity are analyzed using the renormalization group. Based on the density functional theory of inhomogeneous fluids, we show that a term, quartic in the density fluctuations, can be added to the classical capillary-wave model so that a renormalization-group calculation can be performed. By comparing the outcome of such a calculation with rigorous results relating the direct correlation function with surface tension and bending rigidity, we find the scaling dependence of the latter on gravity. The results agree with the expected fact that the interface should become unstable as gravity vanishes.
This study describes the structure of an inhomogeneous fluid of one or several components that forms a spherical interface. Using the stress tensor of Percus-Romero, which depends on the density of one particle and the intermolecular potential, it provides an analytical development leading to the microscopic expressions of the pressure differences and the interfacial properties of both systems. The results are compared with a previous study and agree with the description of the mean field.
We analyze a one-component simple fluid in a liquid-vapor coexistence state, which forms an arbitrarily curved interface. By using an approach based on density functional theory, we obtain an exact and simple expression for the grand potential at the level of mean field approximation that depends on the density profile and the short-range interaction potential. By introducing the step-function approximation for the density profile, and using general geometric arguments, we expand the grand potential in powers of the principal curvatures of the surface and find consistency with the Helfrich phenomenological model in the second order approximation.
Following the route of the stress tensor we study the free energy of a fluid liquid-vapor interface in the van der Waals approximation for planar, cylindrical and spherical interfaces. By performing a systematic expansion in powers of the inverse of the curvature radii, and appropriately defining the Gibbs dividing surface, we find unambiguous expressions for the surface tension, the spontaneous curvature, the bending rigidity and the Gaussian rigidity.
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