Consistency of capillary wave theory in three dimensions: Divergence of the interface width and agreement with density functional theory

摘要

We compare the predictions of the capillary wave model for fluid interfaces with known exact expressions, due to Triezenberg, Zwanzig, and Wertheim, that relate the surface tension to the interfacial structure, and find agreement in all dimensions. It is shown that contrary to the cased3, the interfacial pair correlation function does not obey scaling ind=3 dimensions on length scales less than the capillary lengthLc. Nevertheless, once the sensitive dependence on the gravitational field and the short distance cutoff is properly taken into account, we find no evidence for recent allegations that the capillary wave model leads to inherently inconsistent results for the direct correlation function ind=3. Several issues regarding the connection with density functional theory and the interpretation of the Triezenbergndash;Zwanzig formula, on which these results touch, are discussed.