Effect of capillary waves on surface tension

Abstract

On fluid interfaces in finite-size systems, capillary waves longer than the system size are cut off, and the interfacial tension is higher than its infinite-system value \ensuremath{\sigma}. We quantify this increase using capillary-wave theory to calculate ${\ensuremath{\sigma}}_{2\ensuremath{\pi}/l}$, the surface tension of an interface with no capillary waves longer than l. The effect is small for a liquid-vapor interface near a triple point unless l is on the order of 10 molecular diameters. In contrast, ${\ensuremath{\sigma}}_{2\ensuremath{\pi}/l}$/\ensuremath{\sigma} near a critical point can be significantly larger than unity for reasonably large values of l. We find that ${\ensuremath{\sigma}}_{2\ensuremath{\pi}/l}$/\ensuremath{\sigma}=1.6 for l=20\ensuremath{\xi}, with \ensuremath{\xi} the bulk correlation length in either coexisting phase. Because systems on the order of 20\ensuremath{\xi} are physically realizable, this result has important implications for surface tension in confined geometries. Our normalization of the capillary-wave partition function implies that ${\ensuremath{\sigma}}_{2\ensuremath{\pi}/l}$ also obeys finite-size scaling: ${\ensuremath{\sigma}}_{2\ensuremath{\pi}/l}$/\ensuremath{\sigma}=F(l/\ensuremath{\xi}), where F(x) depends on the shape of the confined geometry but is otherwise universal. The implications of these and other predictions are discussed in light of recent developments involving surface tension and confined geometries.