Finite-size effects in fluid interfaces

Abstract

Finite-size effects in interfacial tensions of fluid interfaces are studied at the level of the Gaussian model of capillary waves. It had been suggested that such effects might play a significant role in surface tension measurements based on capillary rise between plates spaced a small distance D apart, the finite-size correction varying as 1/ D. A reconsideration of the thermodynamics of finite-size effects, followed by careful calculations for the Gaussian model, leads to a finite-size correction varying as 1/ D 2, with a universal coefficient; the effect is too small to be noticeable in current experiments. The calculations have been carried out for rectangular interfaces of arbitrary dimensionality and general shapes subject to many types of boundary conditions. They also have implications for finite-size effects in interfacial free energies in two- and three-dimensional Ising models, which are discussed in connection with recent exact and Monte Carlo calculations.