Interfacial width and shape fluctuations and extensions of the Gaussian model of capillary waves

Abstract

Interfacial density fluctuations are studied at the level of the Gaussian model of capillary waves by means of density functional theory. We consider nonrigid fluctuations and arrive at exact Triezenberg-Zwanzig-type expressions for new interfacial coefficients. These include a width tension, a width rigidity, and other coefficients linked to both shape and width distortions. We find for these coefficients magnitudes of the same orders as those of their tangential counterparts. The corresponding capillary-wave model describes the effect of fluctuations when the density is slowly varying, and the recognition of the additional quantities and their roles may help in the understanding of ellipsometric studies near critical points.