Viscoelastic surface waves and the surface structure of liquids

Abstract

The dispersion relations for surface waves on a planar liquid surface are obtained from first principles. The high-frequency elastic, low-frequency hydrodynamic and intermediate viscoelastic regimes are investigated separately. It is shown that the structure of the liquid surface modifies the expression for Rayleigh's elastic surface waves and Kelvin's capillary waves and allows for the existence of new surface waves besides those of the phenomenological theories. For example, an hydrodynamic counterpart to the Rayleigh waves and an elastic counterpart to the capillary waves are found. The experimental observation of these surface waves could in principle yield direct access to the structure of the liquid surface.