On capillary waves in the gradient theory of interfaces

Abstract

We have solved the equations of motion for an inhomogeneous, nondissipative fluid linearized about a two-phase solution in order to determine the dispersion relation for capillary waves of long wavelength. The solution is reasonably rigorous in that no physical assumptions have been introduced. We find that, in accordance with the results of Turski and Langer and contrary to other workers' claims, the dispersion relation agrees with classical capillary theory only if thermal effects are included.