Damping of Waves by Surface-Active Materials

Abstract

A theory is presented for the damping of waves on a water surface in the presence of dissolved surface‐active material. Equations are given which are valid for any wave on any liquid surface, subject only to the condition that the liquid be incompressible and the liquid layer be sufficiently deep. The equations are solved by the method of successive approximations; the first approximation is fully discussed. The resulting first‐order equations are used in computing damping coefficients for solutions of surface‐active materials, the adsorption of which follows a Langmuir isotherm. The computed damping coefficients depend on surfactant concentration and on frequency, as had already been found in experiments. Extension of the theory to insoluble monolayers is discussed.