Capillary wave scattering from a surfactant domain

The study of capillary wave scattering by a circular region with differentinterfacial properties from the rest of an otherwise homogeneous interface ismotivated by experiments on wave attenuation at a monolayer covered air-waterinterface where domains of one surface phase are dispersed in a second surfacephase. Here the scattering function is calculated for an incident wave offrequency $\omega$ (wavevector $k_0$) scattering from an isolated circulardomain of radius $a$ with surface tension $\sigma_{1}$ which is imbedded in anotherwise infinite interface of surface tension $\sigma_{0}$. The underlyingfluid is treated as irrotational and the three-dimensional flow problemcoupling the heterogeneous surface to the underlying liquid is reduced to a setof dual integral equations, which are solved numerically. With this solutionthe scattering amplitudes and the total scattering cross sections arecalculated as a function of the surface tension ratio $\sigma_{0}/\sigma_{1}$and incident wavenumber $k_0 a$. The analogous problem of a discontinuouschange in bending rigidity is also considered and the solution to the completeviscous problem is outlined in an appendix. Experimental implications of theseresults are discussed.Comment: 18 pages latex, 9 uuencoded figures, ignore latex error