Capillary wave scattering from a surfactant domain

The study of capillary wave scattering by a circular region with different interfacial properties from the rest of an otherwise homogeneous interface is motivated by experiments on wave attenuation at a monolayer‐covered air–water interface where domains of one surface phase are dispersed in a second surface phase. Here the scattering function is calculated for an incident wave of frequency ω (wavevector k 0) scattering from an isolated circular domain of radius a with surface tension σ1 which is imbedded in an otherwise infinite interface of surface tension σ0. The underlying fluid is treated as irrotational and the three‐dimensional flow problem coupling the heterogeneous surface to the underlying liquid is reduced to a set of dual integral equations, which are solved numerically. With this solution the scattering amplitudes and the total scattering cross sections are calculated as a function of the surface tension ratio σ0/σ1 and incident wavenumber k 0 a. The analogous problem of a discontinuous change in bending rigidity is also considered and the solution to the complete viscous problem is outlined in the Appendix. Experimental implications of these results are discussed.