Capillary Wave Scattering from a Surfactant Domain

TL;DR

This paper models how capillary waves scatter when encountering a surfactant domain with different surface tension, providing numerical solutions and discussing experimental implications for wave attenuation at interfaces.

Contribution

It introduces a numerical method to calculate scattering from a surfactant domain with varying surface tension, extending understanding of wave-interface interactions.

Findings

Scattering amplitudes depend on surface tension ratio and wave number.

Total scattering cross sections vary with domain size and tension contrast.

Results have implications for interpreting wave attenuation experiments.

Abstract

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 $\omega$ (wavevector $k_0$) scattering from an isolated circular domain of radius $a$ with surface tension $\sigma_{1}$ which is imbedded in an otherwise infinite interface of surface tension $\sigma_{0}$. 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 $\sigma_{0}/\sigma_{1}$ 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 an appendix. Experimental implications of these results are discussed.