### 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 ω (wavevector k_{0}) scattering from an isolated circular domain of radius a with surface tension σ_{1} which is imbedded in an otherwise infinite interface of surface tension σ_{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 σ0/σ_{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 the Appendix. Experimental implications of these results are discussed.

Original language | English (US) |
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Pages (from-to) | 1872-1885 |

Number of pages | 14 |

Journal | Physics of Fluids |

Volume | 7 |

Issue number | 8 |

DOIs | |

State | Published - Jan 1 1995 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes

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## Cite this

*Physics of Fluids*,

*7*(8), 1872-1885. https://doi.org/10.1063/1.868502