Extinction of sound by spherical scatterers in a viscous fluid

The extinction of sound waves in a viscous fluid due to scattering from viscous fluid and solid elastic spheres is investigated. Exact expressions for scattered and transmitted fields caused by an incident-plane compressional wave of unit amplitude are calculated analytically with both compressional and shear modes supported in the viscous fluid and solid elastic media. Furthermore, it is shown that by boundary coupling, incident compressional acoustic waves generate compressional and shear waves in the scattered and transmitted fields. The general expressions for scattering and extinction cross sections are given, and for the special cases of vanishing viscosity, agreement with well-known solutions is obtained. In the Rayleigh-wave range for small scatterers, simple expressions for the cross sections are obtained, and for lossy scattering, absorption phenomena are shown to dominate scattering phenomena in this range. Finally, the extinction coefficient for a dilute cloud of scatterers is derived and the extinction effects due to viscosity are discussed.