Resonance scattering in suspensions

Measured and theoretical total cross sections for aqueous suspensions of lead glass and polystyrene beads are presented. Attenuation is measured from 1 to 100 MHz in a recirculating suspension circuit using a swept-frequency system and broadband transducer pairs. The theoretical calculations employ the phase shift formalism and the coherent removal of a rigid scatterer background. Good agreement between theory and experiment is obtained for both types of particle, and departures from the rigid sphere cross section are due to resonance scattering. The resonance features in the glass bead cross sections are dominated by broad Rayleigh wave resonances, with frequencies close to those given by the in vacuo free-body resonance condition, and represent departures from the rigid sphere cross section of, at most, 25%. In contrast, the polystyrene bead cross sections are dominated by narrow resonance features with maximum amplitudes up to five times greater than the geometric scattering cross section. It is shown that these resonances, which we call giant resonances, occur at frequencies given by an immersed free-body resonance condition that is derived by assuming the existence of wave trapping in the fluid at the surface of the sphere. This condition yields frequencies that are wholly real, consistent with the observed narrow resonance widths, and leads to an approximate expression for the resonance amplitudes that is in good agreement with the exact calculations. The meridional wave phase speeds are consistent in the appropriate limit with Stonely waves. The giant resonances cease to exist if the meridional wave phase speed approaches the speed of sound in the ambient fluid.