Viscous attenuation of acoustic waves in suspensions

A model for attenuation of acoustic waves in suspensions is proposed that includes an energy loss due to viscous fluid flow around spherical particles. The expression for the complex wavenumber is developed by considering the partial pressures acting on the solid and fluid phases of the suspension. This is shown to be equivalent to the results of the Biot theory for porous media in the limiting case where the frame moduli vanish. Unlike earlier applications of the limiting case Biot theory, however, a value for the attenuation coefficient is developed from the Stokes flow drag force on a sphere instead of attempting to apply a permeability value to a suspension. Accurate modeling of observed phase velocities from suspensions of spherical polystyrene particles in water and oil and successful inversion for kaolinite properties using attenuation and velocity data from kaolinite suspensions at 100 kHz show that this viscous dissipation model is a good representation of the effects controlling the propagation of acoustic waves in these suspensions. The viscous effects are shown to be significant for only a limited range of solid concentration and frequency by the reduced accuracy of the model for attenuation in a kaolinite suspension at 1 MHz.