Viscous Attenuation Of Acoustic Waves In Suspensions

Abstract

A model for attenuation of acoustic waves in suspensions is proposed which 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. If the fluid and solid particle velocities have harmonic time dependence with angular frequency w, the attenuation in this model is proportional to w2 at low frequencies and approaches a constant value at high frequencies. The predicted attenuation is very sensitive to the radius and density of the spherical particles. 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. Attenuation predictions are also compared to amplitude ratio data from an oil-polystyrene suspension. 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.