A direct method for acoustic waves in hard particle–fluid suspensions

A direct method is developed to study acoustic waves in a viscous fluid filled with randomly distributed hard spherical particles. The present method is based on the assumption that the relative shift of the velocity field of immersed hard particles from the host fluid is responsible for dynamic behavior of the suspension, and its role can be formulated by substituting the inertia term of governing equations by the acceleration field of the mass centre of the representative unit cell. Compared to existing models based on rather complicated mathematical formulation and numerical calculations, the present model enjoys conceptual and mathematical simplicity and the generality. Explicit formulas are derived for the attenuation coefficient and effective phase velocity of plane compression waves and shear waves. The efficiency and accuracy of the model are demonstrated by quantitatively good agreement between the predicted results and known data for a wide range of material and geometrical parameters. The proposed model could offer a relatively simple general method and easy-to-use explicit formulas to study acoustic wave propagation in hard particle-viscous fluid suspensions.