Sound Propagation in Gross Mixtures

Abstract

For low acoustic frequencies, a mixture (a porous medium or a suspension) is shown to have an effective density which differs slightly from the density given by Archimedes' principle. This effective density is computed from a physically elementary consideration of viscous, incompressible fluid flow. For higher frequencies, pore or particle size in the mixture becomes comparable with the wavelength of shear waves in the fluid, while still small compared with dilatational wavelength. The theory is extended to such frequencies through the known formula for the fluid's resistance to the oscillations of a rigid sphere. In both cases, the effective compressibility of the mixture is taken to be the volume-average of the component compressibilities. From the effective density and compressibility, the acoustic properties of the mixture are predicted. Predictions are compared with previous theories and with experimental results.

Sound attenuation by small spheroidal particles due to visco-inertial coupling

“…The sound propagation in such a suspension can be adequately modeled by so-called coupled phase models, which have been extensively described. 5,[22][23][24] The idea behind this theoretical approach is that the suspension can be regarded as two separate phases ͑particles and fluid͒, which are coupled by momentum transfer. Exerting a sound field to such a system means that the equations of state, continuity, and momentum conservation can be fulfilled simultaneously only for the characteristic wave number of the suspension.…”

Viscous attenuation of acoustic waves in suspensions

“…The application of the Stokes flow drag force to suspension dissipation is not new (for example, Urick, 1948;Ahuja, 1973) and it has also been applied in terms of the permeability concept (Ament, 1953). These previous applications have all attempted to account for the presence of multiple spheres simply by multiplying /1 by the number of spheres per unit volume, n. Some analytic approximations for the effects of the presence of more than one sphere exist.…”

“…Urick (1947) attempted to estimate the acoustic phase velocity of suspensions of kaolinite by calculating effective bulk density and compressibility, and later (Urick, 1948) derived an attenuation coefficient equivalent to that predicted by zero and first-order scattering theory by looking at the Stokes drag force on a sphere. Ament (1953) estimated an effective density parameter for a suspension based on balancing the forces acting on solid and fluid components of a filter undergoing oscillatory motion. This was applied to suspensions by computing a filter permeability for the medium using Stokes drag force on spherical particles, and a linear approximation to attenuation was developed.…”

Online measurement of particle size distribution during crystallization using ultrasonic spectroscopy

“…5. Literature shows that acoustic velocity increases with increase in particles concentration and decreases with increase in particle size (Ament, 1953;Alizadeh-Khaivi, 2002). Furthermore, the rate of increase in acoustic velocity with concentration also decreases with increase in particle size (Stolojanu and Prakash, 2001).…”