Attenuation of sound in highly concentrated suspensions and emulsions

Abstract

The absorption of sound in emulsions and suspensions is due to viscous and thermal transport processes occurring at the interface of the nonhomogeneities, as well as to the intrinsic absorption in the materials comprising the system. For highly concentrated mixtures, multiple scattering is shown to play an important role. Following the arguments of Waterman and Truell [J. Math. Phys. 2, 512 (1961)], the behavior of the scattering medium may be specified explicitly in terms of the number of scatterers per unit volume, and the farfield amplitude f(O) obtained for a single scatterer. The coefficients of frO) for a single scatterer have been calculated by Allegra and Hawley [J. Acoust. Soc. Am. 51, 1545 (1972)] for systems of solid and fluid particles suspended in a fluid media. PACS numbers: 43.35.Bf, 43.85.Dj, 43.20. Hq LIST OF SYMBOLS A ae, as, at Cv, C• c c! f P P.(cosO), Pn=(cosO) R t T shear-wave potential radius of particle times the wave number of the compressional, shear, and thermal waves, respectively specific heats speed of sound for longitudinal compressional wave speed of sound for spherical compressional wave in elastic isotopic solid frequency of sound wave farfield amplitudes spherical vessel functions wavenumbers of compressional, shear, and thermal wave pressure viscous stress tensor Legendre polynomials, associated Legendre polynomials radial coordinate radius of suspended particle time temperature specific internal energy v e Ol L y =C,/Cv P (• = kp/Cp velocity of volume element real part of a s attenuation coefficient attenuation in pure liquid thermal dilatation ratio of specific heats kronecker symbol volume fraction of particulate material equal to concentration coefficient of shear rigidity polar angie thermal conductivity, complex wave propagation constant coefficient of shear viscosity kinematic viscosity density thermal diffusivity •b0, •bo •bt, •bs, •b, incident, compressional, thermal, shear, and reflected wave potentials •bE, ½s exciting and scattered wave function

On multiple-particle effects in the acoustic characterization of colloidal dispersions

“…Nevertheless, note that multiple-particle effects have also been observed in this kind of system [44]. On the other hand, Davis [45,46] and Sayers [47] analysed dispersions of much larger particle sizes than those considered here. As indicated by Kytömaa [5], this favours the lossless redirection of acoustic waves as described by the above mentioned multiple scattering theories, which in this case becomes the dominating mechanism of sound attenuation.…”

“…However, the models of both Waterman and Truell and Lloyd and Berry have been used successfully in other contexts to interpret acoustic attenuation [14,15,31,[45][46][47]. These results may be understood by looking at the dominating attenuation mechanisms.…”

Viscous attenuation of acoustic waves in suspensions

“…This leads to an attenuation coefficient which is linear in solid concentration, but examination of attenuation data for suspensions shows that this linearity is at best true only for very dilute concentrations of particles. In contrast, Davis (1979) showed that a theory including multiple scattering resulted in an attenuation coefficient with a second order correction term.…”

Broad-band Ultrasonic Spectrometry of CiEj/Water Mixtures. Precritical Behavior

“…These empirical functions also enable some conclusions on underlying molecular mechanisms. , We nevertheless additionally applied relaxation functions which are based on physical models of the liquid structure and microdynamics of the mixtures. Among the functions considered has been a sum of k Debye terms ( k = 1, 2, ...) representing chemical relaxations, expressions that reflect dissipation of sound energy at internal interfaces of microheterogeneous samples, − and particularly relations that result from the assumption of concentration fluctuations in binary mixtures − including a jump- diffusion model. , We found the smallest values in the variance χ 2 , combined with a self-consistent dependence of the parameter values ξ 1 , ..., ξ P on the mixture composition, if the model spectral function was used. The second term on the right-hand side of this equation represents the Romanov-Solov'ev relaxation of sound attenuation by noncritical, noncorrelated fluctuations in the mixture concentration. ,, Again, A RS denotes an amplitude, is a diffusion time, and I is a scaling function which can be written in an explicite form: …”