Acoustic spectroscopy is successful, first of all, in dilute systems. Acoustic theory for the dilute dispersed system does not take into account particle-particle interaction. Dispersed particles oscillating in the acoustic pressure field generate several waves: long scale compression wave and short scale shear and temperature waves. These waves could interfere with other particles motion which could be effectively described as particle-particle interaction.

The particle-particle interaction through the long scale compression waves is a part of the scattering mechanism of the sound attenuation in the concentrated system. The multiple scattering treatment is the most suitable to describe this effect. There is quite elaborated theory of the multiple scattering reviewed by the Harker and Temple Acoustic Bibliography[7]. This aspect of the concentration effects in the acoustic spectroscopy is less important for the colloid science because scattering losses exhibit itself for large particles and high frequencies.

The particle-particle hydrodynamic interaction through the shear waves is much more important for the colloid science. It affects the viscous losses mechanism which is dominant in the dispersions of the small particles. Particle-particle interaction causes the shift of the acoustic spectra to the higher frequencies. This shift can be very significant. For instance, our dilution experiment with the rutile dispersion shows the shift of the characteristic frequency from the 15 Mhz for 4%wt to above 100 Mhz for 74.6%wt. The theory of the sound propagation must take into account this effect. Otherwise the error of the particle size calculation can be enormous.

There were several attempts to adjust the viscous losses theory for the concentrated system . The last one Acoustic Bibliography [ 1 ] combines together the achievements of the previous works. It explores the "coupled phase approach" generalizing it for the polydisperse system. The "cell model" provides expression for the particle drag following Pendse and Strout. At the same time "cell model" concept has been generalized for the polydisperse system as well.

The new theory of the viscous losses has been successfully tested experimentally with the concentrated rutile dispersion. Particle size distribution for this rutile was known. It was lognormal distribution with a median size 0.33 micron and standard deviation 0.2.. Figure 3 and Figure 4 show measured attenuation spectra and also attenuation spectra calculated for the known particle size distribution. It is seen that there is good agreement between theory and experiment for the volume fraction up to 30%. In order to reconcile theory and experiment above 30%vl we should assume aggregation of the particles as it is shown in the work.

The new theory of the viscous losses does not use superposition assumption. It means that theory could be applied for characterization systems with bimodal particle size distribution. In order to test this capability of acoustic spectroscopy we measured mixture of two aluminas with known particle sizes reported by manufacturer: Sumitomo Chemical America. We chose alumina AKP-30 with median size 0.36 micron and alumina AA-2 with median particle size 2 micron. Volume fraction for individual samples and their 50:50 mixture was the same 10%. Experimental and theoretical attenuation spectra are shown on Figure 5. It is seen that there is good agreement between theory and experiment.

Generalization of the thermal losses theory by taking into account particles thermodynamically interaction is even more challenging. Fortunately, it turned out that thermal losses is much less sensitive to particle-particle interaction than viscous ones. Dilution experiment performed in the work Acoustic Bibliography [ 2 ] proved that the contribution of the thermodynamic particle-particle to the thermal losses mechanism is insignificant for the volume fractions up to 30%vl. This experiment has been done with neoprene latex with known particle size distribution: median size is 0.16 micron, standard deviation is 0.24. Experimental and theoretical attenuation spectra are shown on Figure 6. It is seen that experiment and dilute case theory agrees quite well for volume fraction up to 30%. This peculiarity explains the success of the acoustic spectroscopy based on the dilute case theory with emulsions and latices.

We believe that thermodynamic particle-particle interaction is not important because thickness of the thermodynamic layer is much smaller than thickness of hydrodynamic layer. As a result thermodynamic layers overlap at the much higher volume fraction that hydrodynamic ones.