Acoustic Spectroscopy for Concentrated Polydisperse Colloids with High Density Contrast
The acoustic attenuation spectra for rutile dispersions show a pronounced nonlinear increase in attenuation over a volume fraction range from 1% to 42%. A theory is developed to explain this nonlinear effect. This theory takes into account hydrodynamic particle−particle interactions caused by a sound wave. The modification of the acoustic theory has been accomplished using a “cell model” and a “coupled phase theory”. The notion of a “cell” allows us to take into account the hydrodynamic interaction between particles when calculating a drag coefficient. Furthermore, the mass conservation law helps to expand this “cell” concept to include the effects of polydispersity, introducing only one more adjustable parameter. This parameter determines the relationship between the cell and the particle radii. The “coupled phase theory”, generalized here for a polydisperse structured system, relates this drag coefficient to both the attenuation and sound speed spectra. Experimental verification of the modified theory is presented. The rutile samples were well dispersed. The measured attenuation agrees quite well with the attenuation predicted by the new theory for the volume fraction up to 30%. However, in the most highly concentrated slurries it was necessary to postulate some degree of aggregation in order to reconcile the measured and predicted spectra. The modified theory provides a means to calculate reasonable bimodal particle size distributions in these cases.