  The dispersion processes of aqueous samples of clay are studied using
ultrasound attenuation spectroscopy. The attenuation spectra that are acquired
in the frequency range $10-100$ MHz are used to determine the particle size
distributions (PSDs) for different concentrations and ages of the clay
suspensions. Our analysis, using equivalent spherical diameter (ESD) for
circular discs under Stokes drag in samples of concentrations greater than
1.5\% w/v, shows that a substantial fraction of the aggregates in suspension
are actually tactoids that are composed of more than one platelet. This is in
contrast to the general belief that clay disperses into individual platelets in
the concentration range where their suspensions exhibit glassy behavior. We
conclude that the incomplete fragmentation of the clay tactoids arises from the
rapid enhancement of the inter-tactoid Coulombic repulsion.
