Measurement and density normalisation of acoustic attenuation and backscattering constants of arbitrary suspensions within the Rayleigh scattering regime

The scattering and attenuation of megahertz frequency acoustic backscatter in liquid suspensions, is examined for a range of fine organic and inorganic particles in the Rayleigh regime, 10⁻⁴ < ka < 10⁰ (where k is the wavenumber and a the particle radius) which are widely industrially relevant, but with limited existing data. In particular, colloidal latex, mineral titania and barytes sediments, as well as larger glass powders were investigated. A manipulation of the backscatter voltage equation was used to directly measure the sediment attenuation constants, ξ. Decoupling of the combined backscattering-transducer constant, allowing explicit measurement of the backscattering constant, k_s, was achieved through calibration of the transducer constant, k_t. Additionally, the methodology was streamlined via averaging between a number of intermediate concentrations to reduce data variability. This approach enabled the form function, f, and the corresponding total normalized scattering cross-sections, χ to be determined for all species. While f and χ are available in the literature for large glass and sand, this methodology allowed extension for the colloidal organic and inorganic particles. Specific gravity normalisation of f collapsed all data onto a single distribution, with the exception of titania, due to scattering complexities associated with agglomeration. There was some additional variation in χ with measured values of the fine particles up to of magnitude greater than the density-normalised prediction at low ka. Mechanisms accounting for these variations from theory are however analysed, and include viscous attenuation effects, the polydispersity of the particle type and increasing influence of the solvent attenuation. Additionally, thermoacoustic losses appeared to dominate the attenuation behaviour of the organic latex particles. This study demonstrates that particles close to the colloidal regime can be measured successfully with acoustic backscatter, and highlights the great potential of this technique to be applied for in situ or online monitoring purposes in such systems.