Experimental validation of acoustic inversions for high concentration profiling of spherical particles, using broadband technology in the Rayleigh regime

In this study, an acoustic backscatter system was used with single broadband transducers utilising narrowband excitation at multiple frequencies of 2.00, 2.25 and 2.50 MHz, to determine the scattering properties of three sizes of glass particles (40, 78 and 212 µm) in liquid suspensions. A calibration procedure was developed to initially measure the transducer constants, and form function and scattering cross-section values were calculated experimentally. Determined values aligned well with theoretical predictions, where viscous absorption was found to be important for the smallest glass particle size. A logarithmic translation of the signal attenuation gave a linear response, with respect to concentration, up to a maximum measured concentration of 125 gl−1 for the two smallest glass species. However, attenuation data for the largest species were only linear up to ~ 40 gl−1, attributed to significant multiple particle scattering causing an increase in the noise floor. Additionally, a procedure was developed to fit measured attenuation data to a nearfield correction factor correlation, improving measurements in restricted geometries and highly attenuating suspensions. Concentration profiles were produced using both single and dual frequency inversion methods and were found to be accurate up to ~ 25–40 gl−1, after which multiple scattering effects caused errors in the measured backscatter, and instability in the inverted profiles. Additional scatter observed in the dual frequency inversions was modelled in terms of the ratio between the attenuation coefficients at each frequency and compared to the experimental error. A ratio < 0.6 between the attenuation coefficients is suggested to sufficiently minimise errors in the dual frequency inversion.