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

Abstract

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 < 10 0 (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, . Decoupling of the combined backscattering-transducer constant, allowing explicit measurement of the backscattering constant, ks, was achieved through calibration of the transducer constant, kt. 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, , to be determined for all species. While f and 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 withagglomeration. There was some additional variation in , 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.

Concentration profiling of a horizontal sedimentation tank utilising a bespoke acoustic backscatter array and CFD simulations

“…Here, G = ln(ΨrVrms), where 'Vrms' is the root mean square of the return pulse echo voltage at a particular distance 'r' from the transducer and 'Ψ' is the nearfield correction factor, which is estimated using a correlation dependent on transducer face width, distance and frequency, and becomes unity in the acoustic far field (Downing et al, 1995). The G-function relationship should give a linear gradient versus distance (as long as particle concentrations within the 0.05 -0.25 m segment are relatively constant) where dG/dr (taken from the average gradient) can then be linearly correlated to concentration (Bux et al, 2017;Bux et al, 2019;Rice et al, 2014). Additionally, the backscatter power was measured by integrating the returned backscatter voltage strength over the same profile distance (0.05 -0.25 m).…”

“…It is expected that the foremost reason for the difference in performance was due to the low concentration of particles in the system. The dG/dr gradient is essentially a linearised measure of the acoustic signal decay (Bux et al, 2019). Therefore, it would become more accurate at higher concentrations which increasingly attenuate the signal (normally, > 5 g/l (Bux et al, 2017;Bux et al, 2019;Rice et al, 2014)).…”

“…The dG/dr gradient is essentially a linearised measure of the acoustic signal decay (Bux et al, 2019). Therefore, it would become more accurate at higher concentrations which increasingly attenuate the signal (normally, > 5 g/l (Bux et al, 2017;Bux et al, 2019;Rice et al, 2014)). On the other hand, direct dependency between backscatter strength or power and concentration is only true for relatively dilute dispersions, below regions where significant inter-particle scattering acts to alter the attenuation response (particle levels < ~10 g/l (Hunter et al, 2012a;Simmons et al, 2017)).…”

“…The physical relevance of the dG/dr values from the G-function method are briefly noted. It would be expected that values would tend towards small non-zero negatives (associated with the attenuation of water) at low concentrations (Bux et al, 2019;Thorne and Buckingham, 2004).…”

An ultra-compact particle size analyser using a CMOS image sensor and machine learning

“…While the above-mentioned techniques are best suited for measuring particles typically in the submicron region, particle size analysers (PSAs) based on static light scattering or laser diffraction (LD) 7,8 have become the most popular and widely used instruments for measuring particles from hundreds of nanometres to several millimetres. Similar scattering theory is also utilised in systems based on non-electromagnetic wave propagation, such as ultrasonic analysers 9,10 . In LD PSAs, a laser beam is used to irradiate a dilute suspension of particles.…”