Application of ultrasound spectroscopy for nanoparticle sizing in high concentration suspensions: A factor analysis on the effects of concentration and frequency

Population balance modelling for high concentration nanoparticle sizing with ultrasound spectroscopy

“…The method to determine the critical concentration value has been described [11] using a principle component analysis based factor analysis technique to reduce the multivariate attenuation data to a single-variate data. The critical value is the root of the linearly fitted equation of the points of the single-variate data versus concentrations.…”

“…As has been claimed [11] that for silica suspensions, the value of the critical volume concentration below which a linear relationship exists between attenuation and concentration is 0.057. This means that the PSDs from the Malvern Ultrasizer measurements for silica suspensions with particle volume concentration less than 0.057 should be regarded as the true PSD.…”

“…As the ECAH theory does not account for the attenuation contributed from the interactions of particles, the calculated PSD for high concentration solid suspensions would shift to a smaller size region compared to the correct PSD if only the concentration is considered [7]. However, for emulsions, because compared to the compressibility of the droplet particles, the interaction between particles is insignificant, nonlinearity of attenuation on concentration was not found [11], this theory can still apply; and, it was also reported that good results up to 30% [12][13][14][15] even 40% [11] volume concentration could still be obtained.…”

“…By carrying out a factor analysis for these ultrasound spectra [11], which compresses the multiple frequency variables into one single factor to cover over 95% variance, the transformed attenuation -score on this factor (F score) versus concentration is plotted in Fig. 4.…”

Advances in Nanoparticle Sizing in Suspensions: Dynamic Light Scattering and Ultrasonic Attenuation Spectroscopy

“…A silicon nanoparticle (70-100 μm in diameter) suspension with initial volume concentration of 24 % was diluted to prepare a series of samples with eight different concentrations as low as 0.8 vol %, thus the measurement of particle size distribution was implemented at different concentrations, and analysis was highlighted on nonlinear effects of the concentration on the final results. Furthermore, a modification (Liu L., 2009) was presented that in ultrasound particle sizing, factor analysis as a method of dealing with multivariate data can be applied to ultrasound spectra to extract the information of linear dependence of attenuation on concentration and the contribution of frequency to attenuation. On the basis of this work a closed-loop control system was further built to measure and control process parameters (Boonkhao B. and Wang X.Z., 2012).…”