Uncertainties in ultrasonic particle sizing in solid-in-liquid suspensions

Abstract

Abstract-Measurements of the frequency dependence of ultrasonic attenuation can be used as the basis for the estimation of particle size distributions (PSDs) in solid-in-liquid suspensions. The method requires matching the attenuation simulated by a candidate PSD in combination with a wave propagation model to the measured function in a fitting procedure. Uncertainty in the type of candidate PSD, whether based on fractional volume or fractional number of the dispersed particles, can cause errors in the overall estimation process, particularly for the median particle size. These uncertainties are investigated in the first part of this paper. The second part deals with uncertainties associated with the values for the physical properties of the suspended particles, seven of which are required in the simulation stage. It is shown that the particle sizing exercise is relatively insensitive to all of the physical properties except density, for which values are necessary to an accuracy commensurable with that required for the two principal parameters associated with the PSD-median size and standard deviation. The discussion is limited to small (less than 1-μm) silica particles dispersed in water. The results will have more general application.

Ultrasonic particle sizing in aqueous suspensions of solid particles of unknown density

“…Whilst for many materials these data are available from standard handbooks, 6,7 there remain many materials for which such data are either not known or are too costly or too dangerous to measure. In a recent publication, 8 we have challenged the assumption that all of the 14 inputs to the ECAH model are required to be known accurately; we demonstrated that the wave attenuation is relatively insensitive to all of the physical constants except the density of both phases, although it is that of the solid phase which is generally unknown. There is also uncertainty as to what is the effective viscosity of the continuous phase surrounding the particles due to interactions between mode-converted evanescent shear waves scattered from suspended particles in proximity.…”

“…We have investigated the effect of uncertainty in parameter values for silica suspensions in Ref. 8 and here we repeat the exercise for Versamag. The ultrasonic attenuation at 10 MHz in a 6.54% v/v aqueous suspension of Versamag was simulated using the extended ECAH model and the physical properties given in Table I.…”

Particle size distribution measurements of widely distributed carbonyl iron powder particles in concentrated suspensions using ultrasonic attenuation

“…The ultrasonic attenuation technology obtains PSD based on the volume, which should be converted into a number-based one first and compared with PPSD from microscopic images. For a lognormal PSD, the conversion is much simpler, as it just moves the volume-based curve to the left as follows: lnd 50,0 = lnd 50,3 − 3(lnσ) 2 where d 50,3 and d 50,0 are the volume-based and number-based median diameters, respectively [21].…”

Longitudinal and transverse coherent waves in media containing randomly distributed spheres

“…[31]. Applications of effective theories in such random media may range from ultrasonic characterization of suspensions [39] to metamaterials design [40], even for aqueous suspensions, where the shear waves in an even slightly viscous fluid can be of noticeable influence in attenuation measurements for example [41]. This paper is organized as follows: Section 2 deals with the description of the host medium that contains a random distribution of spheres.…”