Ultrasound techniques for characterizing colloidal dispersions

Abstract

Interest in the interaction of acoustic waves with particulate mixtures has a long historydating back to the work of Rayleigh in the 19th century. This interest has intensified over the last fifteen years as advances in electronics and instrumentation science have brought the possibility of using ultrasound to characterize colloidal mixtures both in the laboratory and in-process, and in both of these contexts a small number of instruments are currently in use. The characterization of colloidal mixtures by ultrasound requires a formal theoretical basis which relates the properties of the mixture, particularly the dispersed phase particle size distribution (PSD), to the complex wavenumber governing propagation. The number of theoretical treatments is vast, having evolved over more than a century. This paper is intended to provide a review of these developments in a form which will enable new researchers in the field to climb a very steep learning curve in a relatively short time. We discuss definitions and production techniques for colloidal mixtures and the basic physical phenomena underlying wave propagation through them. We identify two approaches to the propagation problemscattering and coupled-phase; these are treated both separately and comparatively, particularly in relation to limitations that arise when the concentration of particles is high and the basic theories break down. We introduce the basic method for the measurement of PSD and show how dynamic effects such as flocculation and crystallization can be observed and modelled. The core of all ultrasonic characterization procedures is the physical measurement of the ultrasonic wave attenuation coefficient and phase velocity as functions of frequency; here we discuss these techniques on the basis that what is observable or measurable about a colloid depends on both its physical properties and the frequency bandwidth available for measurement. This paper concludes with our view on future developments of measurement technique and theoretical treatments.

Ultrasonic wave propagation in concentrated slurries – The modelling problem

“…It has been comprehensively reviewed in Challis et al [1]. The isolated particle scattering model (the ECAH component [5]- [6]) describes the scattered fields for each partial wave order produced by an incident compressional wave.…”

“…1 Hipp [9] also demonstrates the success of the ECAH/LB model for silica of diameters 300-400 nm at 100MHz, up to concentrations of 15%v/v (a volume fraction of 0.15). An example is shown in Figure 3for 400nm diameter silica at 100 MHz, this time plotted as a function of volume fraction, using Hipp's experimental data [9, Figure 7].…”

“…The storage life and fitness for purpose of these materials depend strongly on the sizes of the particles in the mixture, expressed as the particle size distribution (PSD) and, because of this, there is a continuing requirement to measure PSD both in the laboratory and on a process line. The principal methods available for characterisation of colloids have been summarised by Challis et al [1]. Optical methods most commonly used are based on static, diffusing wave, evanescent wave and dynamic light scattering.…”

“…This implies that model convergence would be difficult to obtain if the candidate PSDs were specified by more than two parameters (see Scott et al [2,3]). Current practice is to specify a log-normal distribution in particle volume fraction or number density versus particle radius; this is parameterised by a median particle size and a distribution width expressed as a standard deviation in log-space, see [1]. Over many decades a large number of attempts have been made to model acoustic wave propagation in particulate mixtures, comprehensively reviewed in [1], and more recently in relation to particle sizing in [4].…”

“…Current practice is to specify a log-normal distribution in particle volume fraction or number density versus particle radius; this is parameterised by a median particle size and a distribution width expressed as a standard deviation in log-space, see [1]. Over many decades a large number of attempts have been made to model acoustic wave propagation in particulate mixtures, comprehensively reviewed in [1], and more recently in relation to particle sizing in [4]. Currently, the model of choice is based on the early work of Epstein and Carhart [5] and Allegra and Hawley [6],together with the multiple scattering model of Lloyd and Berry [7], hereafter referred to as ECAH/LB.…”