Advances in ultrasonic monitoring of oil-in-water emulsions

A modification to the multiple scattering model used to interpret ultrasonic measurements for emulsions is investigated. The new model is based on a development by Luppé, Conoir, and Norris (2012) which accounts for the effects of multiple mode conversions between thermal, shear and compressional modes. The model is here applied to the case of oil in water emulsions in which thermal effects are dominant. The additional contributions are expressed in terms of the scattering coefficients for conversion between compressional and thermal modes and vice versa. These terms are due to the effect of thermal waves produced at one particle being reconverted into the compressional mode at neighboring particles. The effects are demonstrated by numerical simulations for a sunflower oil in water emulsion which show that the additional terms are significant at low frequency and high concentrations. Comparison is also made with experimental data for a hexadecane in water emulsion. Although qualitative agreement is demonstrated, there are some quantitative differences, which are attributed to uncertainties in the physical properties, in the experimental data, or in the assumptions made in the model. © 2013 Elsevier Ltd. All rights reserved

Thermo-elastic multiple scattering in random dispersions of spherical scatterers

Ultrasonic monitoring of concentrated suspensions and emulsions is limited in concentration range due to the inaccuracy of the multiple scattering models currently used to interpret measurements. This paper presents the development of a model for the additional multiple scattering caused by mode conversion to/from thermal waves. These effects are believed to cause significant deviation from established models for emulsions at high concentration, or small particle size, at low frequency. The relevant additional scattering coefficients (transition factors) are developed, in numerical and analytical form, together with the modification to the effective wavenumber. Calculations have been carried out for a bromohexadecane-in-water emulsion to demonstrate the frequency-dependence of the scattering coefficients, and the effective speed and attenuation

Acoustic scattering in dispersions: improvements in the calculation of single particle scattering coefficients

Measurements of ultrasound speed and attenuation can be related to the properties of dispersed systems by applying a scattering model. Rayleigh’s method for scattering of sound by a spherical object, and its subsequent developments to include viscous, thermal, and other effects (known as the ECAH model) has been widely adopted. The ECAH method has difficulties, including numerical ill-conditioning, calculation of Bessel functions at large arguments, and inclusion of thermal effects in all cases. The present work develops techniques for improving the ECAH calculations to allow its use in instrumentation. It is shown that thermal terms can be neglected in some boundary equations up to ∼ 100 GHz in water, and several simplified solutions result. An analytical solution for the zero-order coefficient is presented, with separate nonthermal and thermal parts, allowing estimation of the thermal contribution. Higher orders have been simplified by estimating the small shear contribution as the inertial limit is approached. The condition of the matrix solutions have been greatly improved by these techniques and by including appropriate scaling factors. A method is presented for calculating the required Bessel functions when the argument is large (high frequency or large particle size). The required number of partial wave orders is also considered

Simulation of incoherent and coherent backscattered wave fields from cavities in a solid matrix

This paper reports a study of the backscattered ultrasonic signal from a solid layer containing spherical cavities, to determine the conditions in which an effective medium model is a valid description of the response. The work is motivated by the need to model the response of porous composite materials for ultrasonic non-destructive evaluation (NDE) techniques. The numerical simulation predicts the response of a layer containing cavities at a single set of random locations, and compares it to the predicted response from a homogeneous layer with ensemble-averaged material properties (effective medium model). The study investigates the conditions in which the coherent (ensembleaveraged) response is obtained even from a single configuration of scatterers. Simulations are carried out for a range of cavity sizes and volume fractions. The deviation of the response from effective medium behavior is modeled, along with the trends as a function of cavity radius, volume fraction, and frequency, in order to establish an acceptability criterion for application of an effective medium model

Shear wave reconversion in nano-fluids and the possible detection of impurities and contamination [Abstract]

Shear wave reconversion in nano-fluids and the possible detection of impurities and contamination [Abstract

Ultrasonic wave propagation in concentrated slurries - the modelling problem

The suspended particle size distribution in slurries can, in principle, be estimated from measured ultrasonic wave attenuation across a frequency band in the 10s of MHz range. The procedure requires a computational model of wave propagation which incorporates scattering phenomena. These models fail at high particle concentrations due to hydrodynamic effects which they do not incorporate. This work seeks an effective viscosity and density for the medium surrounding the particles, which would enable the scattering model predictions to match experimental data for high solids loading. It is found that the required viscosity model has unphysical characteristics leading to the conclusion that a simple effective medium modification to the ECAH/LB is not possible. The paper confirms the successful results which can be obtained using core-shell scattering models, for smaller particles than had previously been studied, and outlines modifications to these which would permit rapid computation of sufficient stability to support fast particle sizing procedures

Emergence of the coherent reflected field for a single realisation of spherical scatterer locations in a solid matrix

The acoustic field reflected from a region containing spherical scatterers is most often estimated by use of the coherent field; that is, the field resulting from the summed scattered fields from the scatterers, averaged over all possible configurations of scatterer locations. It is this ensemble-averaged coherent field which is equivalent to the field reflected from a homogeneous medium with properties which can be derived mathematically using ensemble-averaging techniques. Such properties include the effective density, and the effective wavenumber, which can be derived from multiple scattering theories, or by other homogenisation methods. Experimentally, although ensemble-averaging can be effected in practice in fluid systems due to the motion of the scatterers during the measurement time-scale, measurements in solid materials have fixed locations of scatterers. Averaging can only be achieved by using "large" sample areas, multiple samples or measurements in different locations, or "large" receiver areas. However, in the context of NDE applications we are interested in the field resulting from a specific region of material, rather than the average over a large region. Our study addresses the question of when the coherent field (resulting from averaging over many scatterer configurations) can be used as an accurate description of the field reflected by a region of scatterers at fixed locations. In this paper we present results of simulations of the scattered reflected field from a region of solid material containing spherical cavities. Simulations of single realisations of scatterer locations are compared with the coherent field, to demonstrate the validity or otherwise of the use of the coherent field to describe the response of a particular configuration of scatterers. © Published under licence by IOP Publishing Ltd

Ultrasound propagation in concentrated random dispersions of spherical particles: thermal- and shear-mediated contributions to multiple scattering

Ultrasound propagation in concentrated random dispersions of spherical particles: thermal- and shear-mediated contributions to multiple scatterin

Multiple scattering in random dispersions of spherical scatterers: effects of shear-acoustic interactions

The propagation of acoustic waves through a suspension of spherical particles in a viscous liquid is investigated, through application of a multiple scattering model. The model is based on the multiple scattering formulation of Luppé, Conoir and Norris (J. Acoust. Soc. Am. 2012, 131, 1113) which incorporated the effects of thermal and shear wave modes on propagation of the acoustic wave mode. Here, the model is simplified for the case of solid particles in a liquid, in which shear waves make a significant contribution to the effective properties. The relevant scattering coefficients and effective wavenumber are derived in analytical form. The results of calculations are presented for a system of silica particles in water, illustrating the dependence of the scattering coefficients, effective wavenumber, speed, attenuation on particle size and frequency. The results demonstrate what has already been shown experimentally; that the shear-mediated processes have a very significant effect on the effective attenuation of acoustic waves, especially as the concentration of particles increases

A perturbation approach to acoustic scattering in dispersions

Ultrasound spectroscopy has many applications in characterizing dispersions, emulsions, gels, and biomolecules. Interpreting measurements of sound speed and attenuation relies on a theoretical understanding of the relationship between system properties and their effect on sound waves. At its basis is the scattering of a sound wave by a single particle in a suspending medium. The problem has a well-established solution derived by expressing incident and scattered fields in terms of Rayleigh expansions. However, the solution is badly conditioned numerically. By definition, in the long-wavelength limit, the wavelength is much larger than the particle radius, and the scattered fields can then be expressed as perturbation series in the parameter Ka (wave number multiplied by particle radius), which is small in this limit. In addition, spherical Bessel and Hankel functions are avoided by using alternative series expansions. In a previous development of this perturbation method, thermal effects had been considered but viscous effects were excluded for simplicity. Here, viscous effects, giving rise to scattered shear waves, are included in the formulation. Accurate numerical correspondence is demonstrated with the established Rayleigh series method for an emulsion. This solution offers a practical computational approach to scattering which can be embodied in acoustic instrumentatio