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

The torsional waveguide viscosity probe: Design and anomalous behavior

This paper is concerned with the design of viscosity sensors based on a torsional waveguide. The advantages of using guided wave attenuation instead of speed for viscosity estimation are established. The effects of probe material, dimensions and operating frequency on viscosity measurement are discussed in the context of a requirement to match the measured attenuation to the range of viscosity values that are required to be measured, given the constraints on measurability imposed by the overall signal and noise conditions. A prototype probe is shown to work well with Newtonian liquids but to appreciably underestimate the viscosities of polymeric oils; these anomalies are explained quantitatively on the basis of a model of intramolecular relaxation. The probe was unsuccessful when applied to slurries, and a basic explanation is given

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

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-mediated contributions to the effective properties of soft acoustic metamaterials including negative index

Shear-mediated contributions to the effective properties of soft acoustic metamaterials including negative inde

The absorption of ultrasound in emulsions: computational modelling of thermal effects

Around liquid particles in a fluid of contrasting properties (for example, oil in water) in ultrasonic fields there are small regions where thermal waves can propagate with relatively high amplitudes. Herein, we demonstrate the existence and character of these waveforms using three-dimensional finite element modelling based on linearised Navier-Stokes equations. We investigate single particles and small clusters of particles, validating the expected thermal wavelength and the power dissipation due to viscous and thermal effects around the particle. The energy lost due to thermal and viscous dissipation is explored as a function of the average separation distance between the particles (linking to concentration) as well as the applied frequency. The determination of energy loss provides a new method for calculating the attenuation in particle systems. We demonstrate that the effective attenuation of an emulsion in which particles exist in clusters is influenced by the interparticle separation within the cluster, even at the same total particle concentration. Thus, the finite element modelling provides evidence for thermal interactions and their effect in correlated particle systems

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