Estimates of particle size distributions (PSDs) in solid-in-liquid suspensions can be made on the basis of measurements of ultrasonic wave attenuation combined with a mathematical propagation model, which typically requires seven physical parameters to describe each phase of the mixture. The estimation process is insensitive to all of these except the density of the solid particles, which may not be known or difficult to measure. This paper proposes that an unknown density value is incorporated into the sizing computation as a free variable. It is shown that this leads to an accurate estimate of PSD, as well as the unknown density.

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.

Estimates of particle size distributions (PSDs) in solid-in-liquid suspensions can be obtained from measurements of ultrasonic wave attenuation. The technique is based on adaptively fitting theoretical wave propagation models to the measured data across a frequency range. These models break down at high solid concentrations and it is believed that this failure is due to the effective viscosity of the mixture in the vicinity of the particles being different from that of the continuous phase. This paper discusses PSD estimation when a number of different viscosity formulations are incorporated into the wave propagation model. The viscosity model due to Happel provides the best estimate of PSD in suspensions of medium concentration.

The suspended particle size distribution in slurries can, in principle, be estimated from measured ultrasonic wave attenuation across a frequency band in the 10 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. (C) 2014 Elsevier B.V. All rights reserved.

Ultrasonic transducer arrays are extensively used for the nondestructive evaluation of materials for aerospace and other applications. However, their use with composites requires some technique development because of reflections at the layer boundaries and the effects of attenuation. When used in full matrix capture mode, algorithms such as the total focusing method (TFM) must be applied to obtain the image. In composite materials, improvement to the algorithm is required to include the effects of material anisotropy (affecting wave speed) and optimum aperture limits to optimize the signal-to-noise ratio and location detection for a defect in the material. This paper presents simulations of the ultrasonic array signals in multilayer anisotropic materials with and without a simulated defect. A kernel model for plane wave propagation in the material is combined with an angular spectrum decomposition (for finite transducer elements) and transducer frequency response, to model the full array signals. Inclusion of the defect is through its far-field scattering response. The model facilitates the study of imaging algorithm development by identification of the effects of anisotropy, signal-to-noise ratio, and aperture limit. An analytical method for the calculation of the effective group velocity in the composite at low frequency is demonstrated, permitting rapid calculation of time delay laws in practice.

Ultrasonic arrays have seen increasing use for the characterisation of composite materials. In this paper, ultrasonic wave propagation in multilayer anisotropic materials has been modelled using plane wave and angular spectrum decomposition techniques. Different matrix techniques, such as the stiffness matrix method and the transfer matrix method, are used to calculate the reflection and transmission coefficients of ultrasonic plane waves in the considered media. Then, an angular decomposition technique is used to derive the bounded beams from finite-width ultrasonic array elements from the plane wave responses calculated earlier. This model is considered to be an analytical exact solution for the problem; hence the diffraction of waves in such composite materials can be calculated for different incident angles for a very wide range of frequencies. This model is validated against experimental measurements using the Full-Matrix Capture (FMC) of array data in both a homogeneous isotropic material, i.e. aluminium, and an inhomogeneous multilayer anisotropic material, i.e. a carbon fibre reinforced composite.

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 (ensemble-averaged) 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.

This paper reports a study of the backscattering behavior of a solid layer containing randomly spaced spherical cavities in the long wavelength limit. The motivation for the work arises from a need to model the responses of porous composite materials in ultrasonic NDE procedures. A comparison is made between models based on a summation over discrete scatterers, which show interesting emergent properties, and an integral formulation based on an ensemble average, and with a simple slab effective medium approximation. The similarities and differences between these three models are demonstrated. A simple quantitative criterion is established which sets the maximum frequency at which ensemble average or equivalent homogeneous medium models can represent echo signal generation in a porous layer for given interpore spacing, or equivalently, given pore size and concentration.

Industrial applications are increasingly turning to modern composite layered materials to satisfy strength requirements whilst reducing component weight. An important group of such materials are fibre/resin composites in which long fibres are laid down in layers in a resin matrix. Whilst delamination flaws, where layers separate from each other, are detectable using traditional ultrasonic techniques, the presence of porosity in any particular layer is harder to detect. The reflected signal from a layered material can already be modelled successfully by using the acoustic impedance of the layers and summing reflections from layer boundaries. However, it is not yet known how to incorporate porosity into such a model. The aim of the work reported here was to model the backscatter from randomly distributed spherical cavities within one layer, and to establish whether an effective medium, with a derived acoustic impedance, could reproduce the characteristics of that scattering. Since effective medium models are much more readily implemented in simulations of multi-layer structures than scattering per se, it was felt desirable to simplify the scattering response into an effective medium representation.

Bulk wave attenuation in epoxies has been found experimentally to be a linear function of frequency. Anecdotal evidence suggests that the formulations used for bulk wave attenuation to be input to computational propagation models, including models for guided waves, can take many forms: Either the simple linear relationship between attenuation and frequency can be input directly, or any of a number of analytic models could, in principle, be used – examples being the Maxwell, Kelvin-Voigt and Zener anelastic solid models, or the hysteretic damping model sometimes employed for studies of structural vibrations. This paper considers the physical bases of these various models, as well as multiple degree of freedom models that have their origins in dielectric theory. It is shown that a simple two degree of freedom adaptation of the Zener model provides a good simulation of experimentally observed data for both attenuation and phase speed over a wide frequency band.

Classical long wavelength approximate solutions to the scattering of acoustic waves by a spherical liquid particle suspended in a liquid (an emulsion) show small but significant differences from full solutions at very low k(c)a (typically k(c)a < 0.01) and above at k(c)a > 0.1, where k(c) is the compressional wavenumber and a the particle radius. These differences may be significant in the context of dispersed particle size estimates based on compression wave attenuation measurements. This paper gives an explanation of how these differences arise from approximations based on the significance of terms in the modulus of the complex zero-order partial wave coefficient, A(0). It is proposed that a more accurate approximation results from considering the terms in the real and imaginary parts of the coefficient, separately.

This paper is concerned with modeling ultrasonic wave propagation in epoxy materials to better understand NDE procedures and to provide reliable input to more complex models of guided wave propagation in layered structures. Different physical models are considered in the context of how well they simulate the (known) linear relationship between bulk wave attenuation coefficients and frequency. The identified models are then extended to simulate wave propagation in materials with mechanical properties, which vary gradually in the spatial dimension. This is achieved using electric circuit transmission line analogs to the viscoelastic mechanical system. Verifying experimental results are included.

Proportionality between the ultrasonic wave attenuation coefficient in epoxies and other polymers and frequency is a commonly observed but little understood phenomenon. How it is ultimately explained will depend on the breadth of the frequency range over which it is significant. This paper presents results of experiments to measure loss in a single epoxy material over 5 decades of frequency using 4 complementary techniques - dynamic mechanical analysis, microwave excited low-frequency resonances, a novel guidedwave technique based on a metal-epoxy-metal sandwich, and a conventional pulse mode ultrasonic spectrometer. The results are confined to bulk shear waves in the epoxy. They confirm the linear relationship between attenuation and frequency, and it is shown that the broadband behavior of the attenuation and shear wave phase velocity is consistent with the Kramers- Kronig relationships.

This paper is concerned with the design of magnetostrictive transducers for the excitation and detection of guided waves in metal pipes of small diameter (mm) and their application to the study of wave propagation in pipes filled with water or supercritical CO(2). Optimized system design is based on a simulation of the overall signal pathway which includes the electric circuit conditions at the transducers, mode excitability, and the wavenumber filtering effect of the spatial distribution of the exciting alternating magnetic field. A prototype system was built, and experimental observations on small diameter pipes indicated good agreement with expected results from simulations. The reassigned spectrogram has been used to compare expectation on the basis of guided wave dispersion curves for fluid-filled pipes with experimental data.

This paper proposes a novel architecture for a data acquisition system intended to support the next generation of ultrasonic imaging instruments operating at or above 100 MHz. Existing systems have relatively poor signal-to-noise ratios and are limited in terms of their maximum data sampling rate, both of which are improved by a combination of embedded averaging and embedded interleaved sampling. "On-the-fly" pipelined operation minimizes control overheads for signal averaging. A two-clock sampling timing system provides for effective sampling rates that are a factor of 20 or more above the basic sampling rate of the analog-to-digital converter (ADC). The system uses commercial field-programmable gate array devices operated at clock frequencies commensurable with the ADC clock. Implementation is via the Xilinx Xtreme digital signal processing development kit, available at low cost. Sample rates of up to 2160 MHz have been achieved in combination with up to 16384 coherent averages using the above-mentioned off-the-shelf hardware.

A cross-disciplinary experimental study related to both ultrasonic instrumentation and analytical chemistry is reported. The hydrolysis process was conducted by time-resolved titration in a fully automated manner. Acquired ultrasonic records were processed in order to estimate the propagation delay of the ultrasonic pulse in the evolving medium. The limited hardware resolution of two different ultrasonic instruments employed was improved by calculating the center of gravity of the recorded pulses. Application of signal averaging to the acquisition of raw records in the custom-built instrument eliminated spurious records almost completely. The estimated ultrasonic delays were corrected for temperature changes that were measured independently. This procedure transformed the ultrasonic titration curves into two almost straight lines that intersected at the equivalence point. The results obtained showed that it was possible to detect changes as small as 200 ppm by using the ultrasonic instrument in situ at significantly lower setting times compared to a conventional pH-meter.

Random interleaved sampling has become a widespread operating mode for digital storage oscilloscopes. Different repetitions of (notionally) the same waveform are recorded at random time shifts and are interleaved in memory, resulting in an increase of the equivalent sampling frequency. This procedure requires substantial time, particularly if further averaging is required. In this paper, an approach that ensures accurate time shifts is presented for repeated waveform measurements. Operating two independent oscillators with related frequencies forms the accurate shifts. One of these is used to excite a waveform of interest repeatedly, and the other clocks the analog-to-digital converter (ADC). This architecture was implemented using a commercial "off-the-shelf" field programmable gate array. Examples of experimental waveforms, which are sampled at 2160 MHz using an ADC that is clocked at 80 MHz, are presented. They are compared with the simulated and independently measured waveforms where appropriate.

Ultrasonic measurements of attenuation versus frequency were made on model systems comprising olive oil, sucrose, and tripalmitin to represent the constituents of chocolate. Corresponding measurements also were made on chocolate flowing in a pipeline at a pilot plant where the temperature, pressure, and temper of the chocolate were precisely controlled and monitored. Experimental results combined with simulation studies indicate that the effect of ultrasonic scattering from tripalmitin crystals in olive oil is modified by the addition of sucrose crystals at a high concentration. It is proposed that the presence of seed crystals in chocolate (temper) cannot be detected ultrasonically in the practical measurement range 1-12 MHz due to a similar process.

Measurements of ultrasonic compression wave attenuation as a function of frequency can provide a means to monitor suspensions of microscopic particles in liquids on-line in a process setting. Such mixtures are important in many industrial sectors including chemical, mineral, pharmaceutical, agrochemical and food. The ultrasonic data can be used to estimate the dispersed phase particle size distribution and to quantify dynamic effects such as flocculation and crystallization. The technique requires a detailed mathematical model to relate the ultrasonic wavenumber to mixture properties, and there are two distinct approaches to this—scattering and hydrodynamic. Although both have been shown to adequately describe sound propagation in dilute mixtures (up to ∼5% v/v), current models fail for concentrated suspensions of high density particles. The applicability of existing and future models of wave propagation in these suspensions will be greatly improved with more rigorous formulations for the local viscosity in the vicinity of a suspended particle, viscosity being the principal loss mechanism in such mixtures. In this paper five different theoretical formulations for local viscosity are investigated; their effects on wavenumber when included in both scattering and hydrodynamic propagation theories are compared, with reference to experimental data.

The relative proportions of hardener and resin (the stoichiometric ratio, SR) in a curing epoxy thermoset strongly influence the engineering properties of the material. We investigate how NMR, dielectric and ultrasonic techniques can be used to track cure and estimate SR in the material. We show that all three methods are sensitive to SR and can give clear and quantitative indications of excess resin. Detection of excess hardener in the finally cured material is more difficult but can be achieved by combined measures of elastic modulus, from the ultrasonic velocity, and loss angle, from ultrasonic attenuation.