Richard E. Challis

Ultrasound techniques for characterizing colloidal dispersions

Interest in the interaction of acoustic waves with particulate mixtures has a long history—dating 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 problem—scattering 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.

Dependence of inertial measurements of distance on accelerometer noise

An investigation is made into the errors in estimated position that are caused by noise and drift effects in stationary accelerometers. An analytical study is made into the effects of biases in the accelerometer data and the effects of changing the cut-off frequency in the anti-aliasing filter. The root mean square errors in position are calculated as a function of time and sampling frequency. A comparison is made between the theoretical results and experimental data taken from two commercial accelerometers. Recommendations are made regarding the calibration of accelerometers prior to their use in practical situations.

Equivalence between three scattering formulations for ultrasonic wave propagation in particulate mixtures

The aim of this paper is to present a unified approach to the calculation of the complex wavenumber for a randomly distributed ensemble of homogeneous isotropic spheres suspended in a homogeneous isotropic continuum. Three classical formulations of the diffraction problem for a compression wave incident on a single particle are reviewed; the first is for liquid particles in a liquid continuum (Epstein and Carhart), the second for solid or liquid particles in a liquid continuum (Allegra and Hawley), and the third for solid particles in a solid continuum (Ying and Truell). Equivalences between these formulations are demonstrated and it is shown that the Allegra and Hawley formulation can be adapted to provide a basis for calculation in all three regimes. The complex wavenumber that results from an ensemble of such scatterers is treated using the formulations of Foldy (simple forward scattering), Waterman and Truell, and Lloyd and Berry (multiple scattering). The analysis is extended to provide an approximation for the case of a distribution of particle sizes in the mixture. A number of experimental measurements using a broadband spectrometric technique (reported elsewhere) to obtain the attenuation coefficient and phase velocity as functions of frequency are presented for various mixtures of differing contrasts in physical properties between phases in order to provide a comparison with theory. The materials used were aqueous suspensions of polystyrene spheres, silica spheres, iron spheres, pigment (AHR), droplets of 1-bromohexadecane, and a suspension of talc particles in a cured epoxy resin.

A wide bandwidth spectrometer for rapid ultrasonic absorption measurements in liquids

An acoustic near plane‐wave absorption spectrometer has been developed for use in small samples of liquid (30 ml) over bandwidths of up to 60 MHz, using a two transducer short‐pulse transmission technique. The instrument is controlled by computer, and on‐line digital signal processing is used to correct for transducer insertion, radiation coupling, and the transient responses of transmitter and receiver electronics. The raw data acquisition time is short and the instrument in its present form could be used to estimate absorption at 100‐ms intervals. The instrument can be used on both stationary chemical systems and systems undergoing chemical reaction. Experimental results are presented that show excellent agreement with absorption measurements by traditional (slower) techniques.

Errors and uncertainties in the measurement of ultrasonic wave attenuation and phase velocity

This paper presents an analysis of the error generation mechanisms that affect the accuracy of measurements of ultrasonic wave attenuation coefficient and phase velocity as functions of frequency. In the first stage of the analysis we show that electronic system noise, expressed in the frequency domain, maps into errors in the attenuation arid the phase velocity spectra in a highly nonlinear way; the condition for minimum error is when the total measured attenuation is around 1 Neper. The maximum measurable total attenuation has a practical limit of around 6 Nepers and the minimum measurable value is around 0.1 Neper. In the second part of the paper we consider electronic noise as the primary source of measurement error; errors in attenuation result from additive noise whereas errors in phase velocity result from both additive noise and system timing jitter. Quantization noise can be neglected if the amplitude of the additive noise is comparable with the quantization step, and coherent averaging is employed. Experimental results are presented which confirm the relationship between electronic noise and measurement errors. The analytical technique is applicable to the design of ultrasonic spectrometers, formal assessment of the accuracy of ultrasonic measurements, and the optimization of signal processing procedures to achieve a specified accuracy.

Quantitative classification of adhesive bondline dimensions using Lamb waves and artificial neural networks

Adhesive bonding of metal assemblies is gaining acceptance for use with safety critical structures, and there is a need for effective inspection for both quality assurance (QA) and the assessment of condition in service. One aspect of QA is the need for the dimensions of adhesive bondlines to be within tolerance and measurable. This paper describes the application of ultrasonic Lamb waves in the determination of the principal dimensions of two forms of adhered joints (Lap and T-form) between metal plates. Low order Lamb wave modes (s0 and a1) are propagated across adhered bond-lines, and the received signals are transformed to the modulus frequency domain (FD). The FD data are used as input to artificial neural networks (ANNs), which are trained to associate features in the input data with principal bondline dimensions. The performance of different network structures and simplified forms of these is examined, and the technique gives reliable estimates of the required dimensions in bondlines not included in network training. The interconnected weights of simplified networks provide evidence of the features in Lamb wave signals that underlie the successful operation of the method.

Rapid solutions to the transient response of piezoelectric elements by z‐transform techniques

Calculation of the transient response of piezoelectric elements by analytical means is only possible for a small range of exciting functions for which simple Laplace transforms exist. Calculation tends to be tedious due to the large number of terms which must be evaluated. A method is presented by which the Laplace transformed three‐port model of a piezoelectric element is approximated by a discrete time system by application of the z‐transform. A recurrent time domain solution is developed and this is applied in the manner of a digital filter to a variety of exciting functions. The method has the advantage that the response to any real input can be evaluated and it is thus of considerable use in the testing of piezoelectric elements or the measurement of their physical properties in transient tests. Experimental results are presented which show that the technique is reliable and accurate.

Compensation for temperature variation in ultrasonic chemical process monitoring

Chemical processes often involve heat exchange that causes changes in the temperature of the reactor. These temperature changes could affect ultrasonic monitoring of the processes to the same extent as changes in chemical composition. Discrimination between these two factors requires separate monitoring of the temperature. An ultrasonic reflector for pulse-echo monitoring of aqueous solutions with integrated temperature sensing was developed, implemented and experimentally tested. It contains a water filled cavity isolated from the test medium that is used as a reference. A compact 3 mm wide cavity provides changes in propagation delay of about 1 sample per 0.05 o C at a sampling frequency of 2430 MHz. The possibility of achieving even finer resolution is demonstrated.

Models of ultrasonic wave propagation in epoxy materials

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.

Convergence criteria for scattering models of ultrasonic wave propagation in suspensions of particles

Scattering models used to simulate the attenuation and phase velocity of an ultrasonic wave propagating through a suspension of particles involve the summation of an infinite series of partial waves. The accuracy of computation is influenced by the number of terms included in the harmonic series, and the number of terms required depends upon the scatterer size compared with wavelength. It is shown that the errors in modelled attenuation and phase velocity resulting from premature truncation can be significant when modelling higher values of particle diameter-frequency product. A useful and simple heuristic is presented, in which the number of terms in the summation of the infinite series needed for satisfactory convergence to a final value is a function of the particle diameter-frequency product and of the compressive wave velocity in the continuous phase.