Patent CA-2350816-A1 (CA)
Title: Dynamic sound scattering
Inventor: PAGE JOHN H
IPC: G01N29/032
Filed: 2001-06-14
Abstract: This thesis presents the results of three main experimental projects; a study of ultrasonic wave propagation in strongly scattering materials, the use of the results of this first study to develop new techniques in ultrasonic correlation spectroscopy, and the use of these techniques to measure the dynamics of particles in fluidized beds.  The first project involves the investigation of wave propagation in random, inhomogeneous materials that scatter ultrasound strongly (i.e. materials where the scattering mean free path is comparable to the ultrasonic wavelength .lambda.). I have measured the velocities of the weak ballistic pulse that travels through these materials without scattering out of the forward direction. In the intermediate frequency regime, where .lambda. ~ the size of the scatterer, these measurements reveal strong dispersion in the ballistic modes, caused by both resonant scattering in the material and tortuosity effects. The dependence of the dispersion on the volume fraction of scatterers is investigated; very good agreement between the ballistic velocities and an effective medium theory, based on a spectral function approach, is found at all volume fractions. The diffusion approximation for the scattered waves is tested by measuring the ensemble-averaged transmitted intensity in pulsed ultrasonic experiments. The volume fraction dependence of the wave diffusion coefficient and the absorption time is investigated experimentally, and parameters that govern diffusive propagation are modeled using an extension of the spectral function approach.     Using the results of this wave propagation study, we have developed two new ultrasonic spectroscopy techniques. Dynamic Sound Scattering (DSS) uses singly scattered sound to measure the rms velocity of scatterers. Diffusing Acoustic Wave Spectroscopy (DAWS) uses multiply scattered sound, described by the diffusion approximation, to measure the relative motion of scatterers. This thesis explains the underlying principles governing these techniques and the ways that these techniques can be implemented in practice to provide powerful new methods for investigating the dynamics of strongly scattering materials. I also take advantage of the ability of ultrasonic detectors to detect the wave field directly to test the Siegert relation. The Siegert relation is a simple relationship between the field and intensity temporal autocorrelation functions, and is frequently used in the interpretation of analogous light scattering techniques. I have elucidated the conditions under which the Siegert relation is obeyed through a systematic study of this basic wave relation for both single and multiple scattering. We also take advantage of our ability to measure the phase of the scattered waves, and show how the statistics underlying their temporal fluctuations can be used to investigate the scatterer's dynamics.    Using DAWS and DSS, I have investigated the dynamics of particles suspended against sedimentation by a fluid flowing upwards in a fluidized bed. Since ultrasonic wavelengths are on the order of millimeters, the suspensions that can be probed contain particles with diameters on the millimeter scale; this corresponds to a regime that is of interest in industrial applications. Thus DAWS and DSS are well suited to the high Reynolds number, high volume fraction suspensions to which other current techniques are least suited. In our experiments, the velocity fluctuations and velocity correlation lengths are measured as a function of the volume fraction and sample size for a range of Reynolds numbers. At high volume fractions of particles (~ > 0.15), we find surprisingly large values of the rms velocity fluctuations and instantaneous correlation length, with a different dependence on volume fraction to that seen at low ~. The relationship between the velocity and correlation length is explained for all volume fractions by accounting for the fundamental importance of number fluctuations in setting the scale of the dynamics. As the sample size is increased, simple scaling theories predict that the velocity fluctuations will diverge, but some experiments and simulations have suggested that the fluctuations may saturate for large samples. The exact nature of this saturation, and what sets the magnitude of the velocity correlation length that cuts off this divergence, is not well understood; our experiments address this question. At low Reynolds numbers, I find convincing evidence of the importance of cell walls in setting the magnitude of the correlation length, and hence the velocity fluctuations. Furthermore, by measuring all three components of the rms velocity fluctuations, I have discovered simple scaling laws for their dependence on the thinnest dimension of the cell that have not been expected in previous theoretical work. At higher Reynolds numbers, I show that inertial effects modify the dynamics at all length scales, and can be the limiting factor in determining the correlation length. Thus our experiments make a significant contribution in elucidating the mechanisms involved in determining the velocity correlation length, and hence the remarkably large velocity fluctuations, in fluidized suspensions.