Particle size and density of a slurry from ultrasonic backscattering measurements at a solid interface

The pivotal experiment was performed with a setup in which a plastic cylinder was mounted on the top of a horizontal Rexolite plate and a transducer mounted directly below the cylinder; a single layer of stationary 1588-μm acrylic spheres was placed in the cylinder filled with water. Two well-separated signals were received by the transducer operating in the pulse-echo mode: (1) a signal due to the reflection from water at the interface and (2) a time-delayed signal resulting from the backscattering from the spheres of diameter D. The important observation was that the time delay was equal to 2 D/c using standard notation. A method was developed to use the FFT phase difference between the incident and scattered signals at the interface to determine the time-delay as a function of frequency, the backscattering coefficient M versus frequency, a particle size distribution, and an average value of the diameter. Experimental average diameter results are shown in the square brackets for nominal particle sizes: (1) 1588-μm acrylic spheres [1564 μm], (2) polystyrene spheres for diameters from 200 μm to 500 μm [260 μm-536 μm], (3) suspended slurry of 250-300 μm polystyrene spheres at 2.25 MHz [253 μm], (4) 794 μm [759 μm] and 1588-μm [1623 μm] Teflon spheres, (5) 1588-μm stainless steel spheres [1674 μm], and (6) suspended slurry of 250-300 μm polystyrene spheres [275 μm] at 3.5 MHz for seven volume fractions. Density and particle size measurements were obtained for the latter. For the density measurement, the FFT amplitude of the scattered signal was summed from 2 to 4 MHz for each slurry. A plot of the square root of the FFT-amplitude-sum versus the volume fraction yields a straight line, passing through the origin. A calibration of the experimental setup is obtained by fitting a straight line through the data with error bars. Thus, the volume fraction for a slurry of unknown concentration can be determined by measuring the FFT-amplitude-sum. The density of the slurry is obtained from the volume fraction. These results make it feasible to develop an online and real-time pipeline sensor to measure particle size and slurry density.