USING ULTRASONIC DIFFRACTION GRATING
SPECTROSCOPY TO CHARACTERIZE FLUIDS AND
SLURRIES
M. S. Greenwood1, A. Brodsky2, L. Burgess2, and L. J. Bond1
Pacific Northwest National Laboratory, Richland, WA 99352
University of Washington, Seattle, WA 98195
2
ABSTRACT. In ultrasonic diffraction grating spectroscopy, the grating surface is in contact
with the liquid or slurry. The ultrasonic beam, traveling in the solid, strikes the back of the
grating and produces a transmitted m = 1 beam in the liquid. The angle of this beam in the
liquid changes with frequency and the so-called critical frequency occurs when the angle is
90°. At this point, the signal of the reflected m = 0 wave—the signal observed in the
experiment—increases and this increase is used to characterize the liquid or slurry.
INTRODUCTION
The objective is to measure the speed of sound in liquids and slurries and to
measure the particle size of a slurry. The research for liquids is presented here. The
method of ultrasonic diffraction grating spectroscopy (UDGS) is analogous to that for
optics using grating light reflection spectroscopy (GLRS) [1-3]. The optical method has
been successful in determining the particle size of a slurry in the range from about 2 to
200 nanometers and also measuring the index of refraction. Because of the larger
wavelength, ultrasonics can measure larger particle sizes. Ultrasonic diffraction gratings
have been used for nondestructive evaluation [4,5], but, not to the authors' knowledge,
for characterizing fluids and slurries. The ultimate goal of this project, sponsored by the
U.S. Department of Energy's (DOE) Environmental Management Science Program, is to
gain enough knowledge to develop a sensor in which the ultrasonic diffraction grating is
positioned in the wall of a pipeline to measure particle size of a slurry on-line and in real
time. At DOE sites, there is a need to characterize slurries, as the radioactive wastes are
retrieved from underground storage tanks and transported through pipelines, in order to
prevent pipeline plugging. In many industries, there is also need for particle size
measurements for process control. A U.S. patent application has been filed.
BASIC CONCEPTS
The ultrasonic diffraction grating is formed by machining parallel triangularshaped grooves on the flat surface of a half-cylinder, as shown in Fig. 1. The
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/S20.00
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FIGURE 1. Photograph of 300 micron stainless steel ultrasonic grating.
half-cylinder has a diameter of 5.08 cm and the grating has a groove spacing of
300 microns with a 120° included angle. The grating is placed in the immersion chamber
(27.9 cm diameter), shown in Fig. 2, which is filled with the liquid. The send and receive
transducers are suspended from the movable arms. The beam from the send transducer
travels through the liquid, through the stainless steel, and strikes the back surface of the
grating at an angle 9. The receive transducer, oriented at an identical angle 9, receives
the signal reflected by the diffraction grating.
In order to understand how UDGS can be used to measure the speed of sound,
consider a longitudinal wave striking the back of a 300 micron stainless steel grating at
an incident angle of 30°, as shown in Fig. 3. The specularly reflected m = 0 longitudinal
wave, measured in the experiment, is shown, as well as the reflected m = 0 shear wave,
and the transmitted m = 0 longitudinal waves. The positions of the m = 0 waves are, of
course, unchanged when the frequency changes. However, the diffracted m = 1
longitudinal wave in water does change with frequency. Fig. 3 shows its position at a
FIGURE 2. Photograph showing setup of experimental apparatus.
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*ed Shear Wave,
Incident Longitudinal
Wave
Reflected Longitudinal
Wave, m = 0
Diffracted Longitudinal Wave at
5.66 MHz, m * 1, Angle « W deg
Transmitted Lsngitm
Wave, m = 0
FIGURE 3. Diagram showing reflected and transmitted diffracted waves when an incident longitudinal
beam strikes the grating at an angle of 30°.
frequency of 7 MHz and 6 MHz. As the frequency decreases, the angle increases, and at
a frequency of 5.65 MHz, the angle becomes 90°. At this frequency, called the critical
frequency, the wave transforms from a traveling wave and becomes evanescent. This
means that it is an exponentially decaying wave in the liquid or slurry. At a slightly
smaller frequency, the evanescent wave disappears. In order to conserve energy, the
energy is redistributed to all other waves, and an increase in amplitude of the specularly
reflected signal is expected. This increase in amplitude was observed in the GLRS optics
experiments and the first objective of these experiments was to observe a similar increase
in amplitude for the UDGS experiments.
The possibility of UDGS to measure particle size is due to the penetration of the
evanescent wave into the slurry. As the wave interacts with the particles, some
attenuation of the signal occurs. As a result, the signal of the reflected m = 0 wave,
which is measured by the receive transducer, decreases in amplitude. Since the
attenuation is dependent upon particle size, an algorithm can be developed to determine
particle size. Such an algorithm for the data from the GLRS experiments has been
developed [1-3].
Critical Frequency Calculation
The critical frequency fcR is obtained from Snell's law and the grating equation.
The angle 6 is defined as the angle that the incident longitudinal wave, traveling in the
solid, makes with the normal to the grating surface. The angle (fa is the angle of the
longitudinal wave traveling in the liquid. For the m = 0 longitudinal wave in the liquid,
angle <fa is obtained from Snell's law:
sinff
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(1)
where CL is the speed of sound in the solid and c is the velocity of sound in the liquid.
The angles for non-zero values of m are given by the grating equation:
m c
sin^ m -sin^ 0 =——
/ d
,-.
(2)
where the diffraction order m is positive for the orientation shown in Fig. 3, f is the
frequency, and d is the grating spacing. For m = 1, the critical frequency occurs when cpi
is equal to 90° and is given by
fJCR
CR=
———~——— •
(3)
EXPERIMENTAL MEASUREMENTS FOR STAINLESS STEEL GRATINGS
An extensive set of measurements has been obtained for 304 SS gratings having a
grating spacing of 200 microns and 300 microns. Data were obtained for water and sugar
water solutions, 10% by weight, 20%, and 30% and for eight incident angles ranging
from 20° to 55°. Only a small fraction of the data will be presented here.
The data were obtained using a computer-controlled system that has been
developed at Pacific Northwest National Laboratory. The pulser-receiver printed circuit
board outputs a toneburst signal of 200 volts p-p with a maximum amplification of 70 dB.
The change in frequency in these experiments was 0.05 MHz. Data are obtained
sequentially as the frequency changes from an initial frequency to the final frequency and
printed to a file. Signal averaging is also used. In order to account for the transducer
response, data were also obtained for a half-cylinder with a smooth face. Effects of
transmission for the liquid-to-SS transition and for the SS -to-liquid transition were also
included. The send and receive transducers have a diameter of 0.635 cm.
Fig. 4 shows data obtained for the 300 micron SS grating and water, as the
incident angle is varied. The arrows in this figure (and all subsequent figures) indicate
the theoretical values of the critical frequency, calculated from Eq. (3). In order that the
curves do not overlap, the data are offset by the amount shown in the figure(s). The data
shows an increase at the expected critical frequency.
Fig. 5 shows the data obtained for the 300 micron grating at an incident angle of
40° for water, 10% sugar water (SW), 20% SW, and 30% SW. One sees that the critical
frequency, as expected, changes with fluid due to the change in the velocity of sound.
Previously, the velocity of sound in sugar water solutions at room temperature had been
measured. The larger peaks in Fig. 5 do not change with the liquid change and, therefore,
are due to effects in stainless steel. An m = -1 shear wave in stainless steel is produced
and is located in the -x+y quadrant, using the terminology indicated in Fig. 3, and has a
negative angle relative to the +y axis. As the frequency of the incident longitudinal wave
decreases, the m = -1 shear wave approaches -90° and then becomes an evanescent wave
also. The straight line indicates the frequency at which this occurs.
Fig. 6 shows the data obtained for the 200 micron grating for an incident angle of
30°, using water and three sugar water solutions.
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300 micron SS grating, Water
Variation of Critical Frequency with Angle
data + 0.3 V
data + 0.2 V
• 20 deg
• 25 deg
30 deg
x 35 deg
• 40 deg
• 45 deg
+ 50 deg
• 55 deg
5 55
4
6
8
Frequency (MHz)
FIGURE 4. Data obtained using 300 micron SS grating and water for incident angles ranging from 20° to
55°.
Incident Angle = 40 deg, 300 micron SS grating
Variation of Critical Frequency for Water and Sugar Water Solutions
FIGURE 5. Data obtained using 300 micron SS grating and an incident angle of 40° using water, 10%
sugar water (SW), 20 % sugar water and 30% sugar water.
EXPERIMENTAL MEASUREMENTS FOR REXOLITE GRATING
Measurements were also obtained for a plastic Rexolite™ grating having a
grating spacing of 406 microns with a 120° included angle. Fig. 7 shows data obtained
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Incident Angle = 30 deg, 200 micron SS grating
Variation of Critical Frequency for Water and Sugar Water Solutions
0.1
Frequency (MHz)
FIGURE 6. Data obtained using 200 micron SS grating and an incident angle of 30° using water, 10%
SW, 20% SW, and 30% SW.
406 micron Rexolite Grating
Incident Angle = 25 deg
+- Water
*~1038(10%SW)
1081 (20% SW
1127 (30% SW)
Frequency (MHz)
FIGURE 7. Data obtained using 406 micron Rexolite grating at an incident angle of 25° for three sugar
water solutions having a density of 1038 kg/m3, 1081 kg/m3, and 1127 kg/m3.
for water, 10% SW (1038 kg/m3), 20% SW, and 30% SW. The arrows show the critical
frequencies expected. Unfortunately, the minimum is so broad that the precise critical
frequency cannot be determined. However, there is another very interesting feature:
Note the large separation at the maximum between the four sets of data. This is an
indication that the data is quite sensitive to small changes in density. Additional data,
obtained for small changes in the density of the sugar water solution, are shown in Fig. 8.
Changes in density as small as 0.5% can easily be observed.
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406 micron Rexolite Grating
3.5
3.6
3.7
3.8
3.9
Frequency (MHz)
FIGURE 8. Data obtained using 406 micron Rexolite grating for small changes in the density of the sugar
water solutions, ranging from a density of 1005 kg/m3 to 1127 kg/m3.
CONCLUSIONS AND PATH FORWARD
The large amount of data obtained for the two stainless steel gratings consistently
shows that the peak in the data occurs at the critical frequency, similar to those shown in
Figs 3, 4, and 5. Improvements in the grating design and in the experimental apparatus
are currently underway. The goal is to increase the amplitude and resolution of the peak
due to the critical frequency. Results show that the Rexolite grating can be used to
distinguish between small changes in the density of the liquid.
After the design has been maximized for liquids, experiments using slurries will
be undertaken.
ACKNOWLEDGMENTS
This research was supported by the Environmental Management Science Program
of the Office of Environmental Management, U.S. Department of Energy (DOE). Pacific
Northwest National Laboratory is operated for the DOE by Battelle Memorial Institute
under Contract No. DE-AC06-76RL01830.
REFERENCES
1. Brodsky, A. M., Burgess, L. W., and Smith, S. A. AppliedSpectroscopy 52, 332A
(1998).
2. Anderson, B. B., Brodsky, A. M. and Burgess, L. W. Physical Review 54, 912
(1996).
3. Smith, S. A., Brodsky, A. M., Vahey, P. G. and Burgess, L. W. Analytical Chemistry
72,4428 (2000).
4. deBilly, M. and Quentin, G. J. Phys. D: Appl Phys. 15, 1835 (1982).
5. Bridge, B. and Tahir, Z. British Journal ofNDT 31, 9 (1989).
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