Acoustic scattering to measure dispersed oil droplet
size and sediment particle size
Paul D. Panetta1,2, Leslie G. Bland1,3, Grace Cartwright2
and, Carl T. Friedrichs2
1
Applied Research Associates, Inc.
P.O. Box 1346, 1208 Greate Rd.
Gloucester Pt. VA 23062
2
Virginia Institute of Marine Science
P.O. Box 1346, 1208 Greate Rd.
Gloucester Pt. VA 23062
3
University of Virginia
P.O. Box 400246
Charlottesville, VA 22904
Abstract— The use of sound waves in oceanographic
environments is well established including active sonar
applications for mapping seafloors, for submarine detection, and
for passive listening. Acoustic waves have been used for many
years to study the ocean, including detecting and identifying
objects in the water column, and the measuring the seafloor and
sub seafloor properties. One of the key parameters of the acoustic
field is the amplitude of the wave which scatters from the seafloor
or from objects in the water column. The amplitude, time of
flight, and frequency response can be used to map the seafloor,
measure current flow, or to detect and classify objects in the
water column. In addition to these standard uses, acoustics can
also be used to size particulates including sediment, oil droplets
and gas bubbles in the water. Our particular application for this
work is to detect, classify, and size sediment particles and
separately, oil droplets suspended in the water column using
knowledge of the acoustic backscattering and attenuation.
Specifically, we have measured and separated the absorption,
single scattering and multiple scattering contributions to
attenuation measurements. Our results show that the absorption
dominates the attenuation at low ka values << 1 and multiple
scattering and particle-particle interactions dominate at higher
ka values when ka >~1 with a transition between theses ranges
depending on the concentration of the suspensions. The physics
has been proven out on silica particles in water and work is
ongoing on suspended sediment and suspensions of oil droplets.
Index Terms—acoustic, particle size, attenuation, scattering
I. INTRODUCTION
The most common method to measure particulate size in
oceanographic environments is laser scattering and
transmission with the popular Laser In-Situ Scattering and
Transmissometery (LISST) instrument. The LISST works well
in low concentration suspensions below ~ 250 mg/L (400 ppm)
for suspended mud and ~700 ppm for oil droplets in water, but
in field deployments the LISST becomes fouled by biological
growth. Acoustic technologies in oceanographic environments
are effective at very high concentrations in the water column,
in consolidated sediments and solids. Because of the access to
much higher concentrations and resistance to bio-fouling,
acoustic instruments are commonly used to measure current
speed using the Doppler shift from suspended particulates and
suspended sediment concentration. While acoustic instruments
work well in practical applications, measuring the particulate
size is currently limited by the lack of theoretical understanding
of the scattering of the acoustic field and the complicated
interdependence of attenuating mechanisms to the
experimentally measured parameters.
Research work is
ongoing by the authors [1] and others [2,3] to develop high
frequency particle sizing methods. For this paper we focus on
studying the contributions to the attenuation with applications
to oil droplets and suspended sediment.
II. ACOUSTIC INTERACTIONS WITH PARTICULATES
Several properties of an acoustic field can be used to
measure the characteristics of a particle suspension. These
properties include attenuation, backscattering, and the speed of
sound. Physically, the attenuation of transmitted acoustic field
and speed of sound are determined from waves that traverse
across the media and received by a second transducer Figure
1b). Backscattering is the portion of the field which is
scattered directly back to the transmitting transducer. The
backscattered field at various concentrations for 70 microns
glass spheres ranging from 5 to 40 wt% is shown in Figure 1c.
A fourth quantity that can be measured is the scattered sound
which travels as a diffuse field,
Fig. 1 (a) Schematic of ultrasonic measurement apparatus, (b) through
transmitted RF signal for attenuation and velocity determination, (c) directly
backscattered signal, and (d) diffuse field signal.
shown in Figure 1d. Here the coherent reflections from the
opposite side of the container can be seen in the early time
(<200 microseconds). The amplitude of the diffuse field builds
up in the 100 to 400 microseconds range, and then decays in
time. This decay is a direct measure of the absorption
contribution to the attenuation.
Notable in these acoustic signals is the very large time
range they span. The coherent signal used for determining
attenuation and velocity cover approximately 1 microseconds.
The direct backscattered, which is in incoherent summation of
individual scattering events spans approximately 130
microseconds, while the diffusely scattered field persists for
many milliseconds. The physics governing the propagation of
these fields is different in each time domain and is dominated
by specific properties of the suspension.
These measurements have been applied for many decades
to study solid-liquid suspensions and elastic solids with varying
degrees of success.
Performing the conventional
measurements of attenuation, backscattering, and speed of
sound are relatively simple. The more difficult task is to
accurately model the mechanisms contributing to the measured
attenuation and to understand the effects of the different
attenuating mechanisms on the various measurements. The
inversion of the theory for comparison with experimental
results to provide the specific characteristics of the slurry can
be computationally intensive and inaccurate. When describing
acoustic wave propagation in slurries, there are several
important factors, including, particle size and shape,
concentration, heterogeneities, and the degree of multiple
scattering and particle-particle interactions present.
The following sections describe the physics governing the
attenuation, backscattering and diffuse field.
A. Attenuation
As an acoustic field moves through a solid-liquid
suspension, the fluid and the solid attenuate the field through
several different mechanisms. Specifically, the acoustic field
can be scattered at the interfaces between the particle and the
fluid. In addition, energy can be lost through heat generated by
friction as the particle is moved through the viscous fluid.
Changing the direction of motion of the particle as it oscillates
(accelerating and decelerating the particle) also removes energy
from the acoustic field. If the particle is not rigid, then it can
also change shape as the acoustic field moves through the
media, causing additional energy losses. These mechanisms
can be broadly categorized as scattering losses and damping or
absorption losses. While there are many contributions to
energy loss as the acoustic field interacts with the fluid and the
solid phases of the slurry, the dominant contributions are (1)
the heat loss due to the friction between the viscous fluid and
the particles as they move through the slurry, (2) energy loss to
accelerate and decelerate the particle as it oscillates, and (3) the
scattering of sound out of the propagating field. These three
dominant loss mechanisms will now be described including the
regimes where each is dominant. After this description of
attenuation, the appropriate contributions to the backscattering
and diffuse field will be discussed.
Acoustic fields propagating in suspensions suffer attenuation
due to viscous and thermal damping, and scattering
mechanisms. Attenuation of sound propagation in suspensions
can be divided into the following four major regimes.
1) Viscous regime:
When k c R  1 and Re  R /   R  l  /(2 )  1 , attenuation
has been shown to scale with R 2 2 /  . Where kc is the wave
number = 2 , R is the particle radius,  is the boundary
layer thickness,  is the frequency, l and  are the density
and viscosity of the fluid phase, respectively.
2) Inertial regime:
When k c R  1 and Re >> 1, the Basset history term begins to
influence the particle drag. Consequently, the drag becomes
dominated by inertia through the added mass effect. However,
the added mass force is conservative and does not contribute
to losses, and the dominant loss term is the in-phase
component of the Basset force. In this regime, the attenuation
scales with  / R .
3) Multiple scattering regime:
When k c R  1 , the field scatters geometrically. In an
assembly of many randomly arranged particles, the field will
scatter randomly and thus penetrate poorly (high attenuation).
Here attenuation scales with  4 .
4) Resonance Regime:
Particles may exhibit resonance characteristics and the
frequency of the first mode of resonance can be approximated
as the inverse of the time the acoustic field takes to travel
twice the diameter of the particle. For particles that have
sufficiently higher acoustic velocity, transition to multiple
scattering will set in first. However, most plastic particles will
often exhibit resonance absorption at frequencies
below k c R  1 .
Attenuation has been used widely and successfully to
characterize dilute slurries. Allegra and Hawley [4] provided
the groundbreaking theoretical treatment for solid-liquid
suspensions. Their model accounts for the attenuation due to
viscous damping, as a particle moves and changes shape, the
thermal loss as heat is exchanged between the acoustic field
and the particle, and the scattering loss as the propagating wave
is scattered at the interfaces between the fluid and the solid
particles. However, they obtained good agreement between
experimental measurements of attenuation and theoretical
predictions only at low concentrations. Furthermore, their
theory lacks an explicit term for the backscattering amplitude
and does not incorporate particle size distributions,
hydrodynamic effects of relative motion between particle and
fluid, and contributions from multiple scattering.
In addition to the work of Allegra and Hawley, there have
been a significant number of researchers who have studied
wave propagation in various suspensions, including
Commander and Prosperetti [5], Soong et al. [6], Challis et al.
[7], Holmes et al. [8], Atkinson and Kytomaa [9, 10], and
Kytomaa [11]. In recent studies of attenuation in sols and gels,
Holmes and Challis [12,13] showed that the single scattering
models were inadequate at high concentrations. Recently,
Dukin and Goetz [14] studied two particle sizes at low
concentrations. Notable work has been performed by Dave
Scott in industrial applications where he showed that the
attenuation can be used for particle size determination at low
concentrations. [15,16,17]. Furthermore, he produced data
which showed a deviation for the Allegra and Hawley model at
high concentrations, indicating that multiple scattering is
significant and needs to be accounted for in industrial slurries.
In recent work, Spelt and coworkers have shown excellent
theoretical progress in developing a model for slurries that
accurately predicts attenuation at low concentrations for
specific weak scatterers [18]. In addition, they extended their
models using an effective medium technique that shows
promise for accounting for the effects particle-particle
interactions on attenuation in concentrated slurries. Their
results show good agreement in slurries at concentrations up to
only ~ 30 volume % solids, indicating that it is likely that the
theory does not account for enough of the multiple scattering to
provide accurate predictions at higher concentrations. They
also indicated that their approach had limited applicability for
strongly scattering particles with elastic properties that vary
significantly from water. Furthermore, their techniques are
applicable only for dilute suspensions, and the inversion
process is sensitive to the complex resonance behavior of the
particles in slurries and the frequency range for which the
comparison is made. Even though, their theoretical treatment
has limitations, it represents significant progress towards
including multiple scattering effects in the theoretical
description of attenuation in slurries.
Researchers have studied multiple scattering for several
decades. Notably, Davis [19] studied the effects of multiple
scattering on attenuation in suspensions and emulsions. In his
studies, he coupled the single scattering amplitude developed
by Allegra and Hawley [4] and the multiple scattering approach
described by Waterman and Truell [20]. Varadan et al. [21]
modeled multiple scattering by bubbles in water using a TMatrix approach and Lax’s quasi-crystalline approximation for
scattering for kR <1, where k is the wave number and R is the
particle radius. Agreement between the model results and the
experimental results were quite good, which indicates that
multiple scattering terms are important.
The main obstacles for implementing attenuation
measurements to slurry characterization have proven to be the
mathematical complexities of accounting for multiple
scattering at high concentrations, and the accompanying
complex nature of the inversion process. In addition, the
acoustic attenuation measurements require careful alignment of
transducers, further decreasing the accuracy and precision of
the methodologies based on attenuation alone.
B. Backscattering
Backscattering measurements have several advantages over
attenuation measurements, including insensitivity to alignment
of the transducer and small propagation distances, thus making
them ideal for characterizing highly attenuated slurries. In
addition, since the direct backscattered field usually can be
described by single-scattering processes, the mathematical
inversion processes is often more simple and stable than those
used for attenuation. Figure 1c shows typical backscattered
signals in a solid-liquid suspension.
Backscattering in suspensions has been less thoroughly
studied, relative to attenuation, with the efforts largely focused
on geologic and oceanographic applications. Notably, Hay and
Mercer (1985) used the theory developed by Allegra and
Hawley [4] to explicitly determine the backscattering
amplitude as a function of the elastic properties of the scatterers
and the viscous fluid. They further extended their work to
include particle size distributions of sand particles in
suspension. In addition, He and Hay [22] accounted for the
irregular shapes of sand particles by performing an ensemble
average of the scattered pressure. They obtained good
agreement with experimental results for sand particles in
suspension up to kR~1.
Hay [23] further studied
backscattering in flowing suspensions and observed evidence
of concentration fluctuations in the turbulent flow. These
theories were then applied to the inversion problem of
determining the concentration and size of sand particles in
suspension [24 Crawford and Hay 1993].
Reasonable
agreement was obtained for low concentrations and particle
size for a wide range of materials including fused quartz and
granite. Their level of agreement was poor at higher
concentrations.
Other efforts to use backscattering to characterize sediment
have been undertaken by Thorne and Hardcastle [25] where
they performed in-situ sampling during measurements of
turbulent sediments. Agreement between experimental results
and theoretical predictions of particle size and concentration
were quite good over a large range of concentrations. At high
concentrations, the inversion technique was difficult to perform
due to a high attenuation. This difficulty could be related to the
fact that the theory relied on a single scattering approach and
the irregularly shaped particles were assumed to be spherical.
The irregular shape of sand particles was modeled by
Thorne et al. [26], who used a boundary element method and a
finite element method to numerically model the complicated
particle shapes. An alternative approach has been employed by
Schaafsma et al. [27], who used an equivalent spherical scatter
method Schaafsma and Hay [28] to model the irregular shape
of sand particles and showed much better agreement at
frequencies where strong multiple scattering can be significant
(kR~2).
Recently, an attempt at accounting for inhomogeneities in
sediments was performed by Guillon and Lurton [29] where
they modeled the backscattering from buried sediment layers
and accounted for the losses at interfaces between layers. One
of the major problems of this approach is the complexity of the
inversion process.
C. Diffuse Field Absorption
Another aspect of the scattered field that is intimately
related to the properties of the particulate suspension is the
portion that undergoes multiple scattering and diffuses through
the media. These signals arrive at the detector after several
milliseconds as compared to the direct backscatter signals
which typically arrive in a few 10’s of microseconds [30].
After multiple scattering events, the acoustic diffuse field
develops [31], and a portion of the scattered wave eventually
returns to the transducer. Buildup of this field is governed by a
diffusivity term that is a function of the mean free path and,
thus, is related to the size of the scatterers. The decay rate is
related to the energy absorbed from the acoustic field (see
Figure 1d) and is also a function of particle type, size and
concentration. The loss mechanisms in the long time limit for
the diffuse field are dominated only by viscous losses and
particle motion, with little or no scattering losses.
One of the appealing aspects of the diffuse field
measurement of absorption is that it can also be performed with
one or more transducers and sensor alignment is not important.
In addition, the insonified volume can be larger than for the
backscattering for the same frequency because the wave travels
outward as a diffusely propagating wave. These measurements
are especially appealing because they can be used to probe the
absorptive properties of the particles and thus can be used to
isolate specific mechanisms when used in combination with the
attenuation and backscattering.
While the majority of applications of the diffuse field
absorption measurements have focused on characterizing
solids, Weaver and Sachse [32] focused their work on slurries.
In their study, it was significant that measurements were
performed on slurry containing strongly scattering glass
spheres at a concentration of 62 wt %. In addition, Page et al.
[33, 34] reproduced the work of Weaver and Sachse and then
applied the diffuse field technique to measure particle motion
in a non-stationary suspension. Panetta has also utilized these
measurements to characterize solid liquid suspensions and
isolate specific attenuation mechanisms [38].
While the simple model employed by Weaver and Sachse
[32] described the fluid motion in a matrix of immobile
particles, recent work by Rosny and Roux [36, 37, 38] takes
into account the effects of the particle motion on the diffuse
field characteristics. They obtained excellent agreement
between experiments and theory for dilute solutions of moving
particles and fish, showing applicability to marine
environments. They also showed that multiple scattering can
be important and should not be neglected. An important
outcome of their work was the study of the correlation of the
backscattering with time. Page has also advanced his work on
diffusing acoustic wave spectroscopy (DAWS). Specifically,
they have accounted for particle motion and show good
agreement between experiments and theory [39].
A particularly significant theoretical advancement is given
by a series of papers by Turner and Weaver [40, 41, 42, 43]
where they modeled the backscattering in polycrystalline
materials using a radiative transfer approach for all regions of
backscattering from early-occurring single scattering through
late-occurring multiple scattering. While these results are
promising, it is evident that the characteristics of the diffuse
field are rich with information and that theoretical work and
experimental applications to particle size distributions are not
yet well developed.
III. ANALYSIS METHODS
A. Separation of Attenuation Mechanisms
The acoustic measurements of attenuation, backscattering,
and the diffuse field are sensitive to particle properties in
suspensions. To create a method to characterize particulate
suspension, one must separate these attenuating mechanisms so
they can be studied and modeled individually. The authors
developed methods to isolate these attenuating mechanisms in
dilute and highly concentrated slurries [1]. A brief description
of the scientific basis behind the methods used to separate and
isolate attenuation mechanisms will be given in this section.
It was previously mentioned that (i) the attenuation
measured from a “through transmitted” signal is a function of
absorption, single scattering, multiple scattering, and particleparticle interactions,(ii) the backscattering is a function of
absorption and single scattering, and (iii) the diffuse field is a
function of the absorption only. The second point about the
backscattering is an assumption that may or may not be valid
under certain circumstances. We will accept this assumption as
correct for the purposes of this paper and subsequent analysis.
An illustration showing these acoustic signals and equations for
calculating the attenuation is displayed in Figure 2. The
attenuation from the through transmitted signal is calculated by
comparing the signal in the slurry to a reference signal in water.
The attenuation for the backscattering and diffuse field is
calculated by measuring the decay rate of the scattered signals
at individual frequencies. Here  is the attenuation, f is the
acoustic frequency, z is the separation distance of the
transducers, D is the diffraction correction for a circular piston
transducer,  is the transducer efficiency, (f) is the Fourier
amplitude of the received signal,  is the decay rate and v is the
speed of sound.
The attenuation as a function of frequency for 70 micron
silica spheres in water at 10 wt% for each of these
measurements is shown in Figure 3. The through transmitted
attenuation is
-1 -2 0 1 2
Attenuation velocity
High concentration
1 .9
X
1 0
8
0
c e lls / m L
Absorption and single and multiple scattering
c econcentration
lls / m L
Low
1
z
 ref  f   ref  f  

 Dref  slurry  f   slurry  f  
 Dslurry
  f   ln 
67.5
68.0
68.5
Backscattering
0.010
69
0.009
5 MHz 5wt%
0.007
5 MHz 10wt%
40 wt%
Absorption and single scattering
5 MHz 15wt%
0.006
5 MHz 20wt%
0.005
5 MHz 30wt%
70 um SiO2 spheres in water (10 wt%)
5 MHz 40wt%
0.003
  f BS  
5 wt%
0.002
BS
f 
1.2
2v
0.001
0.000
0
20
40
60
80
100
120
Time (microseconds)
Absorption
  f DF 
Diffuse Field
 DF  f

2v
Fig. 2 Ultrasonic measurements of attenuation suing the through transmitted
signal, the backscattering, and the diffuse field. The associated equations are
shown on the right.
highest; the backscattering attenuation is next, followed by the
diffuse field measurement of the attenuation. The frequency
response of the attenuation is shown in Figure 3 and within the
included table where the through transmitted attenuation has a
power of 2.5, backscattering 1.7, and diffuse field 0.3. These
powers indicate the through transmitted attenuation is
dominated by multiple scattering, the diffuse field by
absorption, with the backscattering containing both scattering
and absorption contributions.
The dependence of the attenuation on each mechanism is
shown in the equations below. These equations can be
rearranged to solve for the individual contribution as follows:
Through _ transmission  f    Multiple _ scattering  f    Single _ scattering  f    Absorption  f 
 Backscattering _ decay  f    Single _ scattering  f    Absorption  f 
 Diffuse _ field _ decay  f    Absorption  f 
 Multiple _ scattering  f    Through _ transmission  f    Backscattering _ decay  f 
 Single _ scattering  f    Backscattering _ decay  f    Diffuse _ field _ decay  f 
 Absorption  f    Diffuse _ field _ decay  f 
70 um SiO
Attenuation (N/cm)
2.0
2
(1)
(2)
(3)
(4)
(5)
(6)
spheres in water (10 wt%)
Attenuation (N/cm)
0.004
1.0
0.5
Diffuse field
0.0
2
4
6
8
Frequency (MHz)
0.6
0.4
Single scattering
0.2
Absorption
2
10
12
4
6
8
Frequency (MHz)
10
12
Fig. 4. The isolated attenuation mechanisms plotted as a function of
frequency. The power of the frequency dependence increased as expected.
IV. RESULTS
A. Silica Suspensions
The dependence of these mechanisms on concentration is
shown in Figure 5 and reveals the true power and insight this
method provides into understanding the acoustic properties of
the suspension. For 70 microns glass spheres in water at 5
MHz, the single scattering contribution to attenuation
dominates below 10 wt % while the multiple scattering
contributions to attenuation dominate above ~15 wt%. These
results show why the commercial acoustic instruments, which
rely on attenuation measurements dominated by multiple
scattering and particle-particle interactions, become inaccurate
at high concentrations.
These results summarize the fundamental science
underlying acoustic particle characterization, provide the
insight needed to better use commercial instruments, and
indicate where the commercial instruments are likely to fail or
become inaccurate.
70 um Glass Spheres
0.7
Backscattering
0
Multiple scattering and
particle particle interactions
0.8
0
Through transmitted
attenuation
1.5
1.0
0.0
Attenuation at 5 MHz (N/cm)
RMS Backscattering
0.008
The results from this process are shown in Figure 4 where
each contribution to attenuation is plotted as a function of
frequency. As expected, the frequency dependence of the
multiple scattering increased to 3.5, the single scattering
increased to 2.1, and the absorption dependence on frequency
remained constant.
Multiple scattering and
particle particle interactions
0.6
0.5
0.4
0.3
0.2
Single scattering
Absorption
0.1
0.0
Fig. 3 The attenuation mechanisms as a function of frequency.
0
10
20
30
Concentration (Wt%)
40
50
Fig. 5. The isolated attenuation mechanisms plotted as a function of
concentration. Above ~ 15 wt% the multiple scattering gang particle-particle
interactions dominate the attenuation
Initial results applying these methods to oil suspensions by
measuring the attenuation of the backscattered signal are in the
next section. Early indications in consolidated sediment cores
shows the same methods may be used to determine the grain
size of sediment in the seafloor. Detailed results will be in
future publications.
B. Oil Dispersions
Fig. 6. The acoustic test chamber for oil-dispersant mixtures. The syringe was
used to uniformly mix the suspensions. The acoustic transducer is shown in
the right figure pointing vertically down.
The oil-dispersant mixture was created in a separate chamber
by inserting the dispersant into the chamber full of water with a
pipet. The dispersant-water mixture was then mixed with by
repetitively drawing and emptying it from the syringe. Then,
oil was added by first drawing approximately 20 cc of the
dispersant-water mixture into the syringe then drawing the oil
into the partially full syringe. The syringe with the oildispersant-water mixture was then placed back into the
chamber and repetitively filled and emptied to uniformly
disperse the oil. Care was taken to ensure the total oil
concentration was below the striation limit of the LISST which
was approximately 700 ppm. The image of the acoustic
backscattering for each ping for the chemically dispersed oil is
shown in Figure 7b. The ability for the dispersant to keep the
oil in the water column can be seen by the scattering from the
suspended droplets indicated by the orange/red region
extending to ~100 seconds. The dispersant and water were
incorrectly mixed prior to adding the oil diminishing the
efficiency of the dispersant to disperse the oil. Individual
droplets can also be seen as streaks across the image.
Crude oil in water
3
4.5
6
Depth (cm)
1.5
(a)
0
100
200
100
200
300
400
500
600
300
400
500
600
Dispersant and Oil DOR 1:4
3
4.5
Depth (cm)
1.5
(b)
6
Sonar was used during the recent blowout and associated
oil leak from the Deepwater Horizon incident to image the
plume and calculate the flow rate. In the case of the Deepwater
Horizon blowout they did not have the monitoring tools to
determine the efficacy of the 1.1 million gallons of Corexit
9500 dispersant injected directly into a flowing plume of oil
and natural gas. Dispersants main effect is to decrease the
surface tension at the oil-water interface causing the oil to form
droplets smaller than ~70 microns so they can remain in the
water column long enough to be consumed by naturally
occurring bacteria.
There is a need to develop a deeper understanding of the
scattering of acoustic waves from particulates, sediment, and
oil droplets to effectively utilize the vast array of sonar and
marine acoustic instruments. Specifically, to effectively size
suspended particles in the water column and in consolidated
sediments in the seafloor, it is important to understand the
contributions from single scattering and multiple scattering as
well as the absorption contributions to attenuation that control
the wave propagation, especially in high concentration systems
experienced in the seafloor sediment and subsea blowouts
experienced during the Deepwater Horizon incident.
Measurements were performed at both the Department of
Interior Ohmsett outdoor wave tank in New Jersey, and at the
Applied Research Associates, Inc. labs on the Virginia Institute
of Marine Science Campus.
The acoustic test chamber is shown in Figure 6. To ensure
good mixing of the oil-water-dispersant, we suctioned the
mixture into a 60 cc syringe multiple times prior to performing
our measurements. A water mixture was mixed thoroughly
within the acoustic test chamber while it was within the LISST
testing area in order to calibrate the oil droplet size.
Immediately after mixing with the syringe, the acoustic
transducer was inserted into the chamber pointed down and
data collection was started immediately. The acoustic data
from multiple “pings” every 0.1 seconds for 300 seconds are
shown in Figure 7a for oil and oil-dispersant mixtures
respectively. The mixture of oil droplets caused the acoustic
wave to scatter, creating a bright orange/red pattern between
zero and ~30 seconds. After ~ 30 seconds, scattering from the
droplets caused distinguishable orange/red streaks. As more
droplets floated up towards the surface, the streaks caused by
the droplets generally pointed up with some streaks pointing
left to right or down presumably from random motion in the
chamber. The droplets continued to move through the field of
view of the transducer up to ~ 250 seconds. The raw acoustic
signal approximately 10 seconds after the transducer was
inserted is shown at the right of the image.
0
Time (seconds)
Fig. 7. Acoustic images of the scattering from oil droplets in water over
300 seconds. An individual ping is shown on the right hand side of each figure.
The red/orange regions are high scattering and the black is low scattering. The
long tracks are individual droplets as they float through the field of view of the
5 MHz transducer.
These images visually confirm the ability of the dispersant
to keep oil in the water column over an extended period of
time. To effectively size the droplets, we analyzed the raw
acoustic waveforms shown on the right hand side of Figure 7
by determining the rate of decay of the acoustic signal. The
signal was analyzed when oil remained within the water
column of the testing chamber, often within the first 50
seconds. After this time, most of the oil droplets would have
reached the top of the chamber. A ping range of approximately
15 to 20 seconds was taken within the data and a linear
regression was fit over the data.
The attenuation for isolated drops in water is given by the
following equation [44]:
(7)
Fig. 8. The comparison between our acoustic determination of the droplet size
and the LISST determination. The inset shows the droplet size distribution
from the LISST measurements.
V. CONCLUSIONS
(8)
Where
e = extinction cross section = sum of the scattering
cross section and the absorption cross section
a = droplet radius
f = frequency
fr = resonance frequency
 = damping constant at fr
c0 = speed of sound
 = ratio of specific heat at constant pressure and
volume
P = hydrostatic pressure
= density of water
kr = wave vector at the resonant frequency
The resonant frequency for 100 micron oil droplets is ~
0.055 MHz. At our operating acoustic frequency of 5 MHz,
which is much greater than the resonant frequency, the
attenuation is proportional to the droplet size, a. Thus, we can
directly relate the attenuation to the droplet size. Using this
linear relationship, we then calculated the expected droplet size
based on our acoustic measurements. The comparison between
our acoustic predictions of droplet sizes with the droplet size
measured from the LISST is shown in of Figure 8. The inset
shows the droplet size distribution determined from the LISST.
While there is some spread, the relationship is quite good
considering some of the data is from Ohmsett and some from
lab measurements using two different configurations.
We have shown the contributions to acoustic attenuation can
be separated and isolated through multiple measurements for
silica particles in water. The multiple scattering and particleparticle interactions dominate the attenuation at high kR and
concentration. The absorption dominated the attenuation at
low kR with sing scattering dominating the attenuation at
intermediate kR values. These methods have been applied to
oil dispersions to study the efficacy of dispersants to keep oil
in the water column. Applications to sediment will be
published later.
ACKNOWLEDGMENT
The authors would like to thank Wayne Reisner for
fabricating the sample chambers, Randy Belore from S.L.Ross,
Al Guarino from Mar, Inc. for assistance at Ohmsett and Kyle
Winfield for assistance with the experimental measurements.
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