Journal of Geophysical Research: Oceans

Acoustic scattering from a suspension of flocculated sediments

Authors


Corresponding author: I. T. MacDonald, National Institute of Water and Atmospheric Research, Hamilton, Waikato 3216, New Zealand. (i.macdonald@niwa.co.nz)

Abstract

[1] A series of controlled laboratory experiments have been conducted to investigate the backscatter of high frequency sound (3–5 MHz) from suspensions of fine sediment in its unflocculated (primary) state and at various levels of flocculation. The size and fall-velocity distributions of the flocs were determined using an optical system and a settling tube, thus allowing floc density to be determined. The measurements have conclusively demonstrated that the acoustic properties of the flocculated particles are not solely controlled by the primary particles; some aspect of the floc structure is influencing the scattering characteristics. The overall trend is for the form function (Ks) to increase as the degree of flocculation increases. This trend was also observed in the total scattering cross section ( inline image) but this result is dependent on the assumption that viscous absorption for flocculated particles is negligible. The measured scattering properties are compared to the predicted values from two theoretical models, the elastic (ES) and fluid sphere (FS) models. While the results show that, in their current form, neither model is capable of adequately representing the scattering characteristics of a suspension of flocculated particles, the two models did provide upper (ES) and lower (FS) bounds to the measurements. In terms of the operational use of acoustics to measure the concentration of flocculated sediments, empirical relationships could be fitted to the observations but, until a better theoretical understanding of how sound interacts with flocculated particles is achieved, the fitting of such empirical relations may be somewhat premature.

1. Introduction

[2] Flocculated particles in the marine environment are one of today's great challenges for sediment transport studies. In marine waters, suspended particles rarely exist in their primary state; instead they are typically aggregated, heterogeneous assemblages of mineral grains, biogenic debris, bacteria, and organic material. The pronounced influence suspended fine particles exert on water quality in estuaries and coastal seas is well known [Eisma et al., 1991; Winterwerp, 2002]. A floc or aggregate may constitute of the order 106 individual particles and floc size can range over 4 orders of magnitude within any one floc population, from clay particles of 1 µm diameter to macroflocs of several millimeters. As flocs grow more ambient fluid is trapped in the interstitial spaces between the particles. Therefore, floc density is inversely proportional to floc size, with large flocs having a density only slightly greater than that of the ambient fluid [Dyer and Manning, 1999; Khelifa and Hill, 2006; Manning and Bass, 2006].

[3] Acoustic instruments are routinely used in coastal and estuarine studies for measuring currents and current profiles. Increasingly, such acoustic instruments are also being used to simultaneously estimate suspended-sediment concentration and concentration profiles using the strength of the backscattered acoustic signal, from which sediment transport is calculated [Deines, 1999; Fugate and Friedrichs, 2002]. This method typically relies on taking a large number of water samples and building an empirical relationship between mass concentration of suspended sediment and acoustic backscatter intensity. The approach, however, provides little or no information about the degree of sediment flocculation. An alternative method, which can yield particle size information, is based on the inversion of the backscatter equation for suspended noncohesive sand. Such inversions rely on the specification of two key parameters that describe the scattering characteristics of the suspended particles: the ensemble backscatter form function (Ks) and the ensemble total scattering cross section ( inline image). As Ks increases, the voltage recorded by the receiver increases because more energy is scattered back to the sensor; whereas as inline image increases, the voltage decreases as more energy is scattered away from the sensor. For noncohesive sand particles, these terms are well defined [Moate and Thorne, 2009; Thorne and Hanes, 2002]; however, the suitability of such relationships for cohesive fine sediments is yet to be determined.

[4] Here we present results from a series of controlled laboratory experiments to examine how the particle scattering characteristics change as a result of flocculation. Measured values for Ks and inline image are compared to predicted values from two theoretical models, the elastic sphere (ES) and fluid sphere (FS) models.

2. Theory

[5] When multiple scattering can be ignored the incoherent ensemble mean-square voltage (Vrms) due to backscattering from particles at range r by an acoustic backscatter sensor (ABS) can be written as [Sheng and Hay, 1988; Thorne and Hanes, 2002]

display math(1)

where

display math(2)
display math(3)
display math(4)

where N is the number of particles per unit volume, ψ is the near-field correction, which accounts for the nonspherical spreading that occurs near the transducers [Downing et al., 1995], inline image is the attenuation due to water absorption, inline image is the attenuation due to viscous absorption, a is the particle radius, f(x) is the form function that corresponds to the dimensionless particle parameter x where inline image and k is acoustic wavenumber, n(a) is the particle size probability density function, and inline image is the total scattering cross section of a single particle of radius a. For the simple case of a homogeneous suspension with a single particle size and density, equations (2) and (3) reduce to inline image and inline image, respectively. The Kt term contains system parameters: R is the receive sensitivity, Tv is the electronic gain of the system, p0 is the reference pressure at distance r0 from the transducer face, inline image is transducer directivity, inline image is the angle that subtends the acoustic axis, c is the speed of sound in water, and inline image is the pulse duration.

[6] Taking the natural logarithm of equation (1) yields [Moate and Thorne, 2009; Thorne and Buckingham, 2004]

display math(5)

[7] Equation (5) is now a linear function of inline image versus r, from which the following expressions for inline image and Ks can be derived

display math(6)
display math(7)

where inline image and inline image are the slope and intercept, respectively derived from the fit of equation (5) to ABS observations.

[8] For comparative purposes the measured values for inline image and Ks are compared to the predicted values from two theoretical models: the ES and FS models. These two models were selected as they potentially span the transition from solid (primary) particles to large fluid-like flocs. The models provide expressions for f(x) and inline image which, after substitution into equations (2) and (3) yield inline image and Ks. Expressions for f(x) and inline image for the ES and FS models are shown in equations (8)-(11).

display math(8)
display math(9)
display math(10)
display math(11)

where k is the wave number of sound in water, inline image, bq [Gaunaurd and Überall, 1983] and cq [Anderson, 1950] are complex functions involving Bessel and Hankel functions and their derivatives, for completeness, expression for bq and cq are provided in Appendix A.

3. Methods

3.1. Experimental Arrangement

[9] A series of laboratory experiments was conducted to measure the acoustic backscatter from suspensions of kaolin (Specwhite™ SiO2(47%), Al2O3 (38%), density 2650 kg/m3) in a well-mixed 120 l recirculation tank (Figure 1). Flocculation was controlled through the incremental addition of a commercial flocculant (MAGNAFLOC®). Five mass concentrations were used, nominally 0.2, 0.4, 0.8, 1.6, and 3.2 g/l. The actual concentration was measured gravimetrically at four locations down the tank at five times throughout each experimental run. The measurements showed that the kaolin was uniformly distributed to ±5% throughout the tank.

Figure 1.

ABS recirculation tank.

[10] Acoustic backscatter was measured using an Aquatec Aquascat-1000TM at acoustic frequencies of 3, 4 and 5 MHz. The acoustic “ping” rate was set to 16 Hz, with backscatter profiles at 0.01 m intervals over a range of 0.70 m.

[11] The size distribution of the “primary particles” of kaolin was determined using a Malvern MasterSizer 2000™. The floc size and fall-speed distributions for the flocculated suspension were determined using the optical FLOCView system, which is described later.

[12] Each run took place over a period of three days. First, the tank was filled with deionized-microfiltered water. Once filled, the water was recirculated in the tank for 24 h, which allowed the water to degas and reach room temperature. After 24 h, 10 min of ABS measurements were made to determine the background signal level. Next, the ultrasonically dispersed, unflocculated (“primary”) kaolin particles were added to the tank. To ensure that the particles were thoroughly mixed and a homogenous suspension was achieved, the tank was mixed for a further 21 h. After this mixing period, 20 min of ABS measurements were made to determine the scattering signal of the primary kaolin particles. Immediately after the 20 min measurement period, four water samples at 1, 10, 30 cm and 70 cm below the level of the acoustic transducers were collected from the centre of the tank. The suspended sediment concentration was later determined by gravimetric analysis of the water samples.

[13] After collecting the water samples, the MAGNAFLOC flocculant was added. To allow sufficient time for flocculation to occur, the tank was mixed for 110 min. After this mixing period, 10 min of ABS measurements were made to determine the scattering signal at floc level 1 (FL1), corresponding to the first addition of MAGNAFLOC.

[14] The floc size distribution and settling speed distribution at FL1 were estimated at the end of the ABS measurement period using FLOCView. This consisted of a 0.6 m high settling column, near the bottom of which was a 4 megapixel camera and macrolens which recorded images at up to a rate of 30 Hz. The instrument is shown in Figure 2a. A sample was carefully extracted from the tank and transferred to the settling column using a wide-mouthed (8 mm internal diameter) pipette. Samples were taken from the centre of the tank at a depth of approximately 35 cm below the level of the transducer; samples were drawn into the pipette slowly to minimize damage to the flocs. The pipette was then carefully lifted from the tank and placed so that the tip of the pipette was located just below the water surface in the settling column. Under gravity, the flocs then settled vertically out of the pipette and into the settling column. The sample transfer was made as quickly as possible to minimize the potential for additional flocculation that might occur once the kaolin suspension was no longer subject to the turbulent shear present in the mixing tank. The elapsed time between the start of drawing fluid into the pipette to collecting FLOCView images (containing flocs) was typically about 1–2 min. Figure 2b shows a typical FLOCView image. An automatic particle recognition system was developed to identify particles and to track the particles through a sequence of images, from which floc settling speed is estimated.

Figure 2.

(a) FLOCView setup. (b) FLOCView image.

[15] The sequence of water samples, adding flocculant, mixing period, ABS measurements, and floc size and settling speed measurements was repeated a further three times to obtain floc levels 2, 3, and 4 (FL2, FL3, and FL4), corresponding to each extra addition of MAGNAFLOC. Runs were repeated three times for each concentration.

3.2. Data Processing

3.2.1. Obtaining Estimates for Ks and inline image From ABS Measurements

[16] In order to evaluate equations (6) and (7), values for inline image, inline image, inline image, inline image, Kt and N are required. Aside from inline image which can be obtained directly from literature [Richards et al., 1996], the other terms were evaluated as follows.

3.2.1.1.  inline image and inline image

[17] Figure 3 shows an example of the fit of equation (5) to ABS observations from which inline image and inline image were estimated as described previously. The data shown are for the three runs at 3.2 g/l for FL2 for the 5 MHz transducer. Following Thorne and Buckingham [2004] the first 0.2 m of ABS data were excluded from the analysis in order to avoid potential problems with crosstalk and inaccuracies in the near field correction. Furthermore, values for inline image and inline image were rejected when the coefficient of determination (R2) was less than 0.95.

Figure 3.

ABS measurements of inline image versus r for the three runs at 3.2 g/l for FL2 for the 5 MHz transducer.

3.2.1.2. Kt

[18] The system constant Kt was evaluated using the calibration method of Betteridge et al. [2008]. Over the course of the experiments the calibration process was performed on three separate occasions. On each of these three occasions, the calibration was performed at two different sediment mass concentrations (0.5 and 1.0 g/l). The results of the calibration are shown in Figure 4, which shows profiles of Kt with range. The figure shows that aside from the region close to the transducer which is affected by crosstalk and inaccuracies in the near field correction that Kt is constant with range. The dotted lines in the figures are the Kt value obtained from averaging the calibration data for each frequency over the range 0.3–0.8 m. It is these values that are used for Kt.

Figure 4.

Measurements of Kt with range at (a) 3 MHz, (b) 4 MHz, and (c) 5 MHz. The dotted lines in the figures are the Kt values obtained from averaging the calibration data for each frequency over the range 0.3–0.8 m.

3.2.1.3. N

[19] The suspended sediment mass concentration (M) is related to the number of particles per unit volume (N) as

display math(12)

where v(a) and ρ(a) are the volume and density, respectively of a particle of radius a.

[20] Under the assumption that the particles are spherical, N is given by

display math(13)

[21] For noncohesive sediments, e.g., marine quartz sands, equation (13) is relatively easy to evaluate, since particle density is constant and calculating n(a) is reasonably straightforward, e.g., through traditional techniques such as sieving. For the asymptotic case of uniform spherical grains of a single size, equation (13) reduces simply to inline image. In contrast, for flocculated sediments density decreases with floc size. Furthermore, flocs are fragile and susceptible to breakage, and therefore n(a) cannot be obtained through sieving.

[22] In order to obtain ρ(a) and n(a) so that N could be determined, the FLOCView system was employed. Optical systems [Dyer and Manning, 1999; Fennessy et al., 1994; Manning and Dyer, 1999, 2002; Mikkelsen et al., 2005; Smith and Friedrichs, 2011] such as FLOCView are extensively used in flocculation studies to measure various floc properties (e.g., size, shape, settling velocity, density). What follows is a description of the image processing procedure that ultimately yields ρ(a) and n(a) and therefore N.

[23] The automatic particle recognition system, which identifies and tracks particles, consists of two steps. The first involves segmentation of the FLOCView images to distinguish individual particles from the background. To do this the binary threshold method of Otsu [1979] was used. From the binary image, various particle parameters (size, shape, location) can be extracted; the two of most importance here are the two-dimensional projected area (A) and the particle location (centroid).

[24] The particle centroids were used to track the particles through consecutive images by minimizing the total squared displacement between all identified particles. This step was then repeated for all images within a settling experiment. Some simple additional intensity thresholding was necessary to ensure that only “in-focus” particles were included in the analyses.

[25] At the end of the particle recognition and tracking step, a list of frame number, centroid position and A for each tracked particle was generated. With the distance a particle moved between consecutive images and the time between images both known, the settling velocity (ws) of the particle can be determined. As a single particle is tracked through multiple images, the final step was to produce average particle quantities. Therefore, all quantities derived from FLOCView presented here are averages from each particle realization.

[26] At this stage of the analyses quantities derived from FLOCView are expressed in terms of pixel dimensions. In order to convert from pixel units to IS units, FLOCView was calibrated by taking images of a glass calibration slide. The calibration slide consisted of a grid of circles each with an area of 3.06×10−9 m2. From image analysis, the average number of pixels making up each circle was calculated to be 907; thus the area of each pixel was 3.38×10−12 m2 (1.84 µm × 1.84 µm).

[27] Due to the irregular morphologies of flocs (see Figure 2b) the definition of floc size is somewhat problematic. Following the works of [Graham and Nimmo Smith, 2010; Manning and Bass, 2006] the definition of the equivalent spherical radius is adopted, where a is given by

display math(14)

[28] Figure 5a shows an example of a size distribution obtained from the image analysis procedure. In order to calculate n(a) a log-normal distribution was fitted to the data using the maximum likelihood estimate method. The result of a fit to the size distribution shown in Figure 5a is shown in Figure 5b.

Figure 5.

FLOCView results for run 1, 3.2 g/l, FL1. (a) Particle size distribution. (b) Particle size probability density function. (c) Settling speed distribution. (d) Effective density distribution.

[29] Figure 5c shows the settling speed data that correspond to the size distribution shown in Figure 5a. With a and ws known, the effective density ( inline image) of the flocs can be estimated from a rearranged version of Stokes law:

display math(15)

where inline image is the density of the floc, inline image is the water density (assumed to be 1000 kg/m3), g is the acceleration due to gravity and inline image is the dynamic viscosity.

[30] Figure 5d shows the density estimates using the settling velocity data shown in Figure 5c. Figure 5d shows a decrease in floc density with floc size, with the largest flocs having densities of around 1001 kg/m3.

3.2.1.4. Viscous Absorption ( inline image)

[31] Using Urick's [1948] expression, acoustic attenuation due to viscous absorption for a suspension of spherical particles of radius a is given by

display math(16)

where

display math

with inline image and inline image, where ω is the acoustic angular frequency, ν is the kinematic viscosity of the ambient fluid, and ε is the volume concentration of scatterers. Equation (16) predicts that the viscous absorption depends linearly on sediment concentration. Experimental observations [Urick, 1948] using kaolin have shown that this assumption is valid up to mass concentrations of ca. 200 g/l (the maximum concentration considered here is 3.2 g/l).

[32] Figure 6 investigates the relative importance of the two attenuation terms (αv and αw) that are required to determine inline image. Figure 6a shows the ratio of viscous absorption to water absorption (i.e., αv/αw) as a function of particle radius (a) for the three frequencies used in this study. In Figure 6a, αv was calculated using a particle density of 2650 kg/m3 (i.e., the density of kaolin) and a suspended sediment concentration of 3.2 g/l. αw was calculated for freshwater at a temperature of 25°C. Figure 6a shows that αv is significantly larger than αw in the primary particle range, but for the range of flocculated particle sizes of interest here, αw is larger than αv. However, as an upper limit αv is ca. 20% of the value of αw, αv is thus too large to be ignored. However, as shown in Figure 5d flocs have densities which are considerably less than 2650 kg/m3. As floc density decreases with increase floc size (Figure 6b) αw becomes by far the dominant attenuation mechanism. As will be shown shortly (see Figure 8), the majority of flocs in this study have densities lower than 1100 kg/m3, in which case is αv negligible. We therefore conclude that the attenuation due to viscous absorption must be taken into account for primary particles, but can be neglected (i.e., αv=0) for flocs. The implications for this assumption are explored further in the discussion section.

Figure 6.

(a) Ratio of viscous absorption to water absorption (i.e., αvw) as a function of particle radius for the three transducer frequencies used in this study. (b) αvw for particles with densities of 2650, 1500, 1100, and 1050 kg/m3 for the 3 MHz transducer and a mass concentration of 3.2 g/l.

4. Results

4.1. Size Distributions

4.1.1. Primary Particles

[33] The size distributions of the primary kaolin particles measurement by the Malvern MasterSizer are shown Figure 7. The distribution labelled “raw” in Figure 7 is of a sample taken from the kaolin used in the experiments. The “raw” kaolin sample was continuously dispersed (by ultrasound) while the particle size distribution was measured, and therefore represents the distribution of the unflocculated primary particles. The remaining two distributions were measured from water samples taken from the recirculating tank immediately after the 20 min period of ABS measurements of the primary particles. The sample was transferred to the MasterSizer and measured as quickly as possible to minimize any potential changes to the particle size distribution. Figure 7 shows the distributions measured for the samples taken immediately after the 20 min period of ABS measurements are very similar to that of the “raw” primary particle distribution; it is therefore concluded that the methodology adopted to disaggregate the kaolin in the tank is working satisfactorily. Given how similar the three distributions were, the three were averaged together to form a single distribution that would represent the primary particle distribution in all experiments.

Figure 7.

Size distributions of the primary kaolin particles measurement by the Malvern MasterSizer.

Figure 8.

Effective density estimates for all identified flocs from all 15 experiments.

4.1.2. Flocculated Particles

[34] The number of particles identified for each experiment is shown in Table 1. The table shows a large variability in the number of identified particles, which typically increased with concentration. In a number of cases (e.g., 0.2 g/l run1 FL4) the number of identified particles was too low to provided robust estimates of n(a). By visual inspection of all the measured distributions, a minimum threshold of 150 particles was adopted and any distribution that contained fewer than 150 particles was removed from the analysis. The threshold of 150 represents a trade-off between accuracy and including as many distributions as possible. A table containing the coefficients for the log-normal distributions is available online in the supporting information.

Table 1. Number of Particles Detected by the Automatic Particle Recognition Systema
 Run 1Run 2Run 3
FL1FL2FL3FL4FL1FL2FL3FL4FL1FL2FL3FL4
  1. a

    Numbers in bold highlight distributions in which fewer than 150 particles were detected, and that were subsequently excluded from the analysis.

0.2 g/l441591221131164183444614026319
0.4 g/l5757211254119492203271127586987261
0.8 g/l44663640811157644503536232616861097717
1.6 g/l1082110513501004191597399318231524176220231225
3.2 g/l37071349579103920201610945630181410271398550

4.2. Floc Densities

[35] The estimates of effective density for all identified flocs from across all 15 experiments are shown in Figure 8. All floc effective density estimates were grouped together so that a single relationship between a and inline image could be derived. Due to the self-similar (fractal) geometry of flocs, a power law relationship between a and inline image is frequently applied [Curran et al., 2007; Fennessy et al., 1994; Graham and Nimmo Smith, 2010; Khelifa and Hill, 2006]. The solid black line in Figure 8 shows the result of fitting a power law to the measured effective densities.

4.3. η and κ

[36] From a possible 225, 193 valid estimates for η and κ (R2 > 0.95) were obtained from the experiments. Of the 32 experiments that failed to yield valid estimates, 30 of them arose from the suspensions of primary particles. The only valid estimates for η and κ for the runs involving primary particles occurred at mass concentrations of 1.6 and 3.2 g/l. Interestingly, even at low-mass concentrations the transition from primary particles to FL1 was sufficient to produce valid estimates of η and κ, which is potentially significant as it indicates a significant difference in the scattering characteristics of a suspension of primary particles compared to a suspension of flocs. A table containing the experimentally derived values for η and κ, including an estimate of their errors at the 95% confidence interval, is available online in the supporting information.

4.4. Scattering Properties

[37] An important question that can now be addressed is whether the scattering characteristics are controlled by the properties of the flocculated particles or by the constituent primary particles. This is addressed in Figure 9. In this figure, all the valid estimates of Ks are plotted against the mean particle radius, which is defined as

display math
Figure 9.

Measurements of Ks, including error bars (see text for explanation on how errors were calculated). The blue symbols are Ks derived using η obtained from the primary particles experiments and using the properties of the primary particles. The red symbols are derived using η obtained from the flocculated experiments (FL1–FL4) and the properties of the primary particles. Panels: (a) 3MHz, (b) 4 MHz, and (c) 5 MHz. The data displayed in this figure are available online in the supporting information.

[38] In Figure 9 two sets of Ks estimates (derived using equation (7)) are displayed. Here the blue symbols are Ks derived using η obtained from the primary particles experiments and using the properties of the primary particles (e.g., n(a), N and ρ(a)). The red symbols are derived using η obtained from the flocculated experiments (FL1–FL4) and the properties of the primary particles. As all Ks estimates shown in Figure 7 use the particle size distribution of the primary particles they all have the same a0. The idea here is that if the Ks values before aggregation (blue symbols) agree with those obtained after aggregation (red symbols) then the scattering characteristics are controlled by the primary particles and not by the properties of the flocs, but if they are different then the scattering characteristics are influenced by the presence of the flocs.

[39] In order to see if the Ks values are significantly different, error estimates in Ks are also shown in Figure 9. The goal of the error analysis is not to calculate the absolute error in Ks but to provide an assessment of the relative errors between Ks estimates. Equation (9) shows that Ks is a function of η, Kt, and N. As Kt is a constant throughout the experiments it does not contribute to the relative error between Ks estimates. Error estimates in η were derived at the 95% confidence interval. As the primary particle properties n(a) and ρ(a) have been assumed to be constant the relative source of error in estimating N comes from the concentration (M) measurements. To this point it was assumed that the actual concentration lay within 10% of the measured value.

[40] From Figure 9 it is apparent that the two sets of Ks values do not agree, furthermore the differences between the blue and red symbols are significant as the difference between the two is far greater than the variability predicted by the error analysis. This is an important result as it conclusively demonstrates that the acoustic properties of the flocculated particles are not solely controlled by the primary particles; some aspect of the floc structure is influencing the scattering characteristics.

[41] Particularly for the experiments performed at the lower concentrations, it was not possible to generate a complete set of Ks values from primary particle through to FL4. For the experiments in which a complete set of estimates was made the values are listed in Table 2; the numbers in the brackets are the ratio of flocculated Ks to the primary particle Ks. For all the experiments shown in Table 2, Ks shows a monotonic increase with the degree of flocculation.

Table 2. Ks Values for the Experiments in Which a Full Set of Ks Values Were Obtained From Primary Particle Through to floc Level 4 (FL4)
Concentration (g/l)RunFrequency (MHz)PPFL1FL2FL3FL4
1.6148.5E-103.1E-09 (3.7)5.8E-09 (6.9)6.6E-09 (7.8)7.0E-09 (8.3)
1.6159.9E-103.6E-09 (3.6)6.7E-09 (6.8)7.8E-09 (7.9)8.4E-09 (8.5)
1.6259.7E-103.7E-07 (3.8)6.4E-09 (6.6)7.5E-09 (7.7)7.8E-09 (8.1)
1.6347.2E-102.4E-09 (5.1)4.8E-09 (10.5)6.0E-09 (13.1)6.4E-09 (14.0)
1.6358.8E-103.8E-09 (8.2)6.9E-09 (15.1)7.9E-09 (17.1)8.0E-09 (17.4)
3.2134.6E-102.5E-09 (5.5)5.0E-09 (10.8)6.2E-09 (13.5)6.7E-09 (14.4)
3.2148.0E-103.2E-09 (4.1)6.4E-09 (8.1)6.7E-09 (8.5)7.5E-09 (9.5)
3.2151.5E-095.7E-09 (3.8)7.8E-09 (5.2)9.4E-09 (6.3)1.0E-08 (6.6)
3.2247.4E-103.0E-09 (4.1)5.2E-09 (7.1)6.8E-09 (9.2)7.0E-09 (9.5)
3.2251.3E-095.6E-09 (4.4)7.9E-09 (6.2)8.2E-09 (6.5)8.5E-09 (6.7)
3.2334.3E-102.6E-09 (6.1)5.0E-09 (11.5)6.1E-09 (14.1)6.2E-09 (14.4)
3.2346.6E-103.3E-09 (4.9)5.4E-09 (8.1)6.9E-09 (10.4)7.2E-09 (10.9)

[42] The results shown in Figure 9 and Table 2 clearly demonstrate that the scattering characteristics of flocculated particles are not solely controlled by the scattering characteristics of the constituent primary particles. Hence, we now investigate Ks and inline image in terms of the properties of the flocculated particles. Figure 10 displays inline image and Ks for the primary and flocculated distributions. The values for inline image and Ks shown in Figure 10 were derived using the corresponding particle properties, e.g., for the flocculated distributions the flocculated particle characteristics are used.

Figure 10.

Scattering properties derived from measurements: (a) Ks for primary particles. (b) Ks for flocculated distributions. (c) inline image for flocculated particles. The data displayed in this figure are available online in the supporting information.

[43] A limitation of our methodology is that inaccurate estimates for inline image can be generated for distributions of particles that only weakly backscatter sound (e.g., small particles). This occurs if the measured slope (κ) is comparable to twice the sum of the two attenuation terms (αv and αw) (see equation (6)). As a consequence of their small size and the high attenuation due to viscous absorption, no estimates for inline image can be derived for the distributions of primary particles.

[44] While Figure 10 shows some variability in the estimates for Ks and inline image, the trends in the data are clear: Ks and inline image both increase as the degree of flocculation increases (as indicated by an increase in a0). This is most evident when comparing the derived values for Ks for a suspension of flocculated particles to Ks for a suspension of primary particles.

[45] To compare our results with existing noncohesive data sets [Moate and Thorne, 2009; Sheng and Hay, 1988; Thorne and Meral, 2008] Ks and inline image were translated to inline image and inline image as follows

display math(17)
display math(18)

[46] For the asymptote of a single spherical grain size, equations (17) and (18) reduce to inline image and inline image respectively.

[47] The measured scattering properties now reported as inline image and inline image are compared to predictions from the ES and FS models in Figure 11. For the ES model it is assumed that the flocculated particle has the same physical characteristics as a solid kaolin particle. Hence, the values used in the ES model for a kaolin particle were compressional (cc) and shear wave (cs) velocities of 2056.9 m/s and 1519.1 m/s, respectively [Vanorio et al., 2003], and a solid density (ρs) of 2650 kg/m3.

Figure 11.

Model-data comparisons. (a) inline image for primary particles. (b) inline image for flocculated distributions. (c) inline image for flocculated particles. Colors represent transducer frequency: 3MHz (black), 4MHz (red) and 5 MHz (blue). The symbols represent: • Data, + ES model and □ FS model. The data displayed in this figure are available online in the supporting information.

[48] For the FS model, the two main parameters that need to be specified are the particle density and the compressional wave speed. Under the assumption of the FS model, a fluid particle cannot support shear waves (i.e., cs =0). Particle density was supplied via the relationships derived from the FLOCView measurements (see Figure 8). The compressional wave speed in the particle was modeled as

display math

where cc,f is the speed of sound in water (∼1500 m/s) and ϕ is the particle porosity, which is defined as

display math

[49] Because primary particles are solid, no predictions from the FS model were made for that case.

[50] From Figure 11a it is evident that for the suspensions of primary particles the measured values of inline image compare favorably to those predicted by the ES model. For a suspension of flocculated particles, Figures 11b and 11c show that the measured values of inline image and inline image tend to collapse onto a single line. Figures 11b and 11c also show that neither the ES nor the FS model adequately represents the scattering characteristics for a suspension of flocculated particles. Generally, the ES model overestimates the measured values of inline image and inline image, while the FS model underestimates the measured values of inline image and inline image.

5. Discussion

5.1. Ensemble Backscatter Form Function (Ks)

[51] The results presented here have shown that the scattering properties of cohesive fine sediments are greatly affected by the flocculation process. The results have conclusively demonstrated that the constituent primary particles do not control the scattering characteristics of a suspension the flocculated particles. The overall trend is for Ks to increase as the degree of flocculation increases, at least over the range of a0 values presented here.

5.2. Total Scattering Cross Section ( inline image)

[52] In calculating inline image for a suspension of flocculated particles it was assumed that the attenuation due to viscous absorption was negligible. Treating the flocs as solid particles with reduced density might not be a good approximation and, as a consequence, viscous absorption may still be important. If this were the case then the values for inline image shown in Figure 10c would be an overestimate, as some of the attenuation which was attributed to particle scattering would in fact have resulted from viscous absorption.

[53] The magnitude of viscous losses depends on the relative motion of the fluid and the particle [Hay and Burling, 1982]. In the case of flocs, the decrease in floc density with size, results in a decrease in the floc's particle relaxation time, which can be thought of as a measure of the particle's inertia with respect to the motion of the fluid. Given a reduction in the floc's density with size it would seem unlikely that viscous absorption would increase with floc size. That leaves two possibilities: the first is that the viscous absorption is controlled by the properties of primary particles and is therefore invariant with increasing floc size, and second that the losses from viscous absorption decrease with increasing floc size. If the viscous absorption is constant with size then, while an overestimate, the observed trend in inline image would remain unchanged. If the viscous absorption decreases with increasing floc size then the trends shown in Figure10c do not relate to inline image but to a combination of inline image and αv. Understanding how αv (and therefore inline image) changes with the degree of flocculation warrants further research.

[54] In natural energetic environments dominated by flocculated sediment, flocs have been observed to adjust their size to stay in equilibrium with the local smallest turbulent eddy length scale, i.e., the Kolmogorov microscale [Fugate and Friedrichs, 2003] so there remains a possibility that the floc size distribution evolved while the sample was transferred from the highly turbulent recirculation tank, via the pipette, to the quiescent FLOCview chamber. The greatest growth between the recirculation tank and the FLOCview chamber might be expected for the largest flocs, because they would be the most likely to have been broken up by shear in the recirculation tank and then could reform as shear disappeared in the pipette and FLOCView chamber. As the FLOCView chamber is initially filled with particle free water, flocs settling into the FLOCview chamber experience a significant reduction in the floc concentration. In turn, this reduction greatly reduces the chances of floc collisions resulting from differential settling. Given the quiescent nature of the FLOCview chamber differential settling would be the dominate flocculation mechanism. To this point, visual observations of flocs settling in the FLOCView chamber indicate that aggregation resulting from differential settling is negligible. While it is possible that floc evolution occurs within the pipette, the short residence time of the flocs while in the pipette would greatly limit the possibility of additional flocculation. Unfortunately, we have no way of checking on this evolution but, if it did occurred then the size distribution of flocs in the recirculation tank would be smaller than that measured by FLOCView, and hence values shown in Figure 10 for Ks and inline image would be an overestimate.

5.3. Model-Data Comparison

[55] The observations show that neither the ES nor the FS models in their current form are capable of adequately predicting the scattering characteristics of a suspension of flocculated particles. These two models were selected as they potentially span the transition from solid (primary) particles to large fluid-like flocs. While the two models did provide upper (ES) and lower (FS) bounds to the measurements, the transition from solid to fluid-like particles did not follow expectations. It would seem reasonable to hypothesize that the ES model would work better on the suspension of primary particles, and then as flocculation took place, the measurements would tend toward the FS predictions. If anything, the observations tend more toward the predictions of the ES model as the degree of flocculation increases.

[56] Although the observations show that neither the ES nor the FS model is a good predictor for the backscatter from flocs, there are some very encouraging signs which suggest the ABS may be a useful tool for measuring the concentration of flocculated sediment. Observed inline image values for primary particles are close to those predicted by the ES model. In terms of the flocculated particles, the most promising feature is how the observations for inline image and inline image collapse onto a single curve (when plotted against x). From this it would seem reasonable to assume that flocs scatter sound in a systematic and predictable fashion. Given the rather disappointing performance of both the ES and FS models in their existing form, a new theoretical scattering model for flocculated particles is required. Progress is required in two fundamental areas. First, the scattering model must incorporate an intrinsic feature of flocculated particles, this being the observed decrease in floc density with increasing floc size. Second, investigations are required to identify what type of waves propagate in flocs: compressional or shear or both? Furthermore, an important aspect of this work will be developing relationships that predict how Cc and Cs vary with floc density.

[57] The starting point for incorporating the decrease in floc density with increasing floc size in the scattering model is to describe flocs as fractal objects [Dyer and Manning, 1999; Jiang and Logan, 1991; Kranenburg, 1994; Lee et al., 2002; Li et al., 1998, 2004]. The key relationship when using a fractal description of flocs is that the mass of a floc (mf) scales with the floc diameter (d) as

display math

where Df is the fractal dimension.

[58] Using a fractal description Lee et al. [2000] developed expressions for various floc properties. The expression of most interest here is the density-size relationship which is given by

display math

where d0 is the diameter of the primary particles. Incorporating this type of equation into scattering equations would produce the required density-size dependence.

[59] In the theory outlined by Buckingham [2000] for wave propagation in saturated, unconsolidated marine bed sediments, algebraic expressions for Cc and Cs, which are functions of sediment porosity and acoustic frequency, are derived. The application or the adaptation of these expressions to flocculated particles warrants further consideration.

5.4. Operational Considerations

[60] In terms of the purely operational use of acoustics for measuring the concentration of flocculated sediments, an empirical or heuristic relationship could be fitted to the observations. Such an approach is routinely used for determining the scattering characteristics of noncohesive sediments [Moate and Thorne, 2009; Sheng and Hay, 1988; Thorne and Hanes, 2002].

[61] Figure 12 shows the results of fitting our measured values of inline image and inline image for flocculated distributions to the heuristic expressions proposed by Moate and Thorne [2009] (their equations (18) and (18)). From Figure 12 it is apparent that a reasonable fit between measurements and the expression of Moate and Thorne [2009] can be achieved. This result highlights the potential suitability of such an approach for a suspension of flocculated particles. The dashed line in Figure 12 shows the expression of Moate and Thorne [2009] derived from measurements of a suspension of quartz sediments. A comparison of the dashed and solid line shows that the values for inline image and inline image for flocculated kaolin particles are several orders of magnitude smaller than those for quartz sediments. This result clearly demonstrates that expressions derived for quartz are not suitable for use on flocculated particles. From a sedimentologist's point of view, it is use of inline image and inline image in the inverse problem [Lee and Hanes, 1995; Moate and Thorne, 2009; Thorne and Hanes, 2002; Thosteson and Hanes, 1998] which yields estimates of concentration and particle size that is of primary interest.

Figure 12.

Results of fitting measured values of (a) inline image and (b) inline image to the heuristic expression of Moate and Thorne [2008].

[62] In terms of estimating concentration and particle size from a suspension of flocculated kaolin particles the heuristic expressions derived for inline image and inline image in this study could form the basis of such an inversion. However, until a better theoretical understanding of how sound interacts with flocculated particles is achieved, the fitting of such empirical relations may be somewhat premature.

6. Conclusions

[63] The measurements presented here have shown that the scattering properties of cohesive fine sediments are greatly affected by the flocculation process. Perhaps the most fundamental result is that the measurements have conclusively demonstrated that the constituent primary particles do not solely control the scattering characteristics of a suspension the flocculated particles.

[64] Over the range of floc sizes investigated here, the overall trend is for the ensemble backscatter form function (Ks) to increase as the degree of flocculation increases. This trend was also observed in total scattering cross section ( inline image) but this result is dependent on the assumption that viscous absorption for flocculated particles is negligible. Further investigation on how viscous absorption is affected by flocculation is a key research question that merits further consideration.

[65] The results have also shown that, in their current form, neither the elastic or the FS model is capable of adequately representing the scattering characteristics of a suspension of flocculated particles, although the two models did provide upper (ES) and lower (FS) bounds to the measurements.

[66] In terms of the operational use of acoustics to measure the concentration of flocculated sediments, empirical or heuristic relationships could be fitted to the observations but, until a better theoretical understanding of how sound interacts with flocculated particles is achieved, the fitting of such empirical relations may be somewhat premature.

Appendix A: Model Terms

[67] For the ES model inline image is given [Gaunaurd and Überall, 1983]

display math

and

display math
display math
display math
display math
display math
display math
display math

where inline image is the spherical Bessel function, inline image is the Hankel function, the primes denote first derivatives, c is the speed of sound in the fluid, cs and cc are the shear and compressional wave speeds respectively, inline image is the fluid density and inline image is the density of the particle.

[68] For the FS model inline image is given by Anderson [1950]

display math

and

display math
display math

where inline image is the spherical Neumann function, inline image and inline image are the wave number in the fluid medium and in the FS respectively, inline image is the density of the FS, inline image is the speed of sound in the FS, and all other terms are previously defined.

Acknowledgments

[69] This work is supported by the UK Natural Environment Research Council project FLOCSAM. The authors would like to acknowledge their coresearchers at the University of Plymouth. I.T.M. would like to thank G. Flowerdue and S. Rix for manufacturing several parts for the recirculation tank. We would also like to thank Malcom Green for his valuable input into the manuscript. The authors would like to thank the reviewers of an earlier version of this paper for their valuable comments and suggestions which have been incorporated into this revised version.

Ancillary