3. Results

## 3.1. Experiments with cohesive sediments coming from food for fish

A first analysis of particles coming from fish food, using a Coulter counter analyzer, which destroys flocs, is shown below. The pellets were previously sieved and only those passing sieve 200 (0.075 mm) were conserved. It is observed (see Figure 4) that an average diameter of primary particles is 28 μm.

Using the same fish food sediments optical methods were developed in a sedimentation tank. The following settling velocities were obtained at 60 cm from the top of the sedimentation tank by using PTV. It is observed in Table 2 that the settling velocity increases until a certain value (D = 200 μm) and then decreases for larger floc diameters. This behavior is not reflected in classical settling velocity models.

at 15 min (t = 15), at 45 min (t = 45) and at 1 h (t = 60). An average diameter of primary particles of

Floc size 75 100 150 200 250 300 350 400 Ws (cm/s) 0.51 0.62 0.68 0.8 0.79 0.74 0.66 0.54

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Table 2. Average settling velocities for fish food in a sedimentation tank (cm/s).

In the experiments using the reduced model of an aquaculture recirculation tank, Eqs. (6) and (7) were used for the statistical analysis in order to define the parameters n, α and β. These parameters were defined according to the best correlation coefficient in the relationships Ws vs. D and F vs. D/d. Figure 6 shows the best fit of F vs. D/d according to Eq. (7). Table 3 shows

The average value for the coefficient α was 0.077 and the average value of the coefficient β was 0.726. The latter exponent value is larger than the one obtained by [22] for a similar model, which can be explained with the structure of aquaculture flocs compared to Kaolinite, which is

Figure 7a–d shows the best fit relationship between Ws and D using the F vs. D/d relationship previously obtained. The resulting n values at different time steps are specified in Table 4.

Table 4 shows that the value of n increases as the time of the experiment increases. This observation can be related to the increasing loss of density of the floc. As time increases, the flocs are increasing their volume absorbing water. The latter has two implications; the drag

An interesting feature observed in Figure 7a–d is that the settling velocity of the flocs increases for values of floc diameter up to 600 μm and then decreases as floc diameter continues to increase. The settling velocity model proposed in this research is able to reproduce this behavior.

coefficient decreases because the floc becomes more porous and its density decreases.

28 μm was confirmed. Thus, this result was used in the statistical analysis.

Figure 5. Representative values of fish food primary particles obtained by TEM.

the values of α and β obtained at each time.

completely different.

### 3.2. Experiments with real flocs from an aquaculture recirculation tank

Next long-term experiments were performed in a reduced model of an aquaculture recirculation tank (Figure 1), flocs diameters and the corresponding settling velocities were measured for different times using PTV. The sediments used were real flocs coming from a large aquaculture recirculation tank (El Zarco). Some selected samples of the experiments were analyzed by Transmission Electron Microscopy (TEM) (Figure 5), at the beginning of the experiment (t = 0),

Figure 4. Fish food particle sizes from coulter counter (LS 100Q) analysis.


Table 2. Average settling velocities for fish food in a sedimentation tank (cm/s).

For application and calibration of a DH optical system, cohesive sediments from a waste water plant were used. A coagulant was added in order to allow floc formation in the rotating

Holographic images acquired and improved are reconstructed numerically in order to obtain

A first analysis of particles coming from fish food, using a Coulter counter analyzer, which destroys flocs, is shown below. The pellets were previously sieved and only those passing sieve 200 (0.075 mm) were conserved. It is observed (see Figure 4) that an average diameter of

Using the same fish food sediments optical methods were developed in a sedimentation tank. The following settling velocities were obtained at 60 cm from the top of the sedimentation tank by using PTV. It is observed in Table 2 that the settling velocity increases until a certain value (D = 200 μm) and then decreases for larger floc diameters. This behavior is not reflected in

Next long-term experiments were performed in a reduced model of an aquaculture recirculation tank (Figure 1), flocs diameters and the corresponding settling velocities were measured for different times using PTV. The sediments used were real flocs coming from a large aquaculture recirculation tank (El Zarco). Some selected samples of the experiments were analyzed by Transmission Electron Microscopy (TEM) (Figure 5), at the beginning of the experiment (t = 0),

The physical components of the digital holographic system used are described in Table 1.

3D characteristics of flocs. The Fresnel method was used for image reconstruction [31].

3.1. Experiments with cohesive sediments coming from food for fish

3.2. Experiments with real flocs from an aquaculture recirculation tank

Figure 4. Fish food particle sizes from coulter counter (LS 100Q) analysis.

annular flume.

118 Applications in Water Systems Management and Modeling

3. Results

primary particles is 28 μm.

classical settling velocity models.

Figure 5. Representative values of fish food primary particles obtained by TEM.

at 15 min (t = 15), at 45 min (t = 45) and at 1 h (t = 60). An average diameter of primary particles of 28 μm was confirmed. Thus, this result was used in the statistical analysis.

In the experiments using the reduced model of an aquaculture recirculation tank, Eqs. (6) and (7) were used for the statistical analysis in order to define the parameters n, α and β. These parameters were defined according to the best correlation coefficient in the relationships Ws vs. D and F vs. D/d. Figure 6 shows the best fit of F vs. D/d according to Eq. (7). Table 3 shows the values of α and β obtained at each time.

The average value for the coefficient α was 0.077 and the average value of the coefficient β was 0.726. The latter exponent value is larger than the one obtained by [22] for a similar model, which can be explained with the structure of aquaculture flocs compared to Kaolinite, which is completely different.

Figure 7a–d shows the best fit relationship between Ws and D using the F vs. D/d relationship previously obtained. The resulting n values at different time steps are specified in Table 4.

Table 4 shows that the value of n increases as the time of the experiment increases. This observation can be related to the increasing loss of density of the floc. As time increases, the flocs are increasing their volume absorbing water. The latter has two implications; the drag coefficient decreases because the floc becomes more porous and its density decreases.

An interesting feature observed in Figure 7a–d is that the settling velocity of the flocs increases for values of floc diameter up to 600 μm and then decreases as floc diameter continues to increase. The settling velocity model proposed in this research is able to reproduce this behavior.

Figure 6. Fractal dimension vs. D/d: (a) at time 0 (upper left), (b) at time 15 min (upper right), (c) at time 45 min (lower left), and (d) at time 60 min (lower right).


Table 3. Best fit coefficients for the relationship F vs. D.

This behavior has been shown to occur in nature for different kind of flocs, coming from estuaries, waste water treatment plants, and rivers [10, 19]. Most of the settling velocity models for cohesive sediments show an increase of settling velocity for all diameters which is not observed in this research. The larger flocs are formed after a long experimental period. In Figure 7a and b, there are few flocs larger than 600 μm, which is not the case for experimental periods of 45 and 60 min (Figure 7c and d). The practical implication of this phenomenon for aquaculture recirculation tanks is that residence times should not be very long because the larger flocs formed are even more difficult to settle down.

was located before the junction with the Usumacinta, and in the Usumacinta, it was located 20 km upstream of the junction with the Grijalva. Samples were obtained at three vertical water columns in each cross section. For the Grijalva River, the samples were obtained at levels varying from 0.5 to 11 m (maximum water depth) each 1 m. At the Usumacinta River, samples were obtained at levels varying from 0.5 to 17 m (maximum water depth) each 1 m. Figures 8 and 9 show the suspended sediment concentration profiles for the Grijalva and Usumacinta Rivers, respectively. In these figures, the vertical axis refers to the level z adimentionized with the flow depth H, while the horizontal axis refers to the ratio of the concentration C to a reference

Figure 7. Settling velocity vs. D: (a) at time 0 (upper left), (b) at time 15 min (upper right), (c) at time 45 min (lower left),

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An average value of Rouse parameter ZR = 0.214 was obtained in the Grijalva River, which is

An average value of ZR = 0.069 was obtained in the Usumacinta river. This value is represen-

representative of a small increase of suspended sediment charge near the bottom.

tative of near constant suspended sediment charge in the water column.

concentration Ca.

and (d) at time 60 min (lower right).

Time (min) n 0 1.1 15 1.15 45 1.2 60 1.25

Table 4. Values of n for best fit relationship between Ws vs. D.

#### 3.3. Experiments with suspended cohesive sediments of Grijalva and Usumacinta rivers

A sampling of suspended cohesive sediments in the Grijalva and Usumacinta rivers was done during high river level on the month of December 2016. The sampling location for the Grijalva

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Figure 7. Settling velocity vs. D: (a) at time 0 (upper left), (b) at time 15 min (upper right), (c) at time 45 min (lower left), and (d) at time 60 min (lower right).


Table 4. Values of n for best fit relationship between Ws vs. D.

This behavior has been shown to occur in nature for different kind of flocs, coming from estuaries, waste water treatment plants, and rivers [10, 19]. Most of the settling velocity models for cohesive sediments show an increase of settling velocity for all diameters which is not observed in this research. The larger flocs are formed after a long experimental period. In Figure 7a and b, there are few flocs larger than 600 μm, which is not the case for experimental periods of 45 and 60 min (Figure 7c and d). The practical implication of this phenomenon for aquaculture recirculation tanks is that residence times should not be very long because the larger

Figure 6. Fractal dimension vs. D/d: (a) at time 0 (upper left), (b) at time 15 min (upper right), (c) at time 45 min (lower

Time (min) α β 0.070 0.703 0.049 0.863 0.111 0.609 0.077 0.727

3.3. Experiments with suspended cohesive sediments of Grijalva and Usumacinta rivers

A sampling of suspended cohesive sediments in the Grijalva and Usumacinta rivers was done during high river level on the month of December 2016. The sampling location for the Grijalva

flocs formed are even more difficult to settle down.

Table 3. Best fit coefficients for the relationship F vs. D.

left), and (d) at time 60 min (lower right).

120 Applications in Water Systems Management and Modeling

was located before the junction with the Usumacinta, and in the Usumacinta, it was located 20 km upstream of the junction with the Grijalva. Samples were obtained at three vertical water columns in each cross section. For the Grijalva River, the samples were obtained at levels varying from 0.5 to 11 m (maximum water depth) each 1 m. At the Usumacinta River, samples were obtained at levels varying from 0.5 to 17 m (maximum water depth) each 1 m. Figures 8 and 9 show the suspended sediment concentration profiles for the Grijalva and Usumacinta Rivers, respectively. In these figures, the vertical axis refers to the level z adimentionized with the flow depth H, while the horizontal axis refers to the ratio of the concentration C to a reference concentration Ca.

An average value of Rouse parameter ZR = 0.214 was obtained in the Grijalva River, which is representative of a small increase of suspended sediment charge near the bottom.

An average value of ZR = 0.069 was obtained in the Usumacinta river. This value is representative of near constant suspended sediment charge in the water column.

Figure 8. Suspended sediment concentration profiles for the Grijalva River. (a) 55 m from left bank and (b) 90 m from left bank.

Figure 9. Suspended sediment concentration profiles for Usumacinta river. (a) 25 m from left bank and (b) 140 m from left bank.

Experiments in the rotating annular flume using 50 L samples for the Grijalva and Usumacinta rivers were performed at shear rates similar to those encountered in the field. Table 5 shows the values of shear velocity (u\*) obtained in the sampling stations of the Grijalva (width 180 m) and Usumacinta (width of 340 m) rivers. The value of u\* was obtained by the horizontal u' and vertical fluctuating velocities w' (u<sup>∗</sup> <sup>2</sup> <sup>¼</sup> <sup>u</sup><sup>0</sup> w0Þ, where the over bar indicates an average over the water depth. The velocities were measured the same day of suspended sediment sampling with an Acoustic Doppler Current profiler (ADCP).

Images of flocs after experimental runs of 1.5 h in the Grijalva river samples and 3.5 h in the Usumacinta river samples, in the annular flume using PTV, gave us an average size of flocs of 307 μm in the Grijalva and 209 μm in the Usumacinta. Table 6 shows the statistical values of flocs obtained in large runs at a shear velocity u\* = 0.070 m/s (the average value in the Usumacinta river see Table 5) and Table 7 at u\* = 0.043 m/s (the average value at the Grijalva river, see Table 5).

river, gave an estimated value of 1.2 μm for the Grijalva river and 3.8 μm for the Usumacinta.

River Distance from left bank (m) u\* (m/s) Grijalva 55 0.048

Usumacinta 25 0.064

Time (min) D (μm) Number of data

Table 6. Average floc size at the Usumacinta River from PTV experiments in the rotating annular flume.

Time (min) D (μm) Number of data

Table 7. Average floc size at the Grijalva River from PTV experiments in the rotating annular flume.

 306 33,434 308 25,550 313 22,652 311 21,321 297 23,460

 217 33,200 188 17,254 172 21,542 164 12,232 242 32,560 247 25,441 232 23,450

90 0.045 195 0.036

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140 0.082 210 0.065

When Eq. (6) is used along with the already found average values of D and d, the values of settling velocity are obtained for different floc sizes (Table 8) using Eq. (7), with values of α = 0.07 and β = 0.72. The values of S were 1.29 for the Usumacinta river and 1.55 for the Grijalva river. Different values of n (Table 8) were used to show the sensitivity of the model to

Two representative images are shown in Figures 10 and 11.

Table 5. Shear velocity in Usumacinta and Grijalva rivers.

Mean 209

Mean 307

this compaction index.

Also, microscopic images of some representative flocs were obtained with 40� magnification. An average value of primary particle, after a statistical analysis of 50 flocs images for each

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Table 5. Shear velocity in Usumacinta and Grijalva rivers.

Experiments in the rotating annular flume using 50 L samples for the Grijalva and Usumacinta rivers were performed at shear rates similar to those encountered in the field. Table 5 shows the values of shear velocity (u\*) obtained in the sampling stations of the Grijalva (width 180 m) and Usumacinta (width of 340 m) rivers. The value of u\* was obtained by the horizontal u' and

Figure 9. Suspended sediment concentration profiles for Usumacinta river. (a) 25 m from left bank and (b) 140 m from left

Figure 8. Suspended sediment concentration profiles for the Grijalva River. (a) 55 m from left bank and (b) 90 m from left

water depth. The velocities were measured the same day of suspended sediment sampling

Images of flocs after experimental runs of 1.5 h in the Grijalva river samples and 3.5 h in the Usumacinta river samples, in the annular flume using PTV, gave us an average size of flocs of 307 μm in the Grijalva and 209 μm in the Usumacinta. Table 6 shows the statistical values of flocs obtained in large runs at a shear velocity u\* = 0.070 m/s (the average value in the Usumacinta river see Table 5) and Table 7 at u\* = 0.043 m/s (the average value at the Grijalva river, see Table 5).

Also, microscopic images of some representative flocs were obtained with 40� magnification. An average value of primary particle, after a statistical analysis of 50 flocs images for each

w0Þ, where the over bar indicates an average over the

<sup>2</sup> <sup>¼</sup> <sup>u</sup><sup>0</sup>

vertical fluctuating velocities w' (u<sup>∗</sup>

122 Applications in Water Systems Management and Modeling

bank.

bank.

with an Acoustic Doppler Current profiler (ADCP).


Table 6. Average floc size at the Usumacinta River from PTV experiments in the rotating annular flume.


Table 7. Average floc size at the Grijalva River from PTV experiments in the rotating annular flume.

river, gave an estimated value of 1.2 μm for the Grijalva river and 3.8 μm for the Usumacinta. Two representative images are shown in Figures 10 and 11.

When Eq. (6) is used along with the already found average values of D and d, the values of settling velocity are obtained for different floc sizes (Table 8) using Eq. (7), with values of α = 0.07 and β = 0.72. The values of S were 1.29 for the Usumacinta river and 1.55 for the Grijalva river. Different values of n (Table 8) were used to show the sensitivity of the model to this compaction index.

Table 8 shows that the best estimation of ZR for the Usumacinta river is obtained with n = 1.1 because the average measured ZR (see Figure 8) was ZR = 0.069. Similarly, the best estimation of ZR for the Grijalva river is also obtained with n = 1.1 because the average measured ZR (see Figure 9) was ZR = 0.214. The larger concentrations near the bottom for the Grijalva river are explained by the larger size of flocs in this river (307 μm compared to 209 μm for the Usumacinta). These results indicate that flocs of both rivers are strong flocs (low values of n), which is logical because shear rates at the Usumacinta and Grijalva rivers are high (for comparison u\* at Amazon River varies between 0.07 and 0.1 [1]). It is also observed that the value of ZR in the Usumacinta river is more sensitive to changes in the value of n. It was observed that for large depths it is more difficult to define the n value as it can change even in the same cross section of

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Figure 12 shows the hologram reconstruction of a spherical particle of 50 μm. Figure 12a shows the particle's hologram already filtered, where the different patterns of diffraction are observed; Figure 12b provides greater detail. The relative intensity profile (I/Imax) vs. reconstruction distance (z) is shown in Figure 12c. The maximum intensity is shown where the particle is in focus. Figure 13a shows the digital hologram of flocs, while Figure 13b shows a preprocess in order to avoid noise in the hologram. Rings of interference are observed in both figures, which define the 3D characteristics of the flocs. Figure 13c shows the reconstruction of the binary image. This image only shows the particles that are in the best focus, i.e., where the shape of the particle is clearly defined. In order to find the position in the plane, the diameter, and shape of

Ws (mm/s) ZR

Usumacinta Grijalva Usumacinta Grijalva

1.1 0.19 3.84 0.07 0.223 1.15 0.16 3.87 0.05 0.225 1.2 0.13 3.91 0.04 0.227 1.25 0.10 3.95 0.03 0.229

Figure 12. Results of a reconstruction of hologram process. (a) Originally filtered hologram; (b) one particle hologram;

the river at different levels.

n

3.4. Experiments using digital holography for PIV

Table 8. Estimated values of Ws and corresponding values of ZR.

(c) relative intensity profile, and (d) reconstructed particle.

Figure 10. Primary particles and flocs representative of the Grijalva river.

Figure 11. Primary particles and flocs representative of the Usumacinta river.

Table 8 shows that the best estimation of ZR for the Usumacinta river is obtained with n = 1.1 because the average measured ZR (see Figure 8) was ZR = 0.069. Similarly, the best estimation of ZR for the Grijalva river is also obtained with n = 1.1 because the average measured ZR (see Figure 9) was ZR = 0.214. The larger concentrations near the bottom for the Grijalva river are explained by the larger size of flocs in this river (307 μm compared to 209 μm for the Usumacinta).

These results indicate that flocs of both rivers are strong flocs (low values of n), which is logical because shear rates at the Usumacinta and Grijalva rivers are high (for comparison u\* at Amazon River varies between 0.07 and 0.1 [1]). It is also observed that the value of ZR in the Usumacinta river is more sensitive to changes in the value of n. It was observed that for large depths it is more difficult to define the n value as it can change even in the same cross section of the river at different levels.
