2.1. Experiments using PTV and sediments coming from aquaculture recirculation tanks

Initial experiments were performed with fish food in order to have a better control of primary particles. The sediments where sieved and only those passing sieve 200 (0.075 mm), with a mean density of 1430 kg/m3 were used. A Plexiglas settling column was realized in order to allow the use of PIV and PTV optical methods. The set up consisted of a rectangular tank of cross section 15.5 15.5 cm and 100 cm height. A laser sheet was introduced from above using a double pulsed Nd:Yag laser (15 mJ), high-speed CCD cameras JAI (250 fps and resolution and 1600 � 1400 pixels) were mounted laterally to the column and synchronized by means of a NI-PCIE-1430 card with laser pulses. Both cameras where equipped with 50 mm NIKKON lenses. The cohesive sediments were introduced manually and images were captured at the 30, 60, and 90 cm marks from the bottom of the tank. The resulting frequency histograms are presented in the following of the paper. For the processing of the images, the software used was PTV-SED v2.1, developed at CIRA to analyze the fall velocity of sedimentary particles in two-phase flows. PTV operation comprises of two sequential procedures. The first procedure implies improving image quality through spatial filtering. The second procedure implies detecting particles in each pulse following the five stages proposed: (i) identify maximum and minimum intensity (black or white) over the particle image to determine its size; (ii) from the intensity of pixels of the evaluated particle, a circular area is formed which can be used to determine the cross-sectional particle area (A), and then the equivalent diameter (d) can be estimated using <sup>d</sup> <sup>¼</sup> <sup>2</sup> ffiffiffiffiffiffi <sup>A</sup>=<sup>π</sup> p 1; (iii) from the cross-sectional particle area (A) and pixel intensity, the coordinates (x, y) of the drop centroid are determined; (iv) pairs of double-pulsed particle are identified and the distance separating their centroids (Δx, Δy) is determined; and (v) Particle velocity (vx, vy) is obtained as follows:

$$(v\mathbf{x}, v\mathbf{y}) = \left(\frac{\Delta \mathbf{x}}{\Delta t}, \frac{\Delta \mathbf{y}}{\Delta t}\right) \tag{1}$$

r<sup>f</sup> � r<sup>w</sup> ¼ r<sup>p</sup> � r<sup>w</sup>

can be used for non-spherical particles with equivalent diameters.

Ws 2 ¼

Eqs. (2) and (3), the following relationship for the settling velocity is obtained

Ws ¼

defined as Rep = WsD/ν where ν is the kinematic viscosity of the fluid.

A balance of drag forces and gravitational forces gives Eq. (3)

with S is the primary particles relative density.

Figure 2. Rotating annular flume and PTV set up.

velocity is obtained:

� � D

where rf, rw, and r<sup>p</sup> are densities of floc, water, and primary particles, respectively, D is the floc diameter and d is the primary particles diameter. F is the fractal dimension and the model assumes that the floc is constituted of spherical primary particles of equal diameter. The model

> 4 r<sup>f</sup> � r<sup>w</sup> � �gD

where Ws is the floc settling velocity and CDf is the permeable particle drag coefficient. Using

Using Particle Tracking Velocimetry methods (PTV), Garcia Aragon et al. [19] have shown that a useful relationship for the drag coefficient of a permeable floc has the following form:

CDf <sup>¼</sup> <sup>15</sup>

where the coefficient n depends on the kind of floc and varies, according to a comparison of results of different authors [20], between 1.1 and 1.25. Rep is the particle Reynolds number

Replacing the relationship from Eq. (5) in Eq. (4), the following relationship for the settling

3CDf r<sup>w</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>4</sup>ð Þ <sup>S</sup> � <sup>1</sup> g Dð Þ<sup>F</sup>�<sup>2</sup> <sup>3</sup>CDfð Þ<sup>d</sup> <sup>F</sup>�<sup>3</sup>

vuut (4)

Optical Methods Applied to Hydrodynamics of Cohesive Sediments

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Rep<sup>n</sup> (5)

d � �<sup>F</sup>�<sup>3</sup>

(2)

115

(3)

Then a small scale water recirculation tank made of Plexiglas 35 cm in depth and with 1.03 m diameter was used in the experiments with the same cohesive sediments from fish food. A complete system for water recirculation (Figure 1) was implemented. Water is obtained by a high rise tank with a constant water level in order to supply a constant flow rate by using gravity. Diffusers at different levels on the tank wall control the flow rate and tank water velocity, together with the generation of the circular flow. A settling device in the center of the tank allows solids removal.

Using this recirculation tank settling velocities and sizes of sediments were obtained from commonly used fish food and excreta coming from experimental station El Zarco, which cultivates trout. It is owned by Semarnap, the Mexican state agency of environment, natural resources, and fisheries, and is located at 2800 masl in Salazar Estado de México, México.

The next stage consisted to analyze suspended cohesive sediments coming from the Usumacinta and Grijalva rivers in México. In order to reproduce hydrodynamic conditions prevailing in the river and to analyze the flocculation process during long range experiments, an annular rotating flume, 1.3 m diameter and 15 � 15 cm flume cross section made of Plexiglas, was used (Figure 2). The cohesive sediments were analyzed using PTV, during 1.5 h. long experiments and images were taken every 15 min. From this experiment floc sizes and settling velocities were obtained.

#### 2.2. Theoretical settling velocity models

The greatest challenge in the proposal of a settling velocity model for flocs is the adequate definition of their density. Many models have been formulated for floc density [17], in this research the adopted model is the one proposed by Kranenburg [18], as shown in Eq. (2)

Figure 2. Rotating annular flume and PTV set up.

pulsed Nd:Yag laser (15 mJ), high-speed CCD cameras JAI (250 fps and resolution and 1600 � 1400 pixels) were mounted laterally to the column and synchronized by means of a NI-PCIE-1430 card with laser pulses. Both cameras where equipped with 50 mm NIKKON lenses. The cohesive sediments were introduced manually and images were captured at the 30, 60, and 90 cm marks from the bottom of the tank. The resulting frequency histograms are presented in the following of the paper. For the processing of the images, the software used was PTV-SED v2.1, developed at CIRA to analyze the fall velocity of sedimentary particles in two-phase flows. PTV operation comprises of two sequential procedures. The first procedure implies improving image quality through spatial filtering. The second procedure implies detecting particles in each pulse following the five stages proposed: (i) identify maximum and minimum intensity (black or white) over the particle image to determine its size; (ii) from the intensity of pixels of the evaluated particle, a circular area is formed which can be used to determine the cross-sectional particle area (A), and

particle area (A) and pixel intensity, the coordinates (x, y) of the drop centroid are determined; (iv) pairs of double-pulsed particle are identified and the distance separating their centroids (Δx, Δy)

Then a small scale water recirculation tank made of Plexiglas 35 cm in depth and with 1.03 m diameter was used in the experiments with the same cohesive sediments from fish food. A complete system for water recirculation (Figure 1) was implemented. Water is obtained by a high rise tank with a constant water level in order to supply a constant flow rate by using gravity. Diffusers at different levels on the tank wall control the flow rate and tank water velocity, together with the generation of the circular flow. A settling device in the center of the

Using this recirculation tank settling velocities and sizes of sediments were obtained from commonly used fish food and excreta coming from experimental station El Zarco, which cultivates trout. It is owned by Semarnap, the Mexican state agency of environment, natural resources, and fisheries, and is located at 2800 masl in Salazar Estado de México, México.

The next stage consisted to analyze suspended cohesive sediments coming from the Usumacinta and Grijalva rivers in México. In order to reproduce hydrodynamic conditions prevailing in the river and to analyze the flocculation process during long range experiments, an annular rotating flume, 1.3 m diameter and 15 � 15 cm flume cross section made of Plexiglas, was used (Figure 2). The cohesive sediments were analyzed using PTV, during 1.5 h. long experiments and images were taken every 15 min. From this experiment floc sizes

The greatest challenge in the proposal of a settling velocity model for flocs is the adequate definition of their density. Many models have been formulated for floc density [17], in this research the adopted model is the one proposed by Kranenburg [18], as shown in Eq. (2)

Δx Δt ; Δy Δt � �

ð Þ¼ vx; vy

<sup>A</sup>=<sup>π</sup>

p 1; (iii) from the cross-sectional

(1)

then the equivalent diameter (d) can be estimated using <sup>d</sup> <sup>¼</sup> <sup>2</sup> ffiffiffiffiffiffi

114 Applications in Water Systems Management and Modeling

is determined; and (v) Particle velocity (vx, vy) is obtained as follows:

tank allows solids removal.

and settling velocities were obtained.

2.2. Theoretical settling velocity models

$$
\rho\_f - \rho\_w = \left(\rho\_p - \rho\_w\right) \left(\frac{D}{d}\right)^{F-3} \tag{2}
$$

where rf, rw, and r<sup>p</sup> are densities of floc, water, and primary particles, respectively, D is the floc diameter and d is the primary particles diameter. F is the fractal dimension and the model assumes that the floc is constituted of spherical primary particles of equal diameter. The model can be used for non-spherical particles with equivalent diameters.

A balance of drag forces and gravitational forces gives Eq. (3)

$$\left|\mathcal{W}\_s\right|^2 = \frac{4\left(\rho\_f - \rho\_w\right)gD}{\mathfrak{K}\_{Df}\rho\_w} \tag{3}$$

where Ws is the floc settling velocity and CDf is the permeable particle drag coefficient. Using Eqs. (2) and (3), the following relationship for the settling velocity is obtained

$$W\_s = \sqrt{\frac{4(\mathcal{S} - 1)\mathcal{g}(D)^{F-2}}{\mathfrak{NC}\_{D'}(d)^{F-3}}} \tag{4}$$

with S is the primary particles relative density.

Using Particle Tracking Velocimetry methods (PTV), Garcia Aragon et al. [19] have shown that a useful relationship for the drag coefficient of a permeable floc has the following form:

$$\mathcal{C}\_{Df} = \frac{15}{R\_{ep} \,\mathrm{n}} \tag{5}$$

where the coefficient n depends on the kind of floc and varies, according to a comparison of results of different authors [20], between 1.1 and 1.25. Rep is the particle Reynolds number defined as Rep = WsD/ν where ν is the kinematic viscosity of the fluid.

Replacing the relationship from Eq. (5) in Eq. (4), the following relationship for the settling velocity is obtained:

$$\mathcal{W}\_s = \frac{[13.08(S-1)]^{\frac{1}{2-n}} D^{\frac{F+n-2}{2-n}}}{15^{\frac{1}{2-n}} \nu^{\frac{n}{2-n}} d^{\frac{F-3}{2-n}}} \tag{6}$$

2.4. Application of digital holography for PIV (DHPIV) for cohesive sediments

Green light laser diode 532 nm wave length, 50 mW power

Lens to collimate the wave front Focal distance f = 75 mm, 7 cm diameter

Digital camera Lumenera 100 fps, pixel size Dx = Dy = 5.2 μm, 1200 1400 px

Glass container 5 5 10 cm, glass width 3 mm

Microscope objective 40 Pinhole to expand and collimate beam 10 and 5 μm

Table 1. Physical components of digital holographic system.

Even if there are enormous advances in PIV and PTV techniques, there are shortcomings for 2D applications. The latter is observed in some physical phenomena, for example for the volume determination of a floc, which is only possible with 3D optical techniques. One of these techniques is digital holography for particle image velocimetry (DHPIV). This technique has been shown appropriate, for size distribution, volume determination, and particle velocity in

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117

The DH method consists of specific steps as shown in Figure 3. Most experiments in scientific literature record a hologram following the so called in line system [28–30]. In this configuration, a coherent and collimated laser beam is sent, this is divided in two beams, one is directed toward the particles suspended in the fluid and is called the reference beam, while the dispersed light is called object beam. The two beams interfere to form a hologram which is recorded by the CCD digital camera (Figure 3). A typical particle hologram contains a succession of circular concentric interference strips which define the object in three dimensions.

characterization

fluids [30].

Figure 3. In line digital holographic system.

Polarizing filters

Sample of fluid to analyze

where Ws is in m/s and D and d in m.

As the fractal dimension changes with floc diameter, in this paper, we used a relationship proposed by Garcia-Aragon et al. [16] that has a form similar to the following:

$$F = 3 - \alpha \left[\frac{D}{d}\right]^\beta \tag{7}$$

where α and β are constants that depend on the kind of cohesive sediment. Maggi et al. [21] used flocculated kaolinite minerals in experiments in a settling column and found that the exponent β varies between �0.092 and �0.112.

#### 2.3. Application to suspended load estimation in large rivers

Authors working with the Mississippi river sediment transport Colby [22, 23], realized that the predicted Rouse number was not equal to the measured Rouse number in a series of sampled vertical profiles of the Mississippi. Also, researchers working in the three Gorges Reservoir in the Yangtze River show that settling velocities calculated with diameters obtained from particle size analyzers do not reproduce observed settling velocities, which indicate the existence of flocculation [24]. The formation of flocs in large rivers is the reason why Rouse equation cannot be used with particle sizes from classical granulometric measurements in conjunction with non-cohesive settling velocity equations. Recently, researchers working in the Amazon River and tributaries made similar observations [1]. Their conclusion was that granulometric measurements performed did not represent the real particle size because cohesive sediments agglomerate to form flocs [5, 6, 9] and after sampling, these flocs are destroyed and could not be measured appropriately in laboratory. On a related note, other researchers have shown that particle sizes in the Amazon River are lower than 70 μm [25, 26], which are in the size range of cohesive sediments.

To estimate the suspended sediment profile in stationary flows, the following Rouse equation is generally accepted [27]

$$\left(\frac{\mathbb{C}(y)}{\mathbb{C}(a)}\right) = \left(\frac{H-y}{y} \cdot \frac{a}{H-a}\right)^{Z\_{\mathbb{R}}} \tag{8}$$

where the Rouse parameter is ZR = Ws/Ku\*, C(y) is the suspended sediment concentration at height y above bed, H is flow depth, a is a reference depth above bed, and K is Von-Karman's constant that for low sediment concentration is equal to 0.41.

In this project, Eq. (6) is used to estimate the settling velocity Ws, in conjunction with the Rouse Eq. (8) for the evaluation of the suspended sediment profiles in the Grijalva and Usumacinta rivers, the two largest rivers in Mexico.
