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

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 fluids [30].

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.

Figure 3. In line digital holographic system.

Ws <sup>¼</sup> ½ � <sup>13</sup>:08ð Þ <sup>S</sup> � <sup>1</sup> <sup>1</sup>

proposed by Garcia-Aragon et al. [16] that has a form similar to the following:

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

116 Applications in Water Systems Management and Modeling

exponent β varies between �0.092 and �0.112.

cohesive sediments.

is generally accepted [27]

2.3. Application to suspended load estimation in large rivers

15 <sup>1</sup> <sup>2</sup>�<sup>n</sup>ν <sup>n</sup> <sup>2</sup>�nd F�3 2�n

As the fractal dimension changes with floc diameter, in this paper, we used a relationship

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

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

To estimate the suspended sediment profile in stationary flows, the following Rouse equation

<sup>¼</sup> <sup>H</sup> � <sup>y</sup>

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

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

<sup>y</sup> : <sup>a</sup> H � a

ZR

C yð Þ C að Þ 

constant that for low sediment concentration is equal to 0.41.

rivers, the two largest rivers in Mexico.

D d <sup>β</sup>

F ¼ 3 � α

<sup>2</sup>�nD Fþn�2 2�n

(6)

(7)

(8)


Table 1. Physical components of digital holographic system.

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 annular flume.

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

Holographic images acquired and improved are reconstructed numerically in order to obtain 3D characteristics of flocs. The Fresnel method was used for image reconstruction [31].
