Fractal dimension of large aggregates under different flocculation conditions

Moruzzi, Rodrigo Braga; Oliveira, André Luiz de; Conceição, Fabiano Tomazini da; Gregory, John; Campos, Luiza C.

doi:10.1016/j.scitotenv.2017.07.194

Cited by 62 publications

(33 citation statements)

References 27 publications

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“…So after several successive events during a flocculation process, they become more and more dense and their fractal dimension increases. However, opposite results were recently reported by Moruzzi et al [21] considering only aggregates of large sizes. They observed that higher fractal dimensions were obtained for lower shear rates and concluded that the behaviour of the aggregate structure was dependant on the predominance of the aggregation mechanisms, either cluster-cluster or particle-cluster in relation with shear conditions.…”

Section: Introductioncontrasting

confidence: 60%

Fractal dimensions and morphological characteristics of aggregates formed in different physico-chemical and mechanical flocculation environments

Guérin

Francès

Liné

et al. 2019

Colloids and Surfaces A: Physicochemical and Engineering Aspect

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Flocculation experiments were performed in a Taylor-Couette reactor in turbulent conditions characterized by the mean shear rate. A sequenced hydrodynamic protocol was applied which consists in low and high shear rates steps allowing to promote respectively aggregation and breakage processes. The particle size distribution and the 3D fractal dimension were determined on line by laser diffraction while morphological parameters were characterized off line using an automated microscope coupled with image processing. After a first aggregation-breakage cycle, the flocs formed by charge neutralization have smaller sizes than during the first aggregation step when the main aggregation mechanism is the charge neutralization whereas coarser but more resistant aggregates can be produced by bridging mechanism. During the flocculation process, high shear rates calibrate the flocs, creating small flocs having a size close to the Kolmogorov microscale. These small flocs serve as bricks to form larger flocs when lower shear rates are applied and a full reproducibility is observed after one or two cycles of the sequence depending on the aggregation mechanism. A clear correspondence was put in evidence between the shear rate conditions and the volume base mean size or fractal dimension of flocs. The morphological fractal dimension, as well as the fractal dimension derived from laser measurements, are in good agreement with the mean trend of the morphological data but cannot represent the whole diversity of floc sizes and shapes. The 3D surface base area and perimeter distributions appear as a promising tool allowing a deeper analysis of the impact of physico-chemical and shear conditions on aggregate properties during a flocculation process.

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Section: Introductioncontrasting

confidence: 60%

Fractal dimensions and morphological characteristics of aggregates formed in different physico-chemical and mechanical flocculation environments

Guérin

Francès

Liné

et al. 2019

Colloids and Surfaces A: Physicochemical and Engineering Aspect

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“…The turbulence-induced flocculation of cohesive sediment and other particles (such as polystyrene/ latex particles) in a fluid environment has been investigated by several researchers in many research fields, including chemical and environment engineering, oceanography, and river and estuarine mechanics (e.g., References [11][12][13][14][15][16][17][18][19][20][21][22][23]). Most studies regarding turbulence-induced particle flocculation have focused on two main aspects: (1) the floc properties (mainly characterized by floc size or floc structure) at the steady or equilibrium states, in which the property parameters reach constant values; and (2) temporal variations of the size distribution and the structural and morphological properties of the flocs (commonly characterized by different fractal dimensions of the flocs) during the flocculation/aggregation process.…”

Section: Introductionmentioning

confidence: 99%

“…The c is the floc strength, which strongly depends on the method used to measure the floc size, while the γ is the stable floc size exponent depending on the breakage mechanisms (erosion or fracture) for flocs smaller or larger than the smallest eddy (i.e., Kolmogorov microscale) in the turbulent flow [28,29]. Some studies have focused on the structural and morphological properties of the flocs at the steady state of flocculation with respect to various flow shear conditions (e.g., References [6,17,25,30]). For example, Stone and Krishnappan [30] showed that particle boundaries become more convoluted and the shape of larger particles are more irregular at higher levels of flow shear stress, whereas Zhu et al [6] reported that with increasing flow shear rates, the flocs become less elongated and their boundary lines become tighter and more regular.…”

Section: Introductionmentioning

confidence: 99%

A Simple Explicit Expression for the Flocculation Dynamics Modeling of Cohesive Sediment Based on Entropy Considerations

Zhu

2018

Entropy

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The flocculation of cohesive sediment plays an important role in affecting morphological changes to coastal areas, to dredging operations in navigational canals, to sediment siltation in reservoirs and lakes, and to the variation of water quality in estuarine waters. Many studies have been conducted recently to formulate a turbulence-induced flocculation model (described by a characteristic floc size with respect to flocculation time) of cohesive sediment by virtue of theoretical analysis, numerical modeling, and/or experimental observation. However, a probability study to formulate the flocculation model is still lacking in the literature. The present study, therefore, aims to derive an explicit expression for the flocculation of cohesive sediment in a turbulent fluid environment based on two common entropy theories: Shannon entropy and Tsallis entropy. This study derives an explicit expression for the characteristic floc size, assumed to be a random variable, as a function of flocculation time by maximizing the entropy function subject to the constraint equation using a hypothesis regarding the cumulative distribution function of floc size. It was found that both the Shannon entropy and the Tsallis entropy theories lead to the same expression. Furthermore, the derived expression was tested with experimental data from the literature and the results were compared with those of existing deterministic models, showing that it has good agreement with the experimental data and that it has a better prediction accuracy for the logarithmic growth pattern of data in comparison to the other models, whereas, for the sigmoid growth pattern of experimental data, the model of Keyvani and Strom or Son and Hsu model could be the better choice for floc size prediction. Finally, the maximum capacity of floc size growth, a key parameter incorporated into this expression, was found to exhibit an empirical power relationship with the flow shear rate.

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“…Therefore, a steady-state is supposed during flocculation since aggregation and breakage rates result in aggregate size stable over time (Jarvis et al, 2005). Nevertheless, aggregates with the same size may have different structures (i.e., fractal dimensions) as a result of different arrangements of primary particles within aggregates during flocculation (Vahedi and Gorczyca, 2012;Moruzzi et al, 2017). Further, properties such as density and the velocity of sedimentation are naturally not integrated to the size, but they exhibit relations with the dimension of fractal, as mentioned by Gregory (2009).…”

Section: Introductionmentioning

confidence: 99%

Fractal Aggregates Evolution During Flocculation

Moruzzi

Oliveira

Almeida

2018

Braz. J. Chem. Eng.

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A temporal analysis of fractal aggregates during water flocculation is presented. Water was prepared using kaolin solution and a non-intrusive image-based analysis method was used for two-dimensional fractal dimension assessment (d F). The d F values were determined for aggregates larger than 270 µm from 100 images taken in each combination of velocity gradients (G f) and flocculation times (T f). The G f values of 20, 30, 40, 50 and 60 s-1 and T f values of 2 to 180 minutes were studied, with a ΔT f of 1 minute for 2 ≤ T f ≤ 10 minutes and a ΔT f of 5 minutes for 10 ≤ T f ≤ 180 minutes. Results showed that d F tends toward stability from a T f of 40 minutes, with distinct levels in each G f. Further, d F values decrease from 1.80 to 1.35 for G f from 20 to 60 s-1 .

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Fractal dimension of large aggregates under different flocculation conditions

Abstract: 22The two-dimensional fractal dimension (Df) of large aggregates of kaolin (> 540 μm) 23 during the shear flocculation process for kaolin solution was investigated using non-intrusive 24 in situ image-based acquisition system. Separate experiments were also carried out for three

Cited by 62 publications

References 27 publications

Fractal dimensions and morphological characteristics of aggregates formed in different physico-chemical and mechanical flocculation environments

Fractal dimensions and morphological characteristics of aggregates formed in different physico-chemical and mechanical flocculation environments

A Simple Explicit Expression for the Flocculation Dynamics Modeling of Cohesive Sediment Based on Entropy Considerations

Fractal Aggregates Evolution During Flocculation

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