Modeling spatial distribution of floc size in turbulent processes using the quadrature method of moment and computational fluid dynamics

Prat, Olivier P.; Ducoste, Joel J.

doi:10.1016/j.ces.2004.11.070

Cited by 45 publications

(26 citation statements)

References 38 publications

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“…This median size vs. time behavior depicts the flocculation process of type II, which is also composed of the three following phases: fast floc growth (referred to as type II-phase 1 herein), breakage and restructuring (type II-phase 2), and a steady state (type II-phase 3), as described in Section 1 of this paper. The type II-phase 1 presented in the figure could be approximately described as a simple linear increase process, as shown in several previous studies [9,11,20,21,55], rather than the exponential process reported by many authors [10,18,20,56]. Ehrl et al [17] attributed the difference between the linear and exponential trends of the fast aggregate growth phase to different particle sizes for which the relative importance of Brownian motion and shear-induced aggregations changed correspondingly [9].…”

Section: G=14s -1mentioning

confidence: 60%

Fractal Dimension of Cohesive Sediment Flocs at Steady State under Seven Shear Flow Conditions

Zhu

Wang

et al. 2015

Water

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Abstract:The morphological properties of kaolin flocs were investigated in a Couette-flow experiment at the steady state under seven shear flow conditions (shear rates of 5.36, 9.17, 14, 24, 31, 41 and 53 s −1 ). These properties include a one-dimensional (1-D) fractal dimension (D1), a two-dimensional (2-D) fractal dimension (D2), a perimeter-based fractal dimension (Dpf) and an aspect ratio (AR). They were calculated based on the projected area (A), equivalent size, perimeter (P) and length (L) of the major axis of the floc determined through sample observation and an image analysis system. The parameter D2, which characterizes the relationship between the projected area and the length of the major axis using a power function, , decreased as the shear rate increased almost linearly. The parameter AR, which is the ratio of the length of the major axis and equivalent diameter, decreased from 1.56, 1.59, 1.53 and 1.51 in the low shear rate group to 1.43, 1.47 and 1.48 in the high shear rate group. These changes in Dpf and AR show that the flocs become less convoluted and more symmetrical and that their boundaries become smoother and more regular in the high shear rate group than in the low shear rate group due to breakage and possible restructuring processes. To assess the effects of electrolyte and sediment concentration, 0.1 mol/L calcium chloride (CaCl2) and initial sediment concentration from 7.87 × 10 were used in this preliminary study. The addition of electrolyte and increasing sediment concentration could produce more symmetrical flocs with less convoluted and simpler boundaries. In addition, some new information on the temporal variation of the median size of the flocs during the flocculation process is presented.

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Section: G=14s -1mentioning

confidence: 60%

Fractal Dimension of Cohesive Sediment Flocs at Steady State under Seven Shear Flow Conditions

Zhu

Wang

et al. 2015

Water

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“…An alternative is proposed by the moment methods that consist of following the changes in the first moments of the distribution instead of the full distribution. The number of equations is substantially reduced, and so is the computational time, making it possible to consider a coupling with computational fluid dynamics calculations (Prat and Ducoste, 2006;Zucca et al, 2006). The Quadrature Method Of Moments (QMOM) is now well known.…”

Section: Introductionmentioning

confidence: 99%

QMOM-based population balance model involving a fractal dimension for the flocculation of latex particles

Vlieghe

Coufort-Saudejaud

Liné

et al. 2016

Chemical Engineering Science

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QMOM-based population balance model involving a fractal dimension. Aggregation and breakage kernels involving a fractal dimension. Simulation of the first 6 moments of the particle size distribution. Analytical relations between sink and source terms of the population balance equation. a b s t r a c tAn experimental and computational study of agglomeration and breakage processes for fully destabilized latex particles under turbulent flow conditions in a jar is presented. The particle size distribution (PSD) and the fractal dimension of flocs of latex particles were monitored using an on-line laser diffraction technique. A population balance equation (PBE) was adapted to our problem by including the fractal dimension in its formulation as well as in the aggregation and breakage kernels. The quadrature method of moments was used for the resolution. The adjustment of 4 model parameters was then conducted on the first 6 moments of the PSD for various mean shear rates. The model correctly predicts the evolution of the first 6 moments calculated from the experimental PSD. The experimental results were adequately simulated by a single set of adjusted parameters, proving the relevance of the dependency on the fractal dimension and mean shear rate. A sensitivity analysis was performed on two main adjusted parameters highlighting the major roles of (1) the power to which the mean shear rate is raised in the breakage kernel and (2) the sizes of the colliding aggregates in the collision efficiency model. Finally, analytical relations between the sink and source terms of the breakage or aggregation of the PBE were derived and discussed, highlighting interesting features of the PBE model.

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“…With a small number of moments, it may be not sufficient to accurately reconstruct the FSDs. For example, Prat and Ducoste () and Marchisio, Vigil, et al, () tracked particle aggregation and breakage with three classes. They did not recover the size distributions from the moments, because three classes are not sufficient to show a meaningful FSD.…”

Section: Discussionmentioning

confidence: 99%

An Approach to Modeling Biofilm Growth During the Flocculation of Suspended Cohesive Sediments

et al. 2019

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The floc size distribution (FSD) is crucial to predict cohesive sediment dynamics in aquatic environments. Recently, increasing attention has been given to biofilm effects on the FSDs of suspended particles since the presence of biofilms on particle surfaces may lead to larger flocs and thus higher settling velocities. In this study, results from a settling column experiment conducted by Tang and Maggi (2018; https://doi.org/10.1002/2017JG004165) under nutrient‐free and biomass‐free, nutrient‐affected and biomass‐free, and nutrient‐affected and biomass‐affected conditions, with different suspended sediment concentrations, shear rates, and nutrient concentrations, have been used to validate modeled FSDs that is based on the population balance equation solved by the quadrature method of moments. In addition to the processes of aggregation and breakage, the effects of biofilm are expressed in the growth term of the population balance equation. The logistic growth pattern is used to account for an increase in biomass, which is primarily controlled by the specific growth rate and the carrying capacity. In this study, the biofilm growth rate is assumed nutrient dependent, and the carrying capacity of floc size is hypothesized to be proportional to the Kolmogorov microscale. With eight size classes to interpret a simulated FSD, the predicted and observed FSDs exhibit a reasonable match for all nutrient‐free and biomass‐free, nutrient‐affected and biomass‐free, and nutrient‐affected and biomass‐affected conditions. This simplified bioflocculation model fills the gap between the simulations of the FSDs of cohesive sediments without and with biofilms and has the potential to be included in large‐scale models in the future.

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Modeling spatial distribution of floc size in turbulent processes using the quadrature method of moment and computational fluid dynamics

Cited by 45 publications

References 38 publications

Fractal Dimension of Cohesive Sediment Flocs at Steady State under Seven Shear Flow Conditions

Fractal Dimension of Cohesive Sediment Flocs at Steady State under Seven Shear Flow Conditions

QMOM-based population balance model involving a fractal dimension for the flocculation of latex particles

An Approach to Modeling Biofilm Growth During the Flocculation of Suspended Cohesive Sediments

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