Numerical simulations of particle size distributions: Comparison with analytical solutions and kaolinite flocculation experiments

Shen, Xiaoteng; Maa, Jerome P.‐Y.

doi:10.1016/j.margeo.2016.05.014

Cited by 22 publications

(24 citation statements)

References 49 publications

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“…Note that the mechanism to describe the daughter particle distribution after a parent floc splitting is unclear. It is difficult to observe

{\overset{true¯}{b_{i}}}^{(k)}

directly, and therefore,

{\overset{true¯}{b_{i}}}^{(k)}

is often determined based on assumptions and validated by fitting the measured FSD (e.g., Lee et al, ; Mietta et al, ; Shen & Maa, ). Some predicted size classes are smaller than the median primary particle size, l p , especially the size of the first class under G = 96 s −1 .…”

Section: Resultsmentioning

confidence: 99%

“…As typical values in estuaries and coastal waters, the half saturation parameter K m for DIN is selected as 1.0 × 10 −6 M (Maggi, ), the median size of primary particles ( l p ) is chosen as 8 μm (Tang, ), and an averaged fractal dimension ( n f ) of 2.0 (e.g., Lee et al, ; Maggi, ; Winterwerp, ) is applied for all cases. The breakage coefficient ( E b ) is fixed as 2.0 × 10 −5 to make the flocculation intensity based on the aggregation correction factor α , since Shen and Maa () indicate that the same ratio of α / E b will result in the same prediction of equilibrium FSD for aggregation and breakage processes. This selection also ensures that the FSD in the model arrives at equilibrium or quasi‐equilibrium state before the shear rate changes (i.e., within 3 hr).…”

Section: Methodsmentioning

confidence: 99%

“…Moreover, the fragmentation distribution function b ( L | λ ) illustrates the distribution of the resulting daughter particles after a parent particle λ is destroyed. The binary (equation ), ternary (equation ), and uniform (equation ) distributions may be selected based on the observed FSD under different conditions (Shen & Maa, ).

b (()|, L, λ) = ({, \begin{array}{c} 2 & L = λ / 2^{1 / 3} \\ 0 & otherwise \end{array}),

b (()|, L, λ) = ({, \begin{array}{c} 1 & L = λ \cdot {(1 / 2)}^{1 / 3} \\ 2 & L = λ \cdot {(1 / 4)}^{1 / 3} \\ 0 & otherwise \end{array}),

b (()|, L, λ) = 6 L^{2} / λ^{3} ((), 0 < L < λ) .

…”

Section: Flocculation Modelmentioning

confidence: 99%

“…It is essential to note that with the assumption of binary (equation ), ternary (equation ), and uniform (equation ) breakup, the integral in

{\overset{true¯}{b_{i}}}^{(k / p)}

can be expressed by equations , , and , respectively (Shen & Maa, ).

{\overset{b}{true}}_{i}^{(k / p)} ((), L) = 2^{((), 3 - k / p) / 3} L^{k / p},

{\overset{b}{true}}_{i}^{(k / p)} ((), L) = L^{k / p} ((), 2^{\frac{- k}{3 p}} + 2^{1 - \frac{2 k}{3 p}}),

{\overset{b}{true}}_{i}^{(k / p)} ((), L) = \frac{6 p}{k + 3 p} L^{k / p} .

…”

Section: Flocculation Modelmentioning

confidence: 99%

“…Due to the complexity of biological effects, most numerical models only account for the mineral fraction. Examples of this approach include the one‐class population balance equation (PBE) by Winterwerp (), the two‐class model by Lee et al (), the three‐class model by Shen, Lee, et al (), and multiclass models such as by Maggi et al () and Shen and Maa (, , ). One exception is Maggi (), where the organic and inorganic fractions of aggregates are represented using two single‐class equations with an additional growth term to identify biomass coating, which is among the early contributions to illustrate the effects of microorganism on particle aggregation.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Note that the mechanism to describe the daughter particle distribution after a parent floc splitting is unclear. It is difficult to observe

{\overset{true¯}{b_{i}}}^{(k)}

directly, and therefore,

{\overset{true¯}{b_{i}}}^{(k)}

Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

b (()|, L, λ) = ({, \begin{array}{c} 2 & L = λ / 2^{1 / 3} \\ 0 & otherwise \end{array}),

b (()|, L, λ) = ({, \begin{array}{c} 1 & L = λ \cdot {(1 / 2)}^{1 / 3} \\ 2 & L = λ \cdot {(1 / 4)}^{1 / 3} \\ 0 & otherwise \end{array}),

b (()|, L, λ) = 6 L^{2} / λ^{3} ((), 0 < L < λ) .

…”

Section: Flocculation Modelmentioning

confidence: 99%

“…It is essential to note that with the assumption of binary (equation ), ternary (equation ), and uniform (equation ) breakup, the integral in

{\overset{true¯}{b_{i}}}^{(k / p)}

can be expressed by equations , , and , respectively (Shen & Maa, ).

{\overset{b}{true}}_{i}^{(k / p)} ((), L) = 2^{((), 3 - k / p) / 3} L^{k / p},

{\overset{b}{true}}_{i}^{(k / p)} ((), L) = L^{k / p} ((), 2^{\frac{- k}{3 p}} + 2^{1 - \frac{2 k}{3 p}}),

{\overset{b}{true}}_{i}^{(k / p)} ((), L) = \frac{6 p}{k + 3 p} L^{k / p} .

…”

Section: Flocculation Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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show abstract

Computer Simulation Elucidates Yeast Flocculation and Sedimentation for Efficient Industrial Fermentation

Liu

Hao

et al. 2018

Biotechnology Journal

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Flocculation plays an important role in the immobilized fermentation of biofuels and biochemicals. It is essential to understand the flocculation phenomenon at physical and molecular scale; however, flocs cannot be studied directly due to fragile nature. Hence, the present study is focused on the morphological specificities of yeast flocs formation and sedimentation via the computer simulation by a single floc growth model, based on Diffusion-Limited Aggregation (DLA) model. The impact of shear force, adsorption, and cell propagation on porosity and floc size is systematically illustrated. Strong shear force and weak adsorption reduced floc size but have little impact on porosity. Besides, cell propagation concreted the compactness of flocs enabling them to gain a larger size. Later, a multiple flocs growth model is developed to explain sedimentation at various initial floc sizes. Both models exhibited qualitative agreements with available experimental data. By regulating the operation constraints during fermentation, the present study will lead to finding optimal conditions to control the floc size distribution for efficient fermentation and harvesting.

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Floc size distributions of suspended kaolinite in an advection transport dominated tank: measurements and modeling

Shen

Maa

2017

Ocean Dynamics

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Numerical simulations of particle size distributions: Comparison with analytical solutions and kaolinite flocculation experiments

Cited by 22 publications

References 49 publications

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

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

Computer Simulation Elucidates Yeast Flocculation and Sedimentation for Efficient Industrial Fermentation

Floc size distributions of suspended kaolinite in an advection transport dominated tank: measurements and modeling

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