Effect of variable fractal dimension on the floc size distribution of suspended cohesive sediment

Maggi, Federico; Mietta, F.; Winterwerp, Johan C.

doi:10.1016/j.jhydrol.2007.05.035

Cited by 114 publications

(101 citation statements)

References 54 publications

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“…The Taylor vortices due to flow instability were observed during all the experimental runs because all the angular velocity values of the inner cylinder in this study exceeded this ωi value. To avoid estimating the effects of several mineral compositions on the flocculation process, kaolin (China clay) was used in this experiment because of its obvious flocculation characteristics, as described in many previous experiments [23,[45][46][47][48]. The particle size distribution of the kaolin was determined using a laser particle size analyzer (Horiba LA-920; produced by Horiba Corporation, Tokyo, Japan).…”

Section: Shear Rate Calculationmentioning

confidence: 99%

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: Shear Rate Calculationmentioning

confidence: 99%

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

Zhu

Wang

et al. 2015

Water

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“…Generally, flocculation models can be classified into two groups at present; a population balance equations model (PBE) and a floc growth model (FGM). A PBE, often called a size class flocculation model, is based on discrete size classes, and typically calculates the change of floc numbers in each size class (e.g., [13][14][15]). A PBE has the advantages of considering many mechanisms of flocculation and calculating a size distribution of flocs.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Flocculation Model for Cohesive Sediment Suspended in Water

Shin

Son

Lee

2015

Water

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Existing flocculation models for cohesive sediments are classified into two groups: population balance equation models (PBE) and floc growth models. An FGM ensures mass conservation in a closed system. However, an FGM determines only the average size of flocs, whereas a PBE has the capability to calculate a size distribution of flocs. A new stochastic approach to model the flocculation process is theoretically developed and incorporated into a deterministic FGM in this study in order to calculate a size distribution of flocs as well as the average size. A log-normal distribution is used to generate random numbers based on previous laboratory experiments. The new stochastic flocculation model is tested with three laboratory experiment results. It was found and validated with measured data that the new stochastic flocculation model has the capability to replicate a size distribution of flocs reasonably well under different sediment and carrier flow conditions. Three more distributions (normal; Pearson type 3; and generalized extreme value distributions) were also tested. From the comparison with results of different distribution functions, it is shown that a stochastic FGM using a log-normal distribution has a comparative advantage in terms of simplicity and accuracy.

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“…Flocculation is usually modeled by either simple floc growth equations (i.e., the Lagrangian model developed by Winterwerp 1998Winterwerp , 2002 or by population balance equations (PBEs; Maggi et al 2007;Serra and Casamitijana 1998). In the first case, the temporal evolution of a characteristic floc size is modeled, while the PBEs model the temporal evolution of a floc size distribution(FSD).…”

Section: Introductionmentioning

confidence: 99%

“…We refer to this model as PBE 1 in the remainder of this paper. This model is similar to the PBE presented in Maggi et al (2007) and Mietta et al (2007), but the algorithm for the numerical integration and the choice of the time step have been improved. PBE 1 follows the first of the two approaches described above: All differently sized particles can aggregate and different breakup distribution functions can be applied to this model.…”

Section: Introductionmentioning

confidence: 99%

On the behavior of mud floc size distribution: model calibration and model behavior

et al. 2010

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In this paper, we study a population balance equation (PBE) where flocs are distributed into classes according to their mass. Each class i contains i primary particles with mass m p and size L p . All differently sized flocs can aggregate, binary breakup into two equally sized flocs is used, and the floc's fractal dimension is d 0 = 2, independently of their size. The collision efficiency is kept constant, and the collision frequency derived by Saffman and Turner (J Fluid Mech 1:16-30, 1956) is used. For the breakup rate, the formulation by Winterwerp (J Hydraul Eng Res 36(3):309-326, 1998), which accounts for the porosity of flocs, is used. We show that the mean floc size computed with the Responsible Editor: Susana B. Vinzon PBE varies with the shear rate as the Kolmogorov microscale, as observed both in laboratory and in situ. Moreover, the equilibrium mean floc size varies linearly with a global parameter P which is proportional to the ratio between the rates of aggregation and breakup. The ratio between the parameters of aggregation and breakup can therefore be estimated analytically from the observed equilibrium floc size. The parameter for aggregation can be calibrated from the temporal evolution of the mean floc size. We calibrate the PBE model using mixing jar flocculation experiments, see Mietta et al. (J Colloid Interface Sci 336(1):134-141, 2009a, Ocean Dyn 59:751-763, 2009b) for details. We show that this model can reproduce the experimental data fairly accurately. The collision efficiency α and the ratio between parameters for aggregation and breakup α and E are shown to decrease linearly with increasing absolute value of the ζ -potential, both for mud and kaolinite suspensions. Suspensions at high pH and different dissolved salt type and concentration have been used. We show that the temporal evolution of the floc size distribution computed with this PBE is very similar to that computed with the PBE developed by Verney et al. (Cont Shelf Res, 2010) where classes are distributed following a geometrical series and mass conservation is statistically ensured. The same terms for aggregation and breakup are used in the two PBEs. Moreover, we argue, using both PBEs, that bimodal distributions become monomodal in a closed system with homogeneous sediment, even when a variable shear rate is applied.

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Effect of variable fractal dimension on the floc size distribution of suspended cohesive sediment

Cited by 114 publications

References 54 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

Stochastic Flocculation Model for Cohesive Sediment Suspended in Water

On the behavior of mud floc size distribution: model calibration and model behavior

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