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Flocculation is a special phenomenon for fine sediment or silt in reservoirs and estuaries. Flocculation usually results in changes of size, morphology, and settling velocity of sediment particles and finally changes of bed topography of reservoirs and estuaries. The process of flocculation and sedimentation was simulated based on population balance modeling (PBM) and computational fluid dynamics (CFD); the changes of particle or floc size and their settling velocities over time were examined. The results showed that flocculation is a dynamic and nonlinear process containing aggregation, breakage, reaggregation, and rebreakage between particles, microflocs, and macroflocs. Furthermore, the visual process of flocculation and sedimentation was directly created by the simulation results and is in good agreement with the results of the previous experiments.

Flocculation (floc) of fine sediments is a research focus in the theory of sediment movement mechanics. Many phenomena of the settling velocity of sediment, such as sediment topography of the estuary (sediment barrier), the formation of non-Newtonian fluid, huge sediment-carrying capacity, and pulp rivers, are related to the flocculation of fine sediment [

The mathematical model of flocculation came into focus, when Witten and Sander [

The aim of this study is to apply the PBM to the flocculation and sedimentation process in three dimensions. PBM was incorporated into the computational fluid dynamics (CFD) model by implementing the multiple size group model. The CFD-PBM combination is an effective method to solve the processes of flocculation and multiphase flow simultaneously [

The process of flocculation and sedimentation is the process of a typical solid-liquid two-phase flow interaction. Therefore, the Euler-Euler model was employed within the flocculating system [

The momentum balance for phase

A standard

In these equations,

Assuming that

The Luo and Ghadiri models were adopted to study the aggregation and breakage processes between particles, respectively [

Flocculation and sedimentation experiments were performed on particles diluted to 5 g/L and 15 g/L solid in deionized water in a 1000 ml graduated cylinder. Particles, with a mean diameter of 39.63

The Ansys Fluent 15.0 software was used to solve the equations of mass, momentum, and population balance equations. Considering that the previous experiment of flocculation and sedimentation were carried out in a 1000 ml graduated cylinder, the three-dimensional geometry of this cylinder was built with a 0.068 m diameter and 0.44 m height. The details of the experimental data can be found in the cited references [

Three-dimensional geometry and grid measurements with meshing. (a) geometry; (b) ×20 times; (c) ×40 times; (d) ×30 times.

Water was chosen as the growth medium liquid phase. Considering the range of the initial particle diameter, the solid dispersed phase was divided into 6 groups (Table

Particle size groups.

No. | Bin 0 | Bin 1 | Bin 2 | Bin 3 | Bin 4 | Bin 5 |
---|---|---|---|---|---|---|

Size (×10^{−3} m) (_{50}) |
0.031 | 0.032 | 0.038 | 0.026 | 0.007 | 0.021 |

Volume concentration (%) | 10 | 20 | 20 | 20 | 20 | 10 |

The critical size of flocculation between particles is 0.01∼0.03 mm for different water quality and particle properties [

The process of flocculation and sedimentation between particles or flocs. Note that (a) and (b) represent the process of flocculation and sedimentation between particles at 5 s and 10 s, respectively. Images (c) and (d) represent the process of flocculation and sedimentation between microflocs at 15 s and 20 s, respectively. Finally, (e) and (f) represent the process of flocculation and sedimentation between macroflocs at 25 s and 30 s, respectively. (a) Time = 5 s (particles). (b) Time = 10 s (particles). (c) Time = 15 s (microflocs). (d) Time = 20 s (microflocs). (e) Time = 25 s (macroflocs). (f) Time = 30 s (macroflocs).

The phenomenon of aggregation and breakage can be clearly observed during the process of flocculation and sedimentation, as shown in Figure

It can also be seen from Figure

The time series of the particle or floc size during flocculation and sedimentation is predicted with CFD-PBM, as shown in Figure

Time series of the particle or floc size of each bin: (a) Bin 0. (b) Bin 1. (c) Bin 2. (d) Bin 3. (e) Bin 4. (f) Bin 5.

Three states and sizes of flocs during flocculation and sedimentation in experiments: (a) Particles. (b) Microflocs. (c) Macroflocs. (d) Size in experiments (

The collision frequency between particles can result from Brownian motions, shear flow, or differential settling [

The settling velocity is a key parameter in modeling the settlement process in sedimentation analysis and sediment transport. For noncohesive particles, the settling velocity is dependent on the individual particle size, gravity, and particle shape, which substantially differs from the settling velocity of floc. For example, due to the process of flocculation, muds are often changed to flocs during suspension in estuary coastal areas [

Settling velocities of particle or floc in model and experiments. (a) Time series of the settling velocities, phase 2 represents particles or flocs.

It should be noted that from Figure ^{−1} for particles whose concentration is 5 g/L and 0.005∼0.015 m·s^{−1} for particles whose concentration is 15 g/L, while the calculated settling velocity used in this study is 0.0038∼0.012 m·s^{−1} in 15 s∼30 s (Figure

For the variation of the curve in 0∼15 s, some authors [

Mechanisms of different breakage modes of flocs. In the case of an aggregate rupture, both size and the perimeter change significantly. In the case of aggregate surface erosion, only the perimeter changes, and size remains almost constant.

PBM was proven to be a more advanced model that is capable of approximating flocculation and sedimentation of particles better than previous versions. In contrast to the DLA or DLCCA model, the PBM can simultaneously simulate both the aggregation and breakage processes between microflocs and macroflocs with irregular shape. The presented results lead to the following conclusions:

Particles, microflocs, and macroflocs are the three important states during the process of flocculation and sedimentation. This process is a dynamic and nonlinear process of aggregation, breakage, reaggregation, and rebreakage.

There are three stages in the process of flocculation and sedimentation corresponding to the three above states. Shear effect focuses on the decrease of floc size, while differential settling influences the increase of floc size. Eventually, the equilibrium phase appears in which the breakage rate is equal to the aggregation rate.

The process of flocculation and sedimentation can be reasonably described by aggregate rupture and aggregate surface erosion. They are two different mechanisms important for the settling velocity decreasing in the early stage and fluctuating in the late stage.

Finally, CFD-PBM is an effective method to study the dynamics of flocs and their influence on flocculation and sedimentation, in order to not only gain a deeper understanding of flocculation dynamics, but also to improve the theory of sediment movement.

the Hamiltonian

source item

volume fraction of phase

density of phase

velocity of phase

mass transfer within phase

mass transfer within phase

external body force

lift force

wall lubrication force

virtual mass force

turbulent dispersion force

interaction force between phases

pressure

interphase velocity

gravity acceleration, 9.81 m·s^{−2}.

the turbulence kinetic energy

turbulent energy dissipation rate

generation of turbulence kinetic energy due to the mean velocity gradients

generation of turbulence kinetic energy due to buoyancy.

contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate

constants, 1.44, 1.92, 0.09.

turbulent Prandtl numbers for

turbulent Prandtl numbers for

number density of particles of volume

particle velocity

the linear growth rate

birth rate of aggregation

death rate of aggregation

birth rate of breakage

death rate of breakage

particle volume

floc volume

number of particles

The model description and Figure

The authors declare no conflicts of interest.

Z. P. S. and G. G. Z. performed conceptualization and methodology. Y. Z. Z., G. L. P., and Z. P. S performed investigation and date collection. Z. P. S wrote the original draft. G. G. Z and T. T. H reviewed and edited the draft. G. G. Z supervised the study. G. G. Zhang and Z. P. Shi were responsible for funding acquisition.

The authors thanks Prof. Onyx W. H. Wai from the civil and environmental engineering department of the Hong Kong Polytechnic University for his kind advice which helped us prepare a better manuscript. This work was supported by the Jiangsu Overseas Visiting Scholar Program for University Prominent Young & Middle-aged Teachers and Presidents (2018), National Natural Science Foundation of China (grant no. 51879227), Qing Lan Project (2016), and Science and Technology Project of Department of Housing and Urban-Rural Development of Jiangsu province (grant no. 2016ZD80).