Modelling Flocculated Cell Suspensions using a Population Balance Approach: Applications to Microfiltration

2002 ◽  
Vol 752 ◽  
Author(s):  
S. Ranil Wickramasinghe ◽  
Binbing Han ◽  
Saengchai Akeprathumchai ◽  
Xianghong Qian
Keyword(s):  
Distribution Function ◽  
Size Distribution ◽  
Volume Fraction ◽  
Particle Diameter ◽  
Population Balance ◽  
Balance Model ◽  
Floc Size ◽  
Balance Approach ◽  
Fragment Distribution ◽  
Log Normal

ABSTRACTExperimental results for flocculation of yeast and CHO cells using cationic polyelectrolytes are presented. These results suggest the existence of a self-similar floc size distribution. The experimentally determined floc size distributions have been modelled using a population balance approach. For flocculated yeast suspensions, the variation of the floc volume fraction with dimensionless particle diameter is predicted by the population balance model assuming a binary fragment distribution function. However, for CHO cell flocs, the floc volume fraction is predicted using a log normal fragment distribution function. Since the efficiency of unit operations such as microfiltration may be improved by flocculation of the feed suspension characterization of the particle size distribution is of great importance.

scholarly journals Simulation of Floc Size Distribution in Flocculation of Activated Sludge Using Population Balance Model with Modified Expressions for the Aggregation and Breakage

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Zhenliang Li ◽  
Peili Lu ◽  
Daijun Zhang ◽  
Fuzhong Song
Keyword(s):  
Activated Sludge ◽  
Size Distribution ◽  
Velocity Gradient ◽  
Population Balance ◽  
Balance Model ◽  
Population Balance Model ◽  
Collision Efficiency ◽  
Volume Percentage ◽  
Floc Size ◽  
Breakage Rate

The floc size distribution of activated sludge was simulated successfully by population balance model in the previous study (Population Balance Model and Calibration Method for Simulating the Time Evolution of Floc Size Distribution of Activated Sludge Flocculation. Desalination and Water Treatment, 67, 41-50). However, nonignorable errors exist in the simulation for the volume percentage of large flocs. This paper describes the application of a modified population balance model in the simulation of the time evolution of floc size distribution in activated sludge flocculation process under shear-induced conditions. It was found that the application of modified size dependent collision efficiency, modified breakage rate expression by assuming a maximum value, and binominal daughter-particles distribution function could improve the population balance model for activated sludge flocculation and successfully predict the dynamic changes in volume percentage distribution and mean floc size of activated sludge under different shear conditions. The results demonstrate that the maximum breakage rate was independent on the velocity gradient, and both the collision efficiency and breakage rate coefficient show a power-law relationship with the average velocity gradient; the former decreases while the latter increases with the rise of the average velocity gradient. These findings would help to understand the dynamics of activated sludge flocculation.

Modelling the activated sludge flocculation process combining laser light diffraction particle sizing and population balance modelling (PBM)

2002 ◽  
Vol 45 (6) ◽  
pp. 41-49 ◽  
Author(s):  
I. Nopens ◽  
C.A. Biggs ◽  
B. De Clercq ◽  
R. Govoreanu ◽  
B.-M. Wilén ◽  
...  
Keyword(s):  
Experimental Data ◽  
Laser Light ◽  
Population Balance ◽  
Light Diffraction ◽  
Balance Model ◽  
Floc Size ◽  
Shear Rates ◽  
Breakage Rate ◽  
On Line ◽  
Floc Size Distributions

A technique based on laser light diffraction is shown to be successful in collecting on-line experimental data. Time series of floc size distributions (FSD) under different shear rates (G) and calcium additions were collected. The steady state mass mean diameter decreased with increasing shear rate G and increased when calcium additions exceeded 8 mg/l. A so-called population balance model (PBM) was used to describe the experimental data. This kind of model describes both aggregation and breakage through birth and death terms. A discretised PBM was used since analytical solutions of the integro-partial differential equations are non-existing. Despite the complexity of the model, only 2 parameters need to be estimated: the aggregation rate and the breakage rate. The model seems, however, to lack flexibility. Also, the description of the floc size distribution (FSD) in time is not accurate.

Numerical Simulation of Droplet Size Distribution in Vertical Upward Annular Flow

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
Y. Liu ◽  
W. Z. Li
Keyword(s):  
Size Distribution ◽  
Droplet Size ◽  
Annular Flow ◽  
Liquid Droplet ◽  
Large Diameter ◽  
Droplet Size Distribution ◽  
Population Balance ◽  
Balance Model ◽  
Diameter Distribution ◽  
Two Fluid

The liquid droplet size distribution in gas-liquid vertical upward annular flow is investigated through a CFD (computational fluid dynamics)-PBM (population balance model) coupled model in this paper. Two-fluid Eulerian scheme is employed as the framework of this model and a population balance equation is used to obtain the dispersed liquid droplet diameter distribution, where three different coalescence and breakup kernels are investigated. The Sauter mean diameter d32 is used as a bridge between a two-fluid model and a PBM. The simulation results suggest that the original Luo–Luo kernel and the mixed kernel A (Luo’s coalescence kernel incorporated with Prince and Blanch’s breakup kernel) can only give reasonable predictions for large diameter droplets. Mixed kernel B (Saffman and Turner’s coalescence kernel incorporated with Lehr’s breakup kernel) can accurately capture the particle size distribution (PSD) of liquid droplets covering all droplet sizes, and is appropriate for the description of liquid droplet size distribution in gas-liquid annular flow.

POPULATION BALANCE MODEL OF ICE CRYSTALS SIZE DISTRIBUTION DURING ICE SLURRY STORAGE

2014 ◽  
Vol 22 (02) ◽  
pp. 1440001 ◽  
Author(s):  
AIXIANG XU ◽  
ZHIQIANG LIU ◽  
TENGLEI ZHAO ◽  
XIAOXIAO WANG
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Crystal Size ◽  
Population Balance ◽  
Ice Crystals ◽  
Balance Model ◽  
Ice Slurry ◽  
Slurry Storage

Particle size distribution and number of ice crystals have a great influence on the flow and heat transfer performance of ice slurry. A population balance model (PBM) containing population and mass balances has been built to simulate numerically the development of ice particle size distribution during adiabatic ice slurry storage. The model assumes a homogeneously mixed and long-term storage tank in which the effect of breakage and aggregation between ice crystals was considered. For solving the population balance equations (PBEs) in the PBM, a semi-discrete finite volume scheme was applied. Finally, the effect of breakage and aggregation on development of ice particle size distribution was analyzed respectively. The results show that both breakage and aggregation are the two important effects on the particle size distribution and evolution of ice particle during storage, but they have opposite effect on the development of ice crystal size. In storage, breakage and aggregation have almost equivalent effect in the initial phase, but aggregation has dominant effect at last. The PBM results are in good agreement with experimental results by Pronk et al. [Effect of long-term ice slurry storage on crystal size distribution, 5th Workshop on Ice Slurries of the IIR (2002), pp. 151–160]. Therefore, the PBM presented in this paper is able to predict the development of particle size distribution during ice slurry storage.

Small Angle Scattering from Nanocrystalline Pd

1988 ◽  
Vol 132 ◽  
Author(s):  
G. Wallner ◽  
E. Jorra ◽  
H. Franz ◽  
J. Peisl ◽  
R. Birringer ◽  
...  
Keyword(s):  
Crystallite Size ◽  
Size Distribution ◽  
Small Angle ◽  
Volume Fraction ◽  
Structural Parameters ◽  
Spatial Arrangement ◽  
Small Angle Scattering ◽  
X Rays ◽  
Angle Scattering ◽  
Log Normal

ABSTRACTThe microstructure of nanocrystalline Pd was investigated by small angle scattering of neutrons and X-rays. The samples were prepared by compacting small crystallites produced by evaporation and condensation in an inert gas atmosphere. The strong scattering signal is interpreted to arise from crystallites embedded in a matrix of incoherent interfaces. Size distributions were deduced from the scattering curves. They consist of two parts: the crystallite size distribution dictated by the production process, and a structureless contribution due to the correlation in the spatial arrangement of the crystallites. The crystallite size distribution may be described by a log-normal distribution centred at R=2nm. The characteristic form of the correlation contribution arises from the dense packing of non-spherical crystallites. From the scattering cross-section in absolute units the volume fraction vc of crystallites was obtained as vc≈0.3, and the mean atomic density ρi in the interfaces as ρi≈0.52. The change of structural parameters during thermal annealing of the samples was studied. Up to high temperatures an appreciable volume fraction of crystallites with nearly unchanged size remains along with large particles.

Modeling of the formation kinetics and size distribution evolution of II–VI quantum dots

2017 ◽  
Vol 2 (4) ◽  
pp. 567-576 ◽  
Author(s):  
Stefano Lazzari ◽  
Milad Abolhasani ◽  
Klavs F. Jensen
Keyword(s):  
Quantum Dots ◽  
Size Distribution ◽  
Semiconductor Nanocrystals ◽  
Population Balance ◽  
Nanocrystal Size ◽  
Balance Model ◽  
Population Balance Model ◽  
Formation Kinetics

A population balance model describes the formation of II–VI semiconductor nanocrystals and predicts experimentally observed properties of the nanocrystal size distribution.

scholarly journals CFD Prediction of Gas-Liquid Flow in an Aerated Stirred Vessel Using the Population Balance Model

2014 ◽  
Vol 35 (1) ◽  
pp. 55-73 ◽  
Author(s):  
Zbyněk Kálal ◽  
Milan Jahoda ◽  
Ivan Fořt
Keyword(s):  
Size Distribution ◽  
Bubble Size ◽  
Water System ◽  
Population Balance ◽  
Bubble Size Distribution ◽  
Balance Model ◽  
Stirred Vessel ◽  
Rushton Turbine ◽  
Size Groups ◽  
Gas Liquid Flow

Abstract The main topic of this study is the experimental measurement and mathematical modelling of global gas hold-up and bubble size distribution in an aerated stirred vessel using the population balance method. The air-water system consisted of a mixing tank of diameter T = 0.29 m, which was equipped with a six-bladed Rushton turbine. Calculations were performed with CFD software CFX 14.5. Turbulent quantities were predicted using the standard k-ε turbulence model. Coalescence and breakup of bubbles were modelled using the homogeneous MUSIG method with 24 bubble size groups. To achieve a better prediction of the turbulent quantities, simulations were performed with much finer meshes than those that have been adopted so far for bubble size distribution modelling. Several different drag coefficient correlations were implemented in the solver, and their influence on the results was studied. Turbulent drag correction to reduce the bubble slip velocity proved to be essential to achieve agreement of the simulated gas distribution with experiments. To model the disintegration of bubbles, the widely adopted breakup model by Luo & Svendsen was used. However, its applicability was questioned.

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