Abstract: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) an… Show more
“…When the LSR values are 65 and 112 s −1 , it ranges between 2.25 and 2.3. Those orders of magnitude are coherent with those found in the literature [7,20,38,39]. Thereafter, whatever the experiment under consideration, the change in the shear rate value is easily identifiable on the fractal dimension graph.…”
Section: Volume Size Distributions Over the Flocculation Sequenced Scsupporting
Flocculation experiments were performed in a Taylor-Couette reactor in turbulent conditions characterized by the mean shear rate. A sequenced hydrodynamic protocol was applied which consists in low and high shear rates steps allowing to promote respectively aggregation and breakage processes. The particle size distribution and the 3D fractal dimension were determined on line by laser diffraction while morphological parameters were characterized off line using an automated microscope coupled with image processing. After a first aggregation-breakage cycle, the flocs formed by charge neutralization have smaller sizes than during the first aggregation step when the main aggregation mechanism is the charge neutralization whereas coarser but more resistant aggregates can be produced by bridging mechanism. During the flocculation process, high shear rates calibrate the flocs, creating small flocs having a size close to the Kolmogorov microscale. These small flocs serve as bricks to form larger flocs when lower shear rates are applied and a full reproducibility is observed after one or two cycles of the sequence depending on the aggregation mechanism. A clear correspondence was put in evidence between the shear rate conditions and the volume base mean size or fractal dimension of flocs. The morphological fractal dimension, as well as the fractal dimension derived from laser measurements, are in good agreement with the mean trend of the morphological data but cannot represent the whole diversity of floc sizes and shapes. The 3D surface base area and perimeter distributions appear as a promising tool allowing a deeper analysis of the impact of physico-chemical and shear conditions on aggregate properties during a flocculation process.
“…When the LSR values are 65 and 112 s −1 , it ranges between 2.25 and 2.3. Those orders of magnitude are coherent with those found in the literature [7,20,38,39]. Thereafter, whatever the experiment under consideration, the change in the shear rate value is easily identifiable on the fractal dimension graph.…”
Section: Volume Size Distributions Over the Flocculation Sequenced Scsupporting
Flocculation experiments were performed in a Taylor-Couette reactor in turbulent conditions characterized by the mean shear rate. A sequenced hydrodynamic protocol was applied which consists in low and high shear rates steps allowing to promote respectively aggregation and breakage processes. The particle size distribution and the 3D fractal dimension were determined on line by laser diffraction while morphological parameters were characterized off line using an automated microscope coupled with image processing. After a first aggregation-breakage cycle, the flocs formed by charge neutralization have smaller sizes than during the first aggregation step when the main aggregation mechanism is the charge neutralization whereas coarser but more resistant aggregates can be produced by bridging mechanism. During the flocculation process, high shear rates calibrate the flocs, creating small flocs having a size close to the Kolmogorov microscale. These small flocs serve as bricks to form larger flocs when lower shear rates are applied and a full reproducibility is observed after one or two cycles of the sequence depending on the aggregation mechanism. A clear correspondence was put in evidence between the shear rate conditions and the volume base mean size or fractal dimension of flocs. The morphological fractal dimension, as well as the fractal dimension derived from laser measurements, are in good agreement with the mean trend of the morphological data but cannot represent the whole diversity of floc sizes and shapes. The 3D surface base area and perimeter distributions appear as a promising tool allowing a deeper analysis of the impact of physico-chemical and shear conditions on aggregate properties during a flocculation process.
“…Selomulya et al . proposed a population balance model based on restructuring, and that has been used by several researchers in modeling the polymer flocculation of particulate systems • Irreversible breakage: aggregates break apart, losing any chance of further re‐aggregation, likely due to polymer chain rupture (carbon chain session) or relaxation (reconformation) of the adsorbed polymer chains .…”
Water soluble polymer flocculants are important constituents of solid–liquid separation units for the treatment of a variety of process‐affected effluents. The systematic development of a flocculant relies on a good understanding of flocculation process, polymer synthesis, polymer characterization, and, not the least, flocculation performance assessment as desired for a particular treatment process, all of which are essential to establish meaningful relationships between flocculant microstructure and flocculation efficiency. The aim of this article is to communicate the bigger picture of this research area to the readers. The recent advances in the application of bio/natural, synthetic, and stimuli‐responsive flocculants are reviewed. Then, the basic polymer reaction engineering tools to control the microstructure of flocculants are provided and the techniques for the quantification of flocculant microstructure are concisely discussed. This is followed by a review of the methods used for the characterization of particle‐polymer force measurement, and flocculation/dewatering assessment with attention to the characterization of aggregate structures.
“…In Eq. (29) , and are the birth terms due to aggregation and breakage for a particle of size respectively, and correspondingly and are the death terms due to aggregation and breakage [103] , [104] : Fig. 6 Schematic representation of the main possible aggregation mechanisms of microalgae cells.…”
Section: Application Of Pbe Models To the Design Of Downstream Processesmentioning
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