Population balance modeling of aggregation and breakage in turbulent Taylor–Couette flow

Šoóš, Miroslav; Wang, L.; Fox, Rodney O.; Šefčı́k, Ján; Morbidelli, Massimo

doi:10.1016/j.jcis.2006.12.016

Cited by 46 publications

(45 citation statements)

References 59 publications

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“…As was observed by several authors [5,17,38], typical values of d pf at steady state for aggregates produced under turbulent conditions are in the range from 1.1 to 1.4. The d f value can then be estimated using a correlation between perimeter fractal dimension and three-dimensional fractal dimension developed by Lee and Kramer [66] using analysis of aggregates with different size and structure generated by Monte Carlo method.…”

Section: Image Analysissupporting

confidence: 68%

“…This would indicate that in this case the morphology is the same, independent of the applied shear rate. However, although using strong electrolyte both, a shear rate independent morphology with fractal dimension in the range from 2.2 to 3.0 [5,6,17,[36][37][38] or dependency of the fractal dimension on the shear rate covering the range of values from 2 to 2.9 [13,15] were observed. One possible reason for this discrepancy is that various researchers use different experimental techniques without taking much attention to their suitability for the particular problem under examination.…”

Section: Introductionmentioning

confidence: 89%

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Effect of shear rate on aggregate size and morphology investigated under turbulent conditions in stirred tank

Šoóš

Moussa

Ehrl

et al. 2008

Journal of Colloid and Interface Science

153

251

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Section: Image Analysissupporting

confidence: 68%

Section: Introductionmentioning

confidence: 89%

Effect of shear rate on aggregate size and morphology investigated under turbulent conditions in stirred tank

Šoóš

Moussa

Ehrl

et al. 2008

Journal of Colloid and Interface Science

153

251

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“…In the first trend, the median size distribution of the flocs rapidly increases with time at the beginning of flocculation development and then continually slows down until a steady state is approached [7][8][9][10][11][12][13][14][15][16][17][18][19]. This type of size-time profile is henceforth referred to as type I.…”

Section: Introductionmentioning

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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“…Serra et al used polystyrene spheres in a NaCl aqueous solution sheared in a concentric cylinder Taylor-Couette device and found that, despite the fact that the final aggregate size can depend on the primary particle concentration and the shear stress, no significant changes in the fractal dimensions occurred due to restructuring and that these dimensions remained unchanged for different values of the shear rate in the laminar region [70,71]. More recently, Soos et al looked at 10-micron-diameter polystyrene spheres in a Taylor-Couette device under turbulent conditions and showed that the time evolution of the particle cluster size distribution could be captured by standard population balance modeling [72]. They also examined the evolution with time of the perimeter fractal dimension; although, they destabilized the particles outside the Taylor-Couette apparatus and speculated that the shear experienced by pumping the dispersion into the apparatus caused significant restructuring.…”

Section: Wyatt Et Al (2012) Studied the Flocculation Behavior Of A Fmentioning

confidence: 99%

First-principles flocculation as the key to low energy algal biofuels processing.

Hewson¹,

Wyatt²,

Pierce³

et al. 2012

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This document summarizes a three year Laboratory Directed Research and Development (LDRD) program effort to improve our understanding of algal flocculation with a key to overcoming harvesting as a techno-economic barrier to algal biofuels. Flocculation is limited by the concentrations of deprotonated functional groups on the algal cell surface. Favorable charged groups on the surfaces of precipitates that form in solution and the interaction of both with ions in the water can favor flocculation. Measurements of algae cell-surface functional groups are reported and related to the quantity of flocculant required. Deprotonation of surface groups and complexation of surface groups with ions from the growth media are predicted in the context of PHREEQC. The understanding of surface chemistry is linked to boundaries of effective flocculation. We show that the phase-space of effective flocculation can be expanded by more frequent alga-alga or floc-floc collisions. The collision frequency is dependent on the floc structure, described in the fractal sense. The fractal floc structure is shown to depend on the rate of shear mixing. We present both experimental measurements of the floc structure variation and simulations using LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). Both show a densification of the flocs with increasing shear. The LAMMPS results show a combined change in the fractal dimension and a change in the coordination number leading to stronger flocs. 4 ACKNOWLEDGMENTSThis program to improve our understanding of algal flocculation and harvesting was initiated through the Laboratory Directed Research and Development (LDRD) program, and the authors of this report are indebted to many people for their continued support. We have benefited in particular from the braider understanding of the bioenergy landscape provided by Ron Pate,

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Population balance modeling of aggregation and breakage in turbulent Taylor–Couette flow

Cited by 46 publications

References 59 publications

Effect of shear rate on aggregate size and morphology investigated under turbulent conditions in stirred tank

Effect of shear rate on aggregate size and morphology investigated under turbulent conditions in stirred tank

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

First-principles flocculation as the key to low energy algal biofuels processing.

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