Changes in fractal dimension during aggregation

Chakraborti, Rajat K.; Gardner, Kevin H.; Atkinson, Joseph F.; Benschoten, John E. Van

doi:10.1016/s0043-1354(02)00379-2

Cited by 246 publications

(129 citation statements)

References 21 publications

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“…High D F means the primary particles in an aggregate are arranged compactly, while low D F results from large, highly branched and loosely bound structures. According to previous research, methods utilized to characterize the fractal dimension are mainly microscopy, light scattering, and settling techniques (Wu et al, 2002;Koen and Willy, 1997;Chakraborti et al, 2003;Tang et al, 2002).…”

Section: Fractal Dimensionmentioning

confidence: 99%

Characterization of kaolin flocs formed by polyacrylamide as flocculation aids

Zhu

et al. 2009

International Journal of Mineral Processing

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a b s t r a c t a r t i c l e i n f oAlthough the synthetic organic polymers have been widely applied as flocculant aids to improve solid-liquid separation efficiency, it is not very clear how the charge type and molecular weight of the polymers influence the characteristics of flocs. In this paper, floc characteristics, such as floc size, density, structure, strength and reversibility were investigated in details in terms of their response to the polyacrylamide (PAM) with different charge types and molecular weights. Laser light scattering, image analysis and settling technology were employed simultaneously. The results showed that floc size induced by anionic PAM with medium molecular weight (A130) and ultra high molecular weight (A115) was 419 µm and 438 µm respectively, correspondingly, floc size induced by cationic PAM with medium molecular weight (C448) and very high molecular weight (C498) was 731 µm and 796 µm. Meanwhile, floc fractal dimension was inversely proportional to polymer molecular weight and the values were between 1.91 and 2.40. In addition, floc density was affected by molecular weight of anionic PAM more dramatically than that of cationic PAM. For a given floc size, the density increased with molecular weight. Furthermore, flocs formed by cationic PAM showed much greater shear-resistant ability and reversibility than anionic PAM. Nevertheless, the poor reversibility of the flocs formed by high molecular weight was also observed. An explanation for the resultant floc characteristics was offered in terms of flocculation mechanisms.

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Section: Fractal Dimensionmentioning

confidence: 99%

Characterization of kaolin flocs formed by polyacrylamide as flocculation aids

Zhu

et al. 2009

International Journal of Mineral Processing

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“…At present, three common techniques for fractal dimension measurement have been developed, i.e. light scattering, settling and image analysis [12][13][14][15].…”

Section: Fractal Dimensionmentioning

confidence: 99%

Characterization of floc size, strength and structure under various coagulation mechanisms

et al. 2006

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Flocs generated by various coagulation mechanisms exhibit different size, strength and structure. The properties and fractal dimensions of flocs formed under three common coagulation mechanisms, i.e. charge neutralization, sweep and bridging, were investigated at various hydraulic conditions. The results showed that the floc size decreased with the increasing average velocity gradient G and the stable floc size exponent γ was of the following hierarchy: charge neutralization (0.6107) N sweep (0.5618) N bridging (0.3674). Furthermore, fractal dimensions of flocs were the highest when formed by sweep and the lowest when generated by bridging flocculation. The mass fractal dimensions measured by light scattering were between 2.0 and 3.0 and the floc strength was between 0.01 and 0.58 N m − 2 . An intrinsic unity of the relationship among floc size, fractal dimensions, floc strength under the three coagulation mechanisms was demonstrated.

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“…In particular, considering constant aggregate properties (ρ floc =constant and n=constant) is obviously too restrictive. As reported by CHAKRABORTI et al (2003), the fractal dimension varies during the aggregation process. WINTERWERP and VAN KESTEREN (2004) found that the fractal dimension is larger than 2.6 for cohesive sediment beds, whilst for suspended floc is usually lower than 2.2.…”

Section: Resultsmentioning

confidence: 67%

A one-dimensional two-phase flow approach for sedimentation-consolidation modelling

Chauchat¹,

Guillou²,

Bang³

et al. 2012

XIIèmes Journées, Cherbourg

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Résumé :Nous présentons un modèle diphasique pour la sédimentation-consolidation basé sur la résolution des équations de continuité et de quantité de mouvement pour les deux phases liquide et solide. La loi de Darcy-Gersevanov est utilisée pour la fermeture du transfert de quantité de mouvement entre les deux phases et le concept de "contrainte effective" est introduit pour tenir compte de la structuration du lit. Le modèle est validé par rapport à des données expérimentales hautement résolues pour les profils de concentration. Le bon accord obtenu entre les résultats numériques et les données expérimentales montre la capacité prédictive du modèle à deux phases. Mots-clés :Sedimentation -Consolidation -Two-phase flow -Numerical model Abstract:A two-phase flow model for sedimentation-consolidation process is presented. The model is based on solving the continuity and momentum equations for both fluid and solid phases. Darcy-Gersevanov's law is used for the closure of the momentum transfer between the two phases and the concept of "effective stress" is introduced to account for the bed structuring. These closure laws are validated against high resolution experimental data in terms of settling curves and concentration profiles. The good agreement obtained between numerical results and experimental data shows the predictive capability of the two-phase model.

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Changes in fractal dimension during aggregation

Cited by 246 publications

References 21 publications

Characterization of kaolin flocs formed by polyacrylamide as flocculation aids

Characterization of kaolin flocs formed by polyacrylamide as flocculation aids

Characterization of floc size, strength and structure under various coagulation mechanisms

A one-dimensional two-phase flow approach for sedimentation-consolidation modelling

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