Multilevel structure of sludge flocs

In this work, the structure of two kaolin sludges and a waste activated sludge are investigated using both light-scattering and free-settling methods. Fractal dimensions estimated by the light-scattering and free-settling techniques (D(S) and D(F) respectively) differ significantly and support the hypothesis that naturally occurring aggregates possess a multilevel structure. A two-level floc structural model comprised of (i) a primary floc (of fractal dimension D(S)) consisting of primary particles and (ii) a secondary floc (of fractal dimension D(F)) consisting of the microflocs is proposed to interpret the experimental findings. The structural changes of sludge flocs before and after cationic flocculation are interpreted using the proposed two-level model.     

Aggregation behavior of latex particles in shear flow confined between two parallel plates

In this study, the aggregation and breakup behaviors of latex particles in shear flow confined between two parallel plates were investigated using an in situ observation apparatus with a laser scanning confocal microscope. To investigate the effects of shear rate and the gap width between two parallel plates on the size and structure of the aggregates in the steady state, the distributions of the projected cross-sectional area and perimeter-based fractal dimension of the aggregates were measured. As a result, the average size of the aggregates decreases as shear rate increases and the gap width decreases due to the hydrodynamic effect acting on the aggregates. The size distributions of the aggregates become narrow as the gap width decreases. In addition, the fractal dimension, that is, the structure of the aggregates, was almost independent of shear rate and the gap width and approximately 1.2, which suggests that the aggregates are relatively compact.     

The fractal nature of Escherichia coli biological flocs

The fractal structures of Escherichia coli biological flocs were characterised in terms of fractal dimension, which is a measurement of how the bacteria in the flocs occupy space. The dimensional analysis methods, based on power law correlations between floc perimeter, projected area and maximum length, were used to determine the one- and two-dimensional fractal dimensions (D(1) and D(2)) of E. coli flocs formed by flocculation in chitosan solution with a concentration of 10.0 mg chitosan per g dry cell weight (DCW), giving D(1)=1.07+/-0.06 and D(2)=1.70+/-0.08 (+/-S.D.). The three-dimensional fractal dimension (D(3)) of the E. coli flocs was determined by the two-slopes method, using cumulative size distributions of floc length and solid volume, to be 1.99+/-0.08 (+/-S.D.), which is close to the value of D(3)=2.14+/-0.04 (+/-S.D.) measured by the small angle light scattering method. The results demonstrate that E. coli flocs flocculated with chitosan have a fractal nature, as their fractal dimensions D(1), D(2) and D(3) differ from the values of 1, 2 and 3 expected for the spherical Euclidean object, respectively.     

Investigation of Asphaltene Aggregate Size Distribution Under Aggregation and Breakage Phenomena Using Monte Carlo Simulation

In this article, the aggregation and breakage processes are simulated through Monte Carlo method for asphaltene aggregates under shear-induced petroleum mixtures. The simulation results are verified by the aggregate size distributions of two types of asphaltenes having different fractal dimensions extracted from Iranian crude oil types. The obtained aggregate size distributions are affected by shear rate, toluene to heptane ratios and the oil type. The dynamic evolution of asphaltene aggregates shows an ascendant trend with time until they reach a maximum average diameter and then descent to a steady-state size. The asphaltene fractal dimension affects the aggregation process.     

Measurement of Fractal Aggregates of Polydisperse Particles Using Small-Angle Light Scattering

The effect of primary particle polydispersity on the structure of fractal aggregates has been investigated through the salt-induced, diffusion-limited aggregation of mixtures of hematite. The fractal dimension was determined experimentally using three independent methods: q dependence of static light scattering, kinetic scaling, and correlation of aggregate mass and linear size both determined from Guinier scattering. The fractal dimensions D(f) obtained were 1.75+/-0.03, 1.76+/-0.03, and 1.70+/-0.05, respectively. The use of a previously derived fractal mean particle size was validated in allowing data collapse to master curves for the aggregation kinetics data. The fractal mean particle size is shown to have general utility by taking a number weighting to describe polydisperse aggregation kinetics and a mass weighting to describe small q scattering behavior. Copyright 2000 Academic Press.     

Flocculation of hematite particles by a comparatively large rigid polysaccharide: schizophyllan

We studied the flocculation kinetics and structure of hematite aggregates induced by a large rigid extracellular polysaccharide, schizophyllan. Transmission electron microscopy (TEM), atomic force microscopy (AFM), photon correlation spectroscopy (PCS), and static light scattering (SLS) were used to characterize hematite particles, schizophyllan chains, and their flocs, to follow the time evolution of floc sizes, and to determine floc fractal dimensions. A maximum flocculation rate was found at a certain schizophyllan/hematite ratio. The maximum rate was considerably smaller than the rate of diffusion-limited aggregation (DLA) of hematite particles induced by simple electrolytes. To interpret the experimental results and to reveal various factors affecting the optimal dosage, Monte Carlo simulations were performed on the flocculation of small colloidal particles by relatively long, monodisperse linear polymers. The existence of the maximum flocculation rate was confirmed by computer simulation. However, a higher optimal dosage of schizophyllan was obtained in the experiments. The difference in the optimal dosage can be attributed mostly to the higher adsorption affinity of the hematite on schizophyllan aggregates present in the initial solution and the presence of a large fraction of free polymer chains which do not participate in the flocculation process. Both experiments and computer simulations demonstrated the fractal nature of the schizophyllan-hematite flocs. The fractal dimensions of the flocs at the optimal dosage were determined. A higher fractal dimension was obtained from experiments than from computer simulations, suggesting a reconstruction of the floc structure. Finally, a two-stage flocculation mechanism for hematite particles in the presence of a relatively long schizophyllan polymer was proposed. In the first flocculation stage, the hematite particles are preferentially adsorbed onto the schizophyllan aggregates in solution. The second stage consists of the association of these reactive entities with each other and also with naked chains to form fractal flocs by a bridging mechanism, where the hematite particles play the role of ligands.     

The scaling behavior of a highly aggregated colloidal suspension microstructure and its change in shear flow

The nature of the network structure and the evolution of structural change in shear flow were investigated for metal particle dispersions in terms of fractal aggregation of colloidal particles. Polymer-stabilized metal particle inks were prepared via a polyvinyl chloride coating dispersed in solvent. The fractal dimension of 1.74 was calculated with the scaling model based on the power law relationship between the elastic modulus and volume fraction. This scaling behavior can be explained by considering the deformable network structure of soft materials. While the elastic property of the floc was dominant, the limit of linearity was found at the inter-floc link, which is relatively weak and brittle. The steady shear results reveal two mechanisms that contribute to the breakdown of the microstructure in metal particle inks at increasing shear rate. Scaling of steady shear viscosity shows that these mechanisms are related to both inter-floc interactions and the elasticity of the floc itself. Further, these results suggest that individual flocs deform with weak inter-floc interactions and rupture into smaller flocs or aggregates at high shear stress, which is associated with the increased shear rate.     

Surface analysis of cryofixation-vacuum-freeze-dried polyaluminum chloride-humic acid (PACl-HA) flocs

The powder of polyaluminum chloride-humic acid (PACl-HA) flocs was prepared by cryofixation-vacuum-freeze-drying method. The FTIR spectra show that some characteristic functional groups in polyaluminum chloride (PACl), humic acid (HA), and kaolin still existed in the dried flocs. X-ray diffractometry (XRD) patterns indicate that these flocs are amorphous. Nitrogen adsorption-desorption isotherms were obtained for different samples of the dried PACl-HA flocs. The BET specific surface area, BJH cumulative absorbed volume and BJH desorption average pore diameter of them were determined. The peak values of 8.4-11.2 nm (pore diameter) for pore size distribution (PSD) curves indicate that the pores of the dried flocs are mostly mesopores. The surface fractal dimensions D(s) and the corresponding fractal scales determined from both SEM images and nitrogen adsorption-desorption data sets reveal the multi-scale surface fractal properties of the dried PACl-HA flocs, which exhibited two distinct fractal regimes: a regime of low fractal dimensions (2.07-2.26) at higher scales (23-387 nm), mainly belonging to exterior surface scales, and a higher fractal dimensions (2.24-2.37) at lower scales (0.80-7.81 nm), falling in pore surface scales. Both HA addition and kaolin reduction in dried floc can decrease the irregularity and roughness of external surface. However, for the irregularity and roughness of pore surface, the addition of HA or kaolin in dried floc can increase them. Furthermore, some difference was found between the pore surface fractal dimensions D(s) calculated from nitrogen adsorption and desorption data. The pore surface D(s) values calculated through thermodynamic model were much greater than three.     

Analysis of the structure of very large bacterial aggregates by small-angle multiple light scattering and confocal image analysis

This work aims at developing a more accurate measurement of the physical parameters of fractal dimension and the size distribution of large fractal aggregates by small-angle light scattering. The theory of multiple scattering has been of particular interest in the case of fractal aggregates for which Rayleigh theory is no longer valid. The introduction of multiple scattering theory into the interpretation of scattering by large bacterial aggregates has been used to calculate the fractal dimension and size distribution. The fractal dimension is calculated from the form factor F(q) at large scattering angles. At large angles the fractal dimension can also be computed by considering only the influence of the very local environment on the optical contrast around a subunit. The fractal dimensions of E. coli strains flocculated with two different cationic polymers have been computed by two techniques: static light scattering and confocal image analysis. The fractal dimensions calculated with both techniques at different flocculation times are very similar: between 1.90 and 2.19. The comparison between two completely independent techniques confirms the theoretical approach of multiple scattering of large flocs using the Mie theory. Size distributions have been calculated from light-scattering data taking into account the linear independence of the structure factor S(q) relative to each size class and using the fractal dimension measured from F(q) in the large-angle range or from confocal image analysis. The results are very different from calculations made using hard-sphere particle models. The size distribution is displaced toward the larger sizes when multiple scattering is considered. Using this new approach to the analysis of very large fractal aggregates by static light multiple scattering, the fractal dimension and size distribution can be calculated using two independent parts of the scattering curve.     

Evidence of Shear Rate Dependence on Restructuring and Breakup of Latex Aggregates

Small-angle static light scattering has been used to probe the evolution of aggregate size and structure in the shear-induced aggregation of latex particles. The size of aggregates obtained from the particle-sizing instrument (Coulter LS230) was compared with the size of those obtained with another approach utilizing the Guinier equation on the scattering data. Comparison of the two methods for studying the effects of mixing on the evolution of the aggregate size with time revealed similar trends. The aggregate structures were quantified in terms of their fractal dimensions on the grounds of the validity of Rayleigh-Gans-Debye scattering theory for the fractal aggregates. Analysis of the scattering patterns of aggregates verified that restructuring of the aggregates occurred as the aggregates were exposed to certain shear environments, resulting in a scale-dependent structure that could not be quantified by a fractal dimension. The effect of restructuring on aggregate size was particularly noticeable when the aggregates were exposed to average shear rates of 40 to 80 s(-1), whereas no significant restructuring occurred at lower shear rates. At 100 s(-1), the fragmentation of aggregates appeared to be more significant than aggregate compac-tion. Copyright 2001 Academic Press.     

Structure of Hydrous Ferric Oxide Aggregates

The small angle light scattering behavior of hydrous ferric oxide flocs is examined here and found to provide useful insights into the nature of the aggregates formed despite the large size of these aggregates at later times. The flocs appear to exhibit fractal properties over a significant size range though the aggregates appear to be easily disrupted through mixing effects resulting in breakup and/or restructuring to denser assemblages. Background electrolyte concentrations also have some impact on floc structure but mixing effects and apparent destabilization by ferric ions limit the effect of added electrolytes on the stability and structure of ferric oxyhydroxides. Similar estimates of fractal dimensions of these hydrous ferric oxide flocs are obtained both by static light scattering analysis and by a cluster mass scaling approach. The choice of density distribution cutoff function has some impact on derived size and structure parameters and further refinement in this area is needed. Copyright 2000 Academic Press.     

Prediction of three-dimensional fractal dimensions using the two-dimensional properties of fractal aggregates

Fractal dimension analysis using an optical imaging analysis technique is a powerful tool in obtaining morphological information of particulate aggregates formed in coagulation processes. However, as image analysis uses two-dimensional projected images of the aggregates, it is only applicable to one and two-dimensional fractal analyses. In this study, three-dimensional fractal dimensions are estimated from image analysis by characterizing relationships between three-dimensional fractal dimensions (D(3)) and one (D(1)) and two-dimensional fractal dimensions (D(2) and D(pf)). The characterization of these fractal dimensions were achieved by creating populations of aggregates based on the pre-defined radius of gyration while varying the number of primary particles in an aggregate and three-dimensional fractal dimensions. Approximately 2000 simulated aggregates were grouped into 33 populations based on the radius of gyration of each aggregate class. Each population included from 15 to 115 aggregates and the number of primary particles in an aggregate varied from 10 to 1000. Characterization of the fractal dimensions demonstrated that the one-dimensional fractal dimensions could not be used to estimate two- and three-dimensional fractal dimensions. However, two-dimensional fractal dimensions obtained statistically, well-characterized relationships with aggregates of a three-dimensional fractal characterization. Three-dimensional fractal dimensions obtained in this study were compared with previously published experimental values where both two-dimensional fractal and three-dimensional fractal data were given. In the case of inorganic aggregates, when experimentally obtained three-dimensional fractal dimensions were 1.75, 1.86, 1.83+/-0.07, 2.24+/-0.22, and 1.72+/-0.13, computed three-dimensional fractal dimensions using two-dimensional fractal dimensions were 1.75, 1.76, 1.77+/-0.04, 2.11+/-0.09, and 1.76+/-0.03, respectively. However, when primary particles were biological colloids, experimentally obtained three-dimensional fractal dimensions were 1.99+/-0.08 and 2.14+/-0.04, and computed values were both 1.79+/-0.08. Analysis of the three-dimensional fractal dimensions with the imaging analysis technique was comparable to the conventional methods of both light scattering and electrical sensing when primary particles are inorganic colloids.     

Quantification of a single aggregate inner porosity and pore accessibility using hard X-ray phase-contrast nanotomography

The 3D structure of three individual aggregates composed of 165 nm polystyrene primary particles is revealed nondestructively by hard X-ray phase-contrast synchrotron nanotomography. Three-dimensional image analysis allows us for the first time to obtain the complex inner porosity of the entire aggregate. It is demonstrated that despite their rather compact structure, characterized by a fractal dimension equal to 2.7, the produced aggregates are still porous, with porosity increasing with its size. Generated pores have diameters from 100 nm to 3 μm and are almost completely interconnected.     

Fractal Morphology and Breakage of DLCA and RLCA Aggregates

Latex aggregates, formed in 1 M McIlvaine buffer solution and 0.2 M NaCl solution, have been characterized in terms of aggregate size distribution and fractal morphology. This was achieved using three sizing techniques (image analysis, laser scattering, and electrical sensing) in which size distributions and fractal properties of the aggregates were measured. Estimates of fractal dimensions were made using the two-slope method based on dimensional analysis and the small-angle light scattering method. Aggregate suspensions were prepared using both water and a mixture of heavy water/ water as the solvent. The latter essentially eliminated sedimentation, which was observed after one day of aggregation when water alone was used as a solvent. Latex aggregates formed by diffusion-limited colloid aggregation (DLCA) and reaction-limited colloid aggregation (RLCA) had fractal dimensions close to 1.8 and 2.1, respectively. As observed through image analysis, DLCA aggregates possessed a loose tenuous structure, whereas RLCA aggregates were more compact. Disruption of both DLCA and RLCA aggregates has been investigated in laminar flow and turbulent capillary flow. The shear forces introduced by a laminar shear device with a shear rate up to 1711 s(-1) were unable to bring about aggregate breakup; shearing facilitates aggregate growth in the case of DLCA. However, latex aggregates were significantly disrupted after passage through a turbulent capillary tube at 95209 s(-1). Copyright 2000 Academic Press.     

Cooling effects on a model rennet casein gel system: part I. Rheological characterization

The gelation of a model rennet casein system was studied during cooling at different rates. During cooling, casein network structure development was proposed to evolve over a few steps at different length scales: molecules, particles, flocs, or network. Rennet casein flocs are fractal in nature, and fractal dimension and floc size are two variables affecting the rheology and microstructure of a rennet casein gel. Casein structure formation during cooling from 80 to 5 degrees C at four different rates (0.5, 0.1, 0.05, and 0.025 degrees C/min) was monitored by dynamic rheological tests, and a stronger gel developed at a slower cooling rate. During different cooling schedules, similar fractal dimensions were observed due to a lack of difference in the colloidal interactions. Differences among rheological data were possibly caused by variability in floc size, as observed in the second part of this paper. A larger number of smaller-sized flocs enabled gelation at a higher temperature and created a stronger network at a slower cooling rate. Controlling cooling schemes thus provides an approach for manipulating casein gelation and the microstructure for a system of fixed chemical compositions.     

Fractal aggregates of conjugated polymer in solution state

Semirigid conjugated polymers have received much scientific and technological interest due to their unique electrical and photonic semiconducting properties. Spectroscopic studies have indicated that these polymers underwent interchain aggregation in the solution state even at large dilution; however, the origin of this event and the structure of the resultant aggregates remained the crucial issues to be resolved. In the present study, we revealed that the interchain aggregation of a conjugated polymer, poly(2,3-diphenyl-5-hexyl-1,4-phenylenevinylene) (DP6-PPV), in solutions with chloroform and toluene generated network aggregates with the hydrodynamic radii of several micrometers. Small angle neutron scattering (SANS) demonstrated that the internal structure of these aggregates could be characterized by the mass fractal dimensions of 2.2-2.7. The networks were looser in chloroform but became highly compact in the poorer toluene solvent due to severe segmental association. Increasing the temperature alleviated the segmental association in toluene while largely retaining the mass fractal dimension of the aggregates. However, the interchain aggregation was never completely dissipated by the heating, suggesting the existence of two types of segmental association with distinct stability. The highly stable segmental association that could neither be solvated by chloroform nor be disrupted thermally in toluene was attributed to the pi-pi complex already present in the DP6-PPV powder used for the solution preparation. The chains tied firmly by this complex formed network aggregates in the solution and hence reduced the entropy of mixing of the polymer. In the poorer toluene solvent, further segmental association took place within the preexisting aggregates, making the networks more compact. This type of segmental association could be disrupted by moderate heating, and its occurrence was ascribed to the poor affinity of the aliphatic side chains of DP6-PPV for toluene.     

Fractal Study of Mesoporous Structure in Water Molecular Condensed System

Bis-(4-stearoylaminophenyl) ether (BSADE) can aggregate and self-assemble in water. Transmission electron microscopy (TEM) indicated that the morphology of BSADE aggregates in water was entanglement and thin fiber-like, and that a three dimensional network structure was formed. Water molecules were entrapped in this three dimensional network structure and formed a new type of condensed system (so-called water molecular gel). Water molecular gel is a typical mesoporous material which can be characterized by the fractal dimension D. Using gas adsorption method along with measurement of porosity and specific surface area, the fractal dimension D of the complicated pores was 2.1-2.2 for this water molecular gel. Using viscosity method and the Cayley fractal tree, the fractal dimension D of the fiber-like three dimensional network was determined to be 1.98. The formation process of water molecular gel can be described as nucleation followed by a repeated growing and branching cycle.     

Flocculation kinetics and aggregate structure of kaolinite mixtures in laminar tube flow

Flocculation is commonly used in various solid-liquid separation processes in chemical and mineral industries to separate desired products or to treat waste streams. This paper presents an experimental technique to study flocculation processes in laminar tube flow. This approach allows for more realistic estimation of the shear rate to which an aggregate is exposed, as compared to more complicated shear fields (e.g. stirred tanks). A direct sampling method is used to minimize the effect of sampling on the aggregate structure. A combination of aggregate settling velocity and image analysis was used to quantify the structure of the aggregate. Aggregate size, density, and fractal dimension were found to be the most important aggregate structural parameters. The two methods used to determine aggregate fractal dimension were in good agreement. The effects of advective flow through an aggregate's porous structure and transition-regime drag coefficient on the evaluation of aggregate density were considered. The technique was applied to investigate the flocculation kinetics and the evolution of the aggregate structure of kaolin particles with an anionic flocculant under conditions similar to those of oil sands fine tailings. Aggregates were formed using a well controlled two-stage aggregation process. Detailed statistical analysis was performed to investigate the establishment of dynamic equilibrium condition in terms of aggregate size and density evolution. An equilibrium steady state condition was obtained within 90 s of the start of flocculation; after which no further change in aggregate structure was observed. Although longer flocculation times inside the shear field could conceivably cause aggregate structure conformation, statistical analysis indicated that this did not occur for the studied conditions. The results show that the technique and experimental conditions employed here produce aggregates having a well-defined, reproducible structure.