Effect of floc structure on the rate of Brownian coagulation

A modified expression for the Smoluchowski solution for the temporal evolution of the number concentration of flocs subject to Brownian coagulation is proposed, taking into account the effect of the growth of floc structure. In the proposed equation, the effect is expressed as a decrease of free volume in the liquid phase due to the increase of effective floc volume in accordance with the progress of coagulation. The validity of the proposed equation was tested by coagulation experiments using polystyrene latex particles. Direct counting of the number of flocs under microscopy provided accurate data on the temporal evolution of the number concentration of flocs. The obtained rate gradually increases in accordance with the growth of floc structure. This behavior agreed exactly with the prediction based on the proposed equation.     

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.     

Flocculation of kaolin particles by two typical polyelectrolytes: A comparative study on the kinetics and floc structures

The flocculation kinetics of kaolin particles induced by two polyelectrolytes is studied by using small-angle laser light scattering (SALLS). Two different methods, image analysis and SALLS, are used to calculated the fractal dimensions of flocs formed under different flocculation mechanisms. For a high charge density of polydiallyldimethylammonium chloride (PDADMAC), the initially flocculation rates are slow due to the quite low molecular weight. Smaller and more compact flocs are in the particle–particle connections, and restructuring of the flocs occurs in the flocculation process. With cationic polyacrylamide C498 of very high molecular weight and low charge density, however, the initially flocculation rates are much higher due to its rapid adsorption on kaolin particles, but it will take the adsorbed polymer a much longer time to reach equilibrium due to re-conformation. High potentialities of adsorption prevent the particles from entering the interior of the floc structure or rearrangement, which results in a more open floc structure. Different underlying flocculation mechanisms are evident for these two kinds of polyelectrolytes, in which charge neutralization is mainly involved for the low molecular weight and high charge density polymer of PDADMAC while polymer bridging is suggested to be the dominant mechanism for the high molecular weight polyelectrolyte of C498.     

Viscosity effect on the structural compactness of latex flocs formed under weak depletion attractions

Dilute aqueous dispersions of colloidal polystyrene latex spheres were flocculated by adding a nonadsorbing polymer sample, poly(acrylic acid). The structural compactness of the flocs thus formed was characterized in terms of their mass fractal dimension using the small-angle static light scattering technique. It was found that with low poly(acrylic acid) concentrations and thus weak depletion attraction forces, the dispersion medium viscosity had a marked effect on the floc structure. An increase in the viscosity led to formation of denser flocs. This was revealed in three sets of depletion flocculation experiments: (a) adjusting the background electrolyte concentration at a fixed level of poly(acrylic acid), (b) using water and 30% (w/w) glycerol as the respective solvents, and (c) inducing latex flocculation with two poly(acrylic acids) of different molecular weights at the respective critical polyacid concentrations. Direct force measurements were made with atomic force microscopy to isolate the influence of viscosity on floc structure from that of interparticle interaction energies. We conclude that the formation of denser flocs with increasing medium viscosity can be attributed to the reduced diffusivity of particles in the solution. The latter resulted in an enhanced rate of floc restructuring (through relaxation of attached particles) relative to floc growth.     

Early-stage flocculation kinetics of polystyrene latex particles with polyelectrolytes studied in the standardized mixing: Contrast of excess and moderate polyelectrolyte dosage

Standardized mixing procedure was applied to the analysis of flocculation of polystyrene latex (PSL) particles with polyelectrolytes. After confirming the initial enhancement of flocculation rate in the very beginning followed by abrupt stop with excess dosage, attention was shifted to the system of moderate dosage. In the former, effects of ionic strength were further analyzed to find the consistency with adsorption isotherm. In the latter, flocculation started slowly in the beginning, sometime slower than salt-induced rapid coagulation, however, the rate gradually increases in the middle stage. Often, the increased rate exceeds that of salt-induced rapid coagulation. This behavior emerged more clearly in the case of lower ionic strength. This is the indication that the rate of relaxation of polymer on the colloidal surface is a function of surface coverage and ionic strength. The ultimate degree of flocculation is usually higher than that observed for excess dosage. The size distribution of flocs was also examined, however, no clear difference between different experimental conditions was confirmed for the same degree of flocculation.     

Contribution of static light scattering to the textural characterization of large aggregates

The industrial processes of water clarification often imply flocs of millimeter length. The principal motivation of this work relates to the characterization of these large flocs with laser diffractometry, for which the authors propose particular experimental approaches. In addition, a reformulation of the various properties of the flocs accessible by laser diffractometry is presented, in particular for the determination of the size, density, porosity, volume fraction, and fractal dimension. By way of illustration, these experimental and theoretical developments are applied to the characterization of flocs obtained by flocculation of a commercial kaolin. The size, fractal dimension, and density of kaolin floc were examined under various flocculant concentrations. Measurements reveal important variations of the granulometric and textural properties of large flocs in response to flocculation, opening ways of optimization for the associated industrial processes.     

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.     

Flocculation and reflocculation of clay suspension by different polymer systems under turbulent conditions

The focused beam reflectance measurement (FBRM), also known as scanning laser microscopy (SLM), was used as a real-time monitor to study the flocculation and reflocculation of clay suspensions under different shear conditions in the presence of single polymer, dual polymer, microparticle and poly(ethylene oxide)/phenolformaldehyde (PEO/PFR) flocculation systems. For initial flocculation, the high molecular weight PEO and cationic polyacrylamide (CPAM) produced larger flocs than others. However, reflocculation of clay suspensions formed by these non- or low-charged polymers was insignificant after the initial flocs were broken under high shear force. In contrast, high charge density polymers, such as poly(diallyldimethylammonium chloride) (PDADMAC), do not form large initial flocs, but they showed significant reflocculation ability under a continuous shear condition. It is concluded that high flocculation can be obtained by effective polymer bridging, but high reflocculation can only be induced by high electrostatic attractive forces between suspended particles.     

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.     

Flocculation of microgel particles with sodium chloride and sodium polystyrene sulfonate as a function of temperature

The flocculation behavior of poly(N-isopropylacrylamide) (PNIPAM) microgel particles, containing surface sulfate groups, has been studied as a function of sodium chloride [NaCl] concentration, between 0.1 and 800 mM NaCl and over the temperature range 25-60 degrees C. The critical flocculation temperature (CFT) of the particles was determined as a function of NaCl concentration. Three regions of NaCl concentration were established. First, at very low values of [NaCl] (< approximately 25 mM), no CFT value could be determined; this implies that the interparticle electrostatic repulsion is sufficient to prevent any flocculation occurring. This remains the case even at temperatures well in excess of the lower critical solution temperature for PNIPAM in solution, where the particles are essentially deswollen. Second, at intermediate [NaCl] (approximately 25-100 mM), the CFT decreased strongly with increasing [NaCl]. In this region, the electostatic forces are weakened sufficiently for the van der Waals forces to cause flocculation. Third, at higher [NaCl] (> approximately 100 mM), the electrostatic repulsion is screened out, and the CFT decreases linearly with [NaCl]. The reason for this decrease is the fact that aqueous solutions of NaCl become increasingly poorer solvent environments for PNIPAM with increasing [NaCl]. These trends are apparent also in the values determined for the hydrodynamic size of the stable PNIPAM particles as a function of [NaCl] and temperature. It is shown that the flocculation of the PNIPAM particles is consistent with a weak, reversible flocculation model. This is apparent, for example, from the fractal dimensions of the flocs (approximately 2.0), determined from the power law used to fit the time evolution of the hydrodynamic size of the flocs, and also from the estimated depth of the mimimum in the interparticle pair potential, based on the critical size of the primary particles where flocculation just begins to occur. The effect of adding sodium poly(styrene sulfonate) [PSS] to the PNIPAM dispersions, in the absence of NaCl, was also investigated. The minimum amount of PSS required to induce flocculation was found to decrease with increasing temperature.     

The controlled flocculation of particulate dispersions using small particles of opposite charge. II. Investigation of floc structure using a freeze-fracture technique

The flocculation of large negative polystyrene particles by small, positive polystyrene particles, each having an adsorbed layer of poly(vinyl alcohol) (PVA) of molar mass 37,000, was investigated using a freeze-fracture technique. This method involves minimal disturbance of the dispersion and, therefore, direct observation of the structure of the flocs is possible. It is shown that the main mechanism of flocculation for these dispersions is for the small particles to bridge between the large particles.     

Effect of temperature and pH on droplet aggregation and phase separation characteristics of flocs formed in oil–water emulsions after coagulation

Coagulation process is used for destabilization of emulsions to promote aggregation of oil droplets on flocs which can be subsequently removed by sedimentation or flotation. The objectives of this study were to investigate the effect of temperature and pH on the effectiveness of destabilization of olive oil–water emulsions in relation to floc morphology and aggregation characteristics of oil droplets, and to quantify the ability of flocs to capture and separate oil. A cationic polyelectrolyte was used for the coagulation of oil droplets in edible olive oil–water emulsions using a jar test apparatus. The flocs formed in olive oil–water emulsions after coagulant addition were analyzed using microscopic image analysis techniques. Fractal dimension, radius of captured oil droplets on flocs, number of oil droplets aggregated on flocs, and floc size were used to quantitatively characterize and compared the effectiveness of the coagulation process at different conditions (pH and temperature) and the ability of flocs to remove oil from water. Analysis of microscopic images showed that floc size was not always the best measure of effectiveness of coagulation process in oil–water emulsions. The flocs forming at different pH levels and temperatures had significant morphological differences in their ability to aggregate different sizes and numbers of oil droplets, resulting in significant differences in their ability for separating oil. Fractal dimension did not correlate with the ability of flocs to aggregate oil droplets nor the total amount of oil captured on flocs. Temperature had a significant effect on droplet size and number of droplets captured on flocs. The differences in floc sizes at different temperatures were not significant. However, the flocs forming at 20 °C had fewer but larger droplets aggregating larger amounts of oil than flocs formed at 30 °C and 40 °C. The size of droplets at different pH levels was similar, however, there were significant differences in number of droplets aggregating on flocs and floc sizes. The amount of oil captured on flocs at pH 7 and pH 9 was significantly higher than those at pH 5 and pH 11. The calculated fractal dimensions of the flocs (all less than 1.8) indicated that the coagulation process was diffusion limited implying that there was no repulsion between the colliding particles (i.e., droplets and flocs); hence, each collision between flocs and droplets resulted in attachment.     

Light scattering study on the size and structure of calcium phosphate/hydroxyapatite flocs formed in sugar solutions

The formation, flocculation and sedimentation of calcium phosphate particles are among the main physico-chemical reactions that occur during the clarification of cane sugar juice. The mechanisms through which processes occur in juice clarification are still poorly understood. This study (being part of a comprehensive investigation to unravel these mechanisms) reports on the size and structure of calcium phosphate particles and aggregates in water and sugar solutions at 20 degrees C using the small angle laser light scattering technique. The average size of the primary calcium phosphate particles was in the range 10.4+/-1.1 microm to 17.5+/-1.2 microm and the scattering exponents, which describe the structure of the calcium phosphate flocs, varied from 1.97 to 2.76. The flocs formed without flocculant are more compact in water than those formed in sugar solution. The compactness of the flocs was also affected by pH of the solution. This effect has been explained by considering the electrical double layer phenomenon.     

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.     

Cluster-cluster aggregation kinetics and primary particle growth of soot nanoparticles in flame by light scattering and numerical simulations

The agglomeration kinetics of growing soot generated in a diffusion atmospheric flame are here studied in situ by light scattering technique to infer cluster morphology and size (fractal dimension D(f) and radius of gyration R(g)). SEM analysis is used as a standard reference to obtain primary particle size D(P) at different residence times. The number N(P) of primary particles per aggregate and the number concentration n(A) of clusters are evaluated on the basis of the measured angular patterns of the scattered light intensity. The major finding is that the kinetics of the coagulation process that yields to the formation of chain-like aggregates by soot primary particles (size 10 to 40 nm) can be described with a constant coagulation kernel beta(c,exp)=2.37x10(-9) cm3/s (coagulation constant tau(c) approximately = 0.28 ms). This result is in nice accord with the Smoluchowski coagulation equation in the free molecular regime, and, vice versa, it is in contrast with previous studies conducted by invasive (ex situ) techniques, which claimed the evidence in flames of coagulation rates much larger than the kinetic theory predictions. Thereafter, a number of numerical simulations is implemented to compare with the experimental results on primary particle growth rate and on the process of aggregate reshaping that is observed by light scattering at later residence times. The restructuring process is conjectured to occur, for not well understood reasons, as a direct consequence of the atomic rearrangement in the solid phase carbon due to the prolonged residence time within the flame. Thus, on one side, it is shown that the numerical simulations of primary size history compare well with the values of primary size from SEM experiment with a growth rate constant of primary diameter about 1 nm/s. On the other side, the evolution of aggregate morphology is found to be predictable by the numerical simulations when the onset of a first-order "thermal" restructuring mechanism is assumed to occur in the flame at about 20 ms residence time leading to aggregates with an asymptotic fractal dimension D(f,infinity) approximately = 2.5.     

The effect of particle coalescence on the surface area of a coagulating aerosol

The initial stage of particle formation in high temperature processes is characterized by a high density of very small particles undergoing rapid coagulation. When these particles are solid this leads to agglomerates with a high specific surface area. However, at high gas temperatures particle coalescence which is very sensitive to the temperature may reduce the surface area and increase the size of the primary particles. In this paper we generalize the Smoluchowski equation to incorporate the coalescence rate into the aerosol dynamics. Individual agglomerates are characterized by their volume, v, and surface area, a. A Liouville term is added to the coagulation equation determining the movement of the distribution function through a-space due to coalescence. For the rate of coalescence a simple two sphere model has been used. Results for the surface area and the average diameter of the individual primary particles are presented for the case of a collision kernel which is independent of the particle structure. As an example, the theory is applied to fine particle formation in combustion processes under nonisothermal conditions.     

Comparison of stages in oil agglomeration process of quartz with sodium oleate in the presence of Ca(II) and Mg(II) ions

The oil agglomeration of quartz with sodium oleate in the presence of calcium and magnesium ions comprises three consecutive stages: adsorption of cations onto quartz surfaces, which leads to coagulation of the suspension, shear flocculation with sodium oleate and finally, agglomeration of flocs by kerosene. The effects of pH and cation concentration on these stages were investigated and the results were presented comparatively. It was found that all the stages of oil agglomeration of quartz exhibited sharp dependences on pH and cation concentration. That is, these stages generally took place in the pH and concentration ranges in which hydroxy complexes of the cations existed in the suspension. In the case of magnesium ion, the coagulation, shear flocculation and especially oil agglomeration of quartz improved after precipitation of hydroxide. These species of calcium and magnesium ions formed at high pH were adsorbed on the negatively charged surface of quartz, as a result of which the adsorption of sodium oleate became possible and thus the shear flocculation of the particles was achieved. Thereafter, the hydrophobic quartz flocs could be agglomerated by kerosene as bridging liquid. The increase in the shear flocculation efficiency depending on the increase of surface hydrophobicity enhanced the oil agglomeration of quartz with kerosene. The maximum recoveries for all the stages of the quartz were obtained in the presence of 10(-3) M magnesium and 5x10(-3) M calcium ions at pH 11. However, some differences in the behavior of shear flocculation and oil agglomeration of quartz suspension were observed above 10(-3) M concentration of magnesium ion.     

Scaling invariance of the von Smoluchowski rate law

The kinetics of flocculation for colloidal suspensions that occur in natural environments have often been studied in terms of the von Smoluchowski rate law. Recent theoretical studies have analyzed scale-invariant flocculation processes leading to the formation of fractal structures which, in turn, have been observed in experiments on synthetic colloids. In this paper, these processes are described in terms of the scaling invariance of the von Smoluchowski equation itself and are shown to be consistent with asymptotic limits of two of its well known exact solutions, corresponding to transport- or reaction-controlled flocculation. The resulting self-similar forms of these solutions and the associated fractal properties of the floccules are discussed in the context of proposed universality classes. The results are applied to the characterization of heterogeneous colloids found in natural aqueous systems.     

Computer Simulation of Bridging Flocculation Processes: The Role of Colloid to Polymer Concentration Ratio on Aggregation Kinetics

The flocculation of colloidal particles by adsorbing polymers is one of the central issues of colloid science and a very important topic in many industrial, biological, and environmental processes. We report a computer simulation study of a 2- and 3-dimensional model for bridging flocculation betweenlarge linear polymer chains and comparatively small colloidal particles,where the structure and growth kinetics of cluster formation are investigated. This model was developed within the framework of the cluster–cluster aggregation model using mass and fractal dimension dependent diffusion constants, where bridging flocculation is seen as a case of heterocoagulation in which, in addition, macromolecule configurations and lengths play an important role. The simulation of aggregate structure and formation kinetics obtained at different (i) relative particle concentrations, (ii) polymer chain conformations, and (iii) sticking probabilities are described from a qualitatively and quantitative point of view. The results suggest that the formation of large aggregates is a slow process, controlled by the reactivity of the clusters, even when the reaction between microcolloids and macrochains is very fast. Aggregation kinetics are strongly dependent on the particle/chain concentration ratio and on the configurational properties of the chains. It is shown that the scaling laws which are valid for homocoagulation processes are also applicable to the kinetics of bridging flocculation. The corresponding scaling exponents have been calculated.