Turbulent hydrodynamic stress induced dispersion and fragmentation of nanoscale agglomerates

High pressure dispersion nozzles of 2.5-10 mm length and 125 microm diameter have been characterized in terms of fluid dynamics and dispersion experiments at 100-1400 bar. Elongational stresses at the nozzle entry (5 x 10(5) Pa) and turbulent stresses up to 10(5) Pa at a Reynolds number of 25,000 in turbulent channel flow are identified crucial for desagglomeration and aggregate fragmentation. Maximum stresses are calculated on representative particle tracks and related to agglomerate breakage. Agglomerates in the experimental study are in the range of the Kolmogorov micro scale (100-400 nm) and therefore break due to turbulent energy dissipation in viscous flow. Bond strength distributions could be determined experimentally from particle size distributions and fluid dynamics simulations, with primary particle erosion determined as dispersion mechanism for diffusion flame silica particles. Nanoscale agglomerates show a power law scaling for breakage with scaling exponents diverging from theory of floc dispersion. This is attributed to their strong bonding by sinter necks.     

Flocculated flow of microfibrillated cellulose water suspensions: an imaging approach for characterisation of rheological behaviour

Our aim was to characterise the suspension rheology of microfibrillated cellulose (MFC) in relation to flocculation of the cellulose fibrils. Measurements were carried out using a rotational rheometer and a transparent cylindrical measuring system that allows combining visual information to rheological parameters. The photographs were analyzed for their floc size distribution. Conclusions were drawn by comparing the photographs and data obtained from measurements. Variables selected for examination of MFC suspensions were degree of disintegration of fibres into microfibrils, the gap between the cylinders, sodium chloride concentration, and the effects of changing shear rate during the measurement. We studied changes in floc size under different conditions and during network structure decomposition. At rest, the suspension consisted of flocs sintered together into a network. With shearing, the network separated first into chain-like floc formations and, upon further shear rate increase, into individual spherical flocs. The size of these spherical flocs was inversely proportional to the shear rate. Investigations also confirmed that floc size depends on the geometry gap, and it affects the measured shear stress. Furthermore, suspension photographs revealed an increasing tendency to aggregation and wall depletion with sodium chloride concentration of 10⁻³ M and higher.     

Filtration characteristics of a mineral mud with regard to turbulent shearing

The constant 1-MPa pressure filtration characteristics of a flocculated polydisperse phosphate slime slurry were examined in relation to the hydrodynamic conditions of the material's conditioning and its granulometric and textural properties. The dynamic character of the flocculation was studied by laser diffractometry. The aggregation, fragmentation and erosion of the flocs were well differentiated. The effect on the specific filtration resistance of the velocity gradient, size distribution, and porosity of the flocs was defined. With shearing at 120–2050 s⁻¹, the inter-floc porosity increases with decreasing granulometric spreading and increasing intra-floc porosity. A fairly high inter-floc porosity inevitably results in an increased permeability. The best filtration performances were obtained after a conditioning favouring the formation of a small distribution spreading index of floc size distribution and a high porosity cake.     

Sedimentation and electrophoresis of a porous floc and a colloidal particle coated with polyelectrolytes

Sedimentation and electrophoresis of porous colloid complex; a colloidal floc and a colloidal particle covered with adsorbed polyelectrolytes are visited to examine the characteristic length of the transport phenomena. In the sedimentation, the overall size of a floc is dominative in the determination of Stokes drag, while the permeability is determined by the largest pore in the floc. This picture is important when break-up of flocs in a turbulent flow is considered. When a colloidal particles is coated with polyelectrolytes, the characteristic length for diffusion is that of the diameter of colloidal particle plus protruding part of polymer chain adsorbed onto the particle. On the other hand, when the porous colloid complex is placed in the electric field, fluid surrounding the complex can easily penetrate into the complex by means of electro-osmosis. The diffusive part of electric double layer located inside of the complex is the source of strong driving force of this osmotic flow. Flow generated in this regime can be treated as a sort of shear driven. The characteristic length scale for transport phenomena is the Debye length or the distance between charged segments. These lengths are much shorter than the case of sedimentation and Brownian diffusion.     

Drag on two nonuniformly structured flocs moving along the axis of a cylindrical tube

The boundary effect on the drag on two identical, nonuniformly structured flocs moving along the axis of a cylindrical tube filled with a Newtonian fluid is investigated at a small to medium larger Reynolds number. A two-layer model is adopted to simulate various possible structures of a floc, and the flow field inside is described by Darcy–Brinkman model. The results of numerical simulation reveal that a convective flow is present in the rear region of a floc when Reynolds number is on the order of 40. The presence of the tube wall and/or the porous structure of a floc has the effect of reducing that convective flow. For a fixed level of the volume-average permeability of a floc, the influence of the tube wall on the drag depends upon floc structure; the influence on a nonuniformly structured floc is more significant than that on a uniformly structured floc. The more nonuniform the floc structure, the more appreciable the deviation of the drag coefficient–Reynolds number curve from a Stokes’-law-like relation becomes. The smaller the volume-average permeability of a floc and/or the smaller the separation distance between the two flocs, the greater is the deviation, but the presence of the tube wall has the effect of reducing that deviation.     

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.     

Advective flow in spherical floc

Numerous structural models of flocs, such as homogeneous model or radially-varying model, were proposed in literature for predicting the extent of advective flow on the intrafloc transport processes. This work probed the three-dimensional structure of original and chemically flocculated wastewater flocs using the fluorescence in situ hybridization (FISH) and the confocal laser scanning microscope (CLSM) techniques, from which the spherical mesh model on real floc structure was constructed. Simulation results revealed that if an average characteristic of sludge floc, such as porosity or drag force correction factor of sludge floc is of concern, both homogeneous or radially-varying models may be able to apply, particularly for those flocs that were closely compacted. However, the detailed flow patterns inside real floc are much more tortuous than those of the homogeneous or radially-varying models. If local hydrodynamic environment within the floc is of interest, then only the complicated structural model with real floc could be applicable.     

Dynamic simulation of floc breakage with a random breakage distribution

The transient behavior of floc breakage in a lean, batch-stirred tank is investigated. The stochastic nature of breakage distribution (BD), which includes breakage mode (BM) and daughter-floc size distribution (DFSD), makes a deterministic approach unrealistic. The difficulty of representing BM and DFSD through deterministic probability distributions is circumvented by adopting- the Monte Carlo simulation approach to determine their functional forms numerically. On the basis of the conservation of the number of primary particles, the population balance equation describing the transient behavior of the system is solved analytically. The present model involves fewer adjustable parameters than those reported in the literature, yet it is able to take account or the random feature of the breakage phenomenon and the fractal geometry of floc structure.     

Hydrodynamic drag force exerted on activated sludge floc at intermediate Reynolds number

We hung the activated sludge flocs on an elastic nylon stick and then subjected it to a uniform water flow and measured its displacement. The hydrodynamic drag force exerted on the floc was subsequently estimated, both for cationic flocculated flocs and for flocculated and then frozen/thawed flocs. A confocal laser scanning microscope (CLSM) was employed to probe the interior structure of flocs. Polyelectrolyte flocculation leads to a compact global structure, and hence high drag force exerted on the floc by water. The corresponding C(D)Omega value at Re=12-27 for flocs ranges from 1.58 to 3.61. Fast freezing would little affect the hydrodynamic drag force. Slow freezing, in contrast, considerably consolidated the floc structure and hence presented impermeable sphere-like behavior of the slowly frozen/thawed flocs.     

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.     

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.     

Shear-thickening flow of nanoparticle suspensions flocculated by polymer bridging

The steady-shear viscosity, dynamic viscoelasticity, and stress relaxation behavior were measured for suspensions of silica nanoparticles dispersed in aqueous solutions of poly(ethylene oxide) (PEO). The suspensions of silica with diameters of 8-25 nm show striking shear-thickening profiles in steady shear and highly elastic responses under large strains in oscillatory shear. Since the silica particles are much smaller than the polymer coils, one molecule can extend through several particles by intrachain bridging. Each polymer coil may remain isolated as a floc unit and the silica particles hardly connect two flocs. Therefore, the flow of suspensions is Newtonian with low viscosity at low shear rates. When the polymer coils containing several nanoparticles are subjected to high shear fields, three-dimensional network is developed over the system. The shear-thickening flow may arise from the elastic forces of extended bridges. But, the polymer chain is easily detached from particle surface by thermal energy because of large curvature of particles. As a result, the network structures are reversibly broken down in a quiescent state and the suspensions behaves as viscoelastic fluids with the zero-shear viscosity.     

Advective flow in a sludge floc

The interior of sludge floc is highly heterogeneous, while the large pores in the floc control the advective flow. This work for the first time numerically details fluid flow and mass transfer processes in pores of activated sludge floc. The dimensionless permeabilities and mass dispersion coefficients were contoured against pore size ratio and the floc Reynolds number. With a pore size less than 20% of the floc size, the commonly adopted homogeneous model overestimates the floc permeability, and pore velocity is less than 2% of the bulk velocity. This is particularly true for flocs with low porosity. Although the convective flux is low, the dispersive mass transfer rate can be much higher than the diffusional rate, attributable to the strong Taylor dispersion effect. The three-dimensional pore structures in waste activated-sludge floc were identified using confocal laser scanning microscope (CLSM) images. Large pores were used to numerically estimate the permeability and dispersion coefficient for these pores. The permeability and the dispersion coefficient of the tortuous pores can be one order of magnitude lower than those for the equivalent straight pores. Besides the dispersion effect, the pore tortuosity appeared as the most important geometrical factor retarding the advective flow in the sludge pores. In addition, the small side pores connected to the large pore had only a mild effect on the flow process, and can be neglected in analysis.     

Advective flow and floc permeability

This work monitored advection flow through a floc by bubble tracking. Close examination of the motion of a swarm of hydrogen bubbles that passed over a free-falling floc allowed the extent of advection flow to be estimated at 53% for the original activated sludge floc, and 12% for the flocculated floc. The interior permeability of the sludge flocs was estimated from this information. The fluid force exerted on the falling floc was also considered.     

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.     

Effect of floc structure on the rate of shear coagulation

We derived a mathematical expression for the temporal evolution of the number of particles due to shear coagulation, covering the later stage by expanding the initial stage approximation to take into account the formation of floc structure. In the derivation, it is assumed that flocculation proceeds through binary collisions between identical fractal flocs. The capture efficiency between flocs is calculated on the basis of trajectory analysis, which is determined by viscous hydrodynamic interaction between flocs and van der Waals attractive forces between two primary particles located at colliding points of flocs. The validity of the derived equation was tested by a coagulation experiment using polystyrene sulfate latex particles under conditions of rapid coagulation. The experiment was carried out in a laminar Couette flow generated in the gap between two concentric cylinders. Careful and direct observation of flocculation under microscopy provided the data on the fractal dimension as well as the temporal evolution of number concentration of flocs. The measured rate of coagulation gradually increases in accordance with the formation of the fractal structure of flocs. This behavior agreed very well with the prediction based on the derived equation.     

Hierarchical structure of carbon nanotube networks

The hierarchical structure of semidilute suspensions of single-walled carbon nanotubes in polymeric matrices, studied by the use of ultrasmall and small angle neutron scattering, indicates an aggregate size that is independent on both nanotube concentration and polymer matrix and a mesh within the floc that becomes slightly denser with increasing nanotube concentration. The number of clusters grows linearly with concentration of nanotubes. These structural parameters suggest that the interactions between the flocs dictate the concentration-dependent elastic strength scaling of the network, with the absolute values of the specific elastic strength being inversely related to the percolation threshold.     

Cooling effects on a model rennet casein gel system: part II. Permeability and microscopy

Microscopy and permeability studies were performed to further illustrate the cooling effects on rennet casein gel structure and help interpret the rheological observations in the first part of this paper. Samples of gels cooled from 80 to 5 degrees C at four rates (0.5, 0.1, 0.05, and 0.025 degrees C/min) were studied with a confocal laser scanning microscope. A larger number of smaller flocs were generated at slower cooling rates, creating more cross-links within a network and corresponding to a stronger gel. Formation of a larger number of smaller flocs was hypothesized to result from a greater degree of doublet formation because the system spent more time within the temperature region where doublet formation is favored when cooled at slower rates. The doublets represent sites available for floc growth, similar to nucleation sites for crystal growth. Microscopy results further substantiated that the cooling effects were different from the aging effects because cooling affected floc size, and aging enabled the addition of idle flocs into the casein network. The conclusions for the cooling effects on floc size were further supported by permeability tests. A smaller permeability coefficient resulted from smaller flocs obtained with a slower cooling schedule. This study showed the importance of controlling floc numbers to modulate the strength of a gel, and cooling rates provide an approach of modulating functional properties when the chemical composition of a system is fixed.