Floc breakage in agitated suspensions: Theory and data processing strategy

Flow visualization of chemical flocs in a simple extensional flow field reveals two distinct mechanisms for their breakage: splitting into a relatively small number of daughter fragments whose sizes are comparable to the parent flocs, along with continual disintegration by erosion to produce extremely fine particles from the extremities of the parent floc along the axis of extension. In turbulent flow, these two mechanisms still occur, although the kinematics of flow are more complex. This work presents a formulation of the population balance equation that governs the floc size distribution in turbulent flow, incorporating both the splitting and erosion mechanisms discussed above. Experiments were conducted in which floc size distributions of dilute suspensions are measured by a combination of techniques, including computerized optical scanning of photographs and pulse height analysis of signals from a light blockage transducer. The experimentally determined size distributions are then fit to those computed from the population balance equation, using constrained nonlinear least squares. This yields best values of certain coefficients that appear in the governing equation, providing a strategy to obtain a data base to promote deeper theoretical analysis. The method is demonstrated by analyzing data for kaolin-Fe(OH)₃ flocs in aqueous suspensions.     

Destructive aggregation: aggregation with collision-induced breakage

Mean-field population balance equations are used to describe the evolution of particle size distributions in a wide variety of systems undergoing simultaneous aggregation and breakage. In this paper we develop a population balance that includes aggregation combined with collision-induced particle breakage for arbitrary fragment distribution functions, provided that this distribution function depends only on the total mass of the particles undergoing a collision. We then develop a specific distribution function for arbitrary two-body collisions by postulating that each collision produces a transition-state aggregate having the morphology of a linear polymer. The behavior of the resulting equation is then analyzed for the case in which the collision kernel is a constant, and partial analytical solutions are derived and compared to corresponding Monte-Carlo simulation results. The computer simulations are then used to validate a proposed scaling law for the steady-state particle size distribution. Lastly, the behavior of the aggregation with collision-induced-breakage population balance equation is compared and contrasted with the behavior of an analogous aggregation with linear-breakage population balance equation.     

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

An experimental and computational study of aggregation and breakage processes for fully destabilized polystyrene latex particles under turbulent-flow conditions in a Taylor-Couette apparatus is presented. To monitor the aggregation and breakage processes, an in situ optical imaging technique was used. Consequently, a computational study using a population balance model was carried out to test the various parameters in the aggregation and breakage models. Very good agreement was found between the time evolution of the cluster size distribution (CSD) calculated with the model and that obtained from experiment. In order to correctly model the left-hand side of the CSD (small clusters), it was necessary to use a highly unsymmetric fragment-distribution function for breakage. As another test of the model, measurements with different solid volume fractions were performed. Within the range of the solid volume fractions considered here, the steady-state CSD was not significantly affected. In order to correctly capture the right-hand side of the CSD (large aggregates) at the higher solid volume fraction, a modified aggregation rate prefactor was used in the population balance model.     

Effect of emulsion breakage on selectivity in the separation of hydrocarbon mixtures using aqueous surfactant membranes

In liquid membrane separation processes emulsion breakage results in non-selective physical mixing of the feed mixture with the receiving solvent phase. In this paper a model is developed for describing the interphase transfer process, which takes emulsion breakage into account. The overall transfer is envisaged as a result of two parallel transfer mechanisms: (i) diffusive transport across the membrane and (ii) non-selective physical mixing of the feed with the receiving phase due to emulsion breakage. For selective removal of aromatics from non-aromatics in a feed mixture the “ideal” selectivity, β, obtained in the absence of non-selective breakage, will he given as the ratio of the products of the distribution coefficients times the diffusivity in the aqueous membrane phase. Experiments were carried out in a batch stirred cell to determine the permeation rates for a benzene-n-heptane mixture. From the experimentally observed selectivities the contribution due to emulsion breakage was estimated. This fractional breakage was in good agreement with values determined independently using a water-insoluble dye tracer technique, lending support to the developed model. Further experiments were carried out with the system 1-methylnaphthalene-dodecane, and breakage-corrected transfer rates were determined. The model developed in this paper, together with the experimental studies, sheds light on the mechanism of liquid membrane permeation and should aid in scaling-up processes for dearomatization of naphtha and kerosine.     

A bubble breakage model for finite Reynolds number flows

The breakage frequency of bubbles in turbulent liquid flows is modeled as the inverse of the breakage time by Martinez-Bazan et al. [J. Fluid Mech. 401: 157–182; 1999]. In this definition of the breakage frequency, it is assumed that the breakage probability is unity and hence all bubbles will break. This assumption is reasonable in turbulent flows at extremely high Reynolds numbers in which the turbulence energy dissipation is very high. For systems characterized by finite Reynolds numbers the energy dissipation rate decreases rapidly and the breakage probability is reduced significantly. In the present study, the breakage frequency model by Martinez-Bazan et al. has been extended to include the effect that only a fraction of the bubbles breaks at finite Reynolds numbers. For this model extension, an adjusted version of the breakage probability formula proposed by Coulaloglou and Tavlarides [Chem. Eng. Sci. 32: 1289–1297; 1977] was employed. The extended breakage frequency model for finite Reynolds number flows has been evaluated by comparison to recent experimental single bubble breakage data. It can be concluded that extensive experimental analyses are required to gather sufficient experimental data for improved understanding of the physical phenomena and for model validation. In particular, the bubble breakage analysis must be performed simultaneously with the characterization of the local turbulence properties in the flow.     

The equal-size binary breakage problem: evolution toward a steady shape or periodic behavior?

During the last few years, the self-similar particle size distribution for a particle population undergoing breakage in equal size fragments has been derived using approximating, numerical, and analytical means. But very recently it was shown [N.V. Mantzaris, J. Phys. A Math. Gen. 38 (2005) 5111] through transient simulation of the breakage process that the particle size distribution in case of breakage in two equal fragments, never attains a steady shape, i.e., a self-similar form. The new results give rise to questions about the real meaning and utility of the previously derived self-similar distributions for these systems. The scope of the present work is to answer these questions and it is attempted using only analytical (exact) means for the solution of the transient breakage problem. In doing so, the very interesting and rich underlying structure and properties of the solutions of the equal size breakage problem (seemingly, very simple) are revealed. It appears that the utility of the known self-similar distributions for this particular problem has to be redefined but yet not entirely abandoned.     

Monte Carlo studies of the coalescence and breakage characteristics of solid-liquid suspensions under shear

Summary A simple model for the breakage frequency of solid aggregates in a suspension under shear is developed based on the concept of bound liquid. This model is superior to the artificial models used by earlier workers. This is used along withSmoluchowski's expression for the coalescence frequency to simulate the aggregation-desaggregation behavior of suspensions using the Monte Carlo technique. The effect of initial particle size distribution, shear rate, viscosity of the medium, etc., are studied and are found to be in accord with intuitive expectations.With 5 figures     

Effect of solid volume fraction on aggregation and breakage in colloidal suspensions in batch and continuous stirred tanks

Aggregation and breakage of aggregates of fully destabilized polystyrene latex particles in turbulent flow was studied experimentally in both batch and continuous stirred tanks. Small-angle static light scattering (SASLS) was used to monitor the time evolution of two independent moments of the cluster mass distribution (CMD), namely, the mean radius of gyration and the zero angle scattered light intensity. In addition, information about the structure of the aggregates was obtained in terms of the static light scattering structure factor. It was observed that decreasing the solid volume fraction over more than one order of magnitude resulted in monotonically decreasing steady-state values of both moments of the CMD. Using a combination of batch operation and continuous dilution with particle-free solution in the stirred tank, it was found that the steady-state distributions were fully reversible upon changing the solid volume fraction. These observations indicate that the steady-state CMD in this system is controlled by the dynamic equilibrium between aggregation (with the second-order kinetics in cluster concentration) and breakage (with the first-order kinetics in cluster concentration). In addition, by dilution to very low solid volume fractions, we demonstrate the existence of a critical aggregate size below which breakage is negligible.     

Boundary effect on the drag force on a nonhomogeneous floc

The boundary effect on the drag force acting on a spherical floc having a nonhomogeneous structure is examined by considering a spherical floc at the centerline of a cylindrical tube. The floc is simulated by an entity having a two-layer structure, and its porous nature mimicked by varying the relative magnitude of the permeability of its inner and outer layers. The results of numerical simulation reveal that the tube wall has the effect of compressing the streamlines and vorticity contours. Also, as in the case of a rigid entity, the wake in the rear region of a floc, which arises from the convective motion of the fluid, is depressed. For fixed volume-averaged permeability, the influence of the tube wall on the behavior of a heterogeneous floc is more significant than that on the behavior of a homogeneous floc, and the influence varies with the structure of the former. The heterogeneous structure of a floc leads to a deviation in the modified drag coefficient-Reynolds number relation from a Stokes-law-like correlation. The smaller the average permeability of a floc the greater the deviation, but the presence of the tube wall has the effect of reducing the deviation.     

Experimental and modeling study of breakage and restructuring of open and dense colloidal aggregates

In this work we present experimental and simulation analysis of the breakage and restructuring of colloidal aggregates in dilute conditions under shear. In order to cover a broad range of hydrodynamic and interparticle forces, aggregates composed of primary particles with two sizes, d(p) = 90 and 810 nm, were generated. Moreover, to understand the dependence of breakage and restructuring on the cluster structure, aggregates grown under stagnant and turbulent conditions, having substantially different initial internal structures with fractal dimension d(f) equal to 1.7 and 2.7, respectively, were used. The aggregates were broken by exposing them to a well-defined elongational flow produced in a nozzle positioned between two syringes. To investigate the evolution of aggregate size and morphology, respectively, the mean radius of gyration, , and d(f) were monitored during the breakup process using light scattering and confocal laser scanning microscopy. It was found that the evolution of aggregates' fractal dimension during breakage is solely controlled by their initial structure and is independent of the primary particles size. Similarly, the scaling of the steady-state vs the applied hydrodynamic stress is independent of primary particle size, however, depends on the history of aggregate structure. To quantitatively explain these observations, the breakage process was modeled using stokesian dynamics simulations incorporating DLVO and contact interactions among particles. The required flow-field for these simulations was obtained from computational fluid dynamics. The complex flow pattern was simplified by considering a characteristic stream line passing through the zone with the highest hydrodynamic stress inside the nozzle, this being the most critical flow condition experienced by the clusters. As the flow-field along this streamline was found to be neither pure simple shear nor pure extensional flow, the real flow was approximated as an elongational flow followed by a simple shear flow, with a stepwise transition between them. Using this approach, very good agreement between the measured and simulated aggregate size values and structure evolution was obtained. The results of this study show that the process of cluster breakup is very complex and strongly depends on the initial aggregate structure and flow-field conditions.     

Mechanism of glass ampoule breakage prevention during the freeze-drying process of sodium thiopental lyophilization products on addition of sodium chloride

Glass ampoule breakage during the freeze-drying process was prevented by the addition of sodium chloride to the formulation of lyophilization products of sodium thiopental. In order to clarify the ampoule breakage prevention mechanism, the physicochemical behavior of the freeze-drying process was monitored by simultaneous XRD-DSC measurements and thermal mechanical analysis (TMA). During the freezing process of formulated solution, the smaller heat of fusion of crystallized ice with the addition of sodium chloride was observed in comparison to that without sodium chloride. Although a greater amorphous portion remained, a higher crystal habit of hexagonal ice was reproducibly observed in the XRD patterns with the addition of sodium chloride during the freezing process. In the measurement of TMA, the scattering of the thermal expansion rate of formulated solution was significantly reduced by the addition of sodium chloride. These observations indicated that the addition of sodium chloride minimized the scattering of the thermal expansion rate and might be a cause for the inhibition of glass ampoule breakage during the freeze-drying process.     

Moving of a nonhomogeneous, porous floc normal to a rigid plate

The boundary effect on the moving of a porous, nonhomogeneous, spherical floc normal to a rigid plate is analyzed theoretically for the case of low to medium Reynolds number. In particular, the drag force acting on the floc under various conditions is evaluated. A two-layer structure is adopted to simulate the nonhomogeneous nature of a floc. We show that if a floc is away from the plate, the streamlines surrounding the floc are distorted, but the degree of distortion becomes less significant if the floc is near the plate. The modified drag coefficient of a porous floc is orders of magnitude smaller than that of the corresponding rigid particle. For a fixed volume-averaged permeability, the effect of the presence of the plate on the behavior of a nonhomogeneous floc is more significant than that of a homogeneous floc, and this effect depends largely on the structure of a floc. The nonhomogeneous structure of a floc leads to a positive deviation from a Stokes-law-like correlation in the modified drag coefficient, and the smaller the volume-averaged permeability of a floc the greater the deviation. The presence of the plate has the effect of reducing this deviation. The nonhomogeneous structure of a floc on its modified drag coefficient is pronounced when it is close to a boundary.     

Effect of cationic polymethacrylates on the rheology and flocculation of microfibrillated cellulose

Using two cationic methacrylate polymers: poly([2-(methacryloyloxy)ethyl] trimethyl ammonium iodide) (PDMQ) and poly[(stearyl methacrylate)-stat-([2-(methacryloyloxy)ethyl] trimethyl ammonium iodide)] (PSMA13Q), we modified microfibrillated cellulose (MFC) water suspensions. The aim was to affect the flocculation and rheological behavior of the MFC suspension. PDMQ is a strongly cationic polymer while PSMA13Q, also a cationic polymer, contains hydrophobic segments. We studied the MFC/polymer suspension rheological properties with a rotational rheometer in oscillatory and flow measurements. To observe structural changes in suspensions at different shear rates, we measured flow curves with transparent outer geometry and photographed the sample with a digital camera. The oscillatory measurements showed that a small amount of the cationic PDMQ in the MFC suspension strengthened the gel, whereas a small amount of amphiphilic PSMA13Q weakened it. Increased amounts of either polymer increased the gel strength. PSMA13Q also changed the rheological character of the MFC suspension turning it more fluid-like. When we photographed the flow curve measurement, we saw a clear change in the floc structure. This floc structure rupture coincided with a transient region in the flow curve.     

Amifostine protection against mitomycin-induced chromosomal breakage in fanconi anaemia lymphocytes

Fanconi anaemia (FA) is a rare genetic chromosomal instability syndrome caused by impairment of DNA repair and reactive oxygen species (ROS) imbalance. This disease is also related to bone marrow failure and cancer. Treatment of these complications with radiation and alkylating agents may enhance chromosomal breakage. We have evaluated the effect of amifostine (AMF) on basal and mitomycin C (MMC)-induced chromosomal breakage in FA blood cells using the micronucleus assay. The basal micronuclei count was higher among FA patients than healthy subjects. Pre-treatment with AMF significantly inhibited micronucleation induced by MMC in healthy subjects (23.4 +/- 4.0 - MMC vs 12.3 2.9 - AMF --> MMC) MN/1000CB, p < 0.01, one way ANOVA) as well as in FA patients (80.0 +/- 5.8 - MMC vs 40.1 +/- 5.8 - AMF --> MMC) MN/1000CB, p < 0.01, ANOVA). Release of ROS by peripheral blood mononuclear cells treated with AMF -> MMC and measured by chemoluminometry showed that AMF-protection was statistically higher among FA patients than in healthy individuals. Based on these results we suggest that AMF prevents chromosomal breakage induced by MMC, probably by its antioxidant effect.     

Drag of a dispersion of nonhomogeneously structured flocs in a flow field

The influence of floc structure and floc concentration on the drag acting on a floc is investigated theoretically. A two-layer model is adopted to describe floc structure, and a cell model is used to simulate a floc dispersion. The influences of the key parameters of the problem under consideration, including floc concentration, Reynolds number, the ratio (permeability of outer layer/permeability of inner layer), and the ratio (thickness of outer layer/thickness of inner layer), on the drag coefficient are discussed. We show that the more heterogeneous the floc structure is, the greater the drag and the more significant the deviation of curve of variation of drag coefficient against Reynolds number from a Stokes-law-like relation. The drag on a floc declines with the decrease in floc concentration, and, due to the convective flow of the fluid, the distortion of streamlines surrounding a floc becomes more serious and the deviation of the variation of the curve of drag against Reynolds number from a Stokes-law-like relation is more significant.     

The rheological properties of hydrogenated castor oil crystals

The present study focuses on the rheological performance of a surfactant-rich aqueous suspension containing hydrogenated castor oil (HCO) crystals. HCO can be typically crystallized in five distinct shapes: spherically shaped, irregularly shaped, star-shaped (also called rosettes), short needles, and thick or thin fibers. The effect of the differences in shape on the rheological performance is studied, and the rheological properties are compared to the behavior of other triacylglycerol’s (TAG) suspensions. A suspension of TAG crystals usually behaves as a colloidal gel wherein a colloidal gel is defined as a network of flocs, with each floc being an aggregate of smaller subunits. All of these surfactant-rich aqueous suspensions of HCO crystals behaved according to a colloidal gel in the transient regime, independent of the studied crystal shapes, except the long thin fibers at a concentration above 0.1 wt% HCO transitioning from a heterogeneous fractal rod network to a homogeneous rod network, shifting from a colloidal gel to a glass.     

The breakage and damage of plasmid DNA photocatalized by TiO2/carbon nanotube composites

In this paper, the plasmid DNA was used as a target to evaluate the bioeffect of TiO₂/Carbon Nanotube (CNT) composites. The conformational change and breakage of DNA induced by the composites were characterized by the integrated tools of electrochemistry, circular dichroism (CD), atomic force microscopy (AFM), and DNA electrophoresis. At the early stage of incubation, the DNA double helix conformation was substantially changed by TiO₂/CNT composites. Both electrophoresis and electrochemistry results suggested the breakage and damage appeared on the native DNA molecules. When DNA was treated longer by TiO₂/CNT, DNA molecules were broken into fragment. AFM images confirmed the process. The DNA damage was deemed to be a gradual process: supercoiled plasmid DNA was first damaged to nicked‐circle structure, then further to linear form, and then DNA fragment. Copyright © 2011 John Wiley & Sons, Ltd.     

Formation of pyrazine derivatives from D-glucosamine and their deoxyribonucleic acid (DNA) strand breakage activity

Two pyrazine derivatives [fructosazine (3) and deoxyfructosazine (6)] were simultaneously formed in a solution of D-glucosamine hydrochloride under various conditions. They showed deoxyribonucleic acid (DNA) strand breakage activity in plasmid pBR322 comparable to that of D-glucosamine. The DNA strand breakage by fructosazine (3) was stimulated by Cu2+.     

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.