Brownian dynamics simulation of the aggregation of submicron particles in static gas

A Brownian dynamics simulation was conducted to investigate the formation of aggregates that are composed of submicron particles such as soot. Three models were considered for aggregation: a diffusion-limited aggregation model, in which an aggregate grows around a fixed particle; a particle–cluster aggregation model, in which a single aggregate grows by collisions between particles and the aggregate; and a cluster–cluster aggregation (CCA) model, in which many particles and aggregates form multiple aggregates. A comparison of the three aggregation models showed that the CCA model resulted in a soot-like branching shape. The aggregation was investigated by employing the CCA model; it was determined that increase in gas temperature affected the shielding effect of the aggregate branch by changing the displacement and velocity of Brownian particles. Furthermore, these simulations demonstrated that the size and aspect ratio of the field and the particle density also affected aggregation shape.     

用激光多普勒测速计（LDA）分析粘弹性对Metzner和Otto系数的影响

The Metzner and Otto correlation is the single practical method for incorporating non-Newtonian effects in the mixing process. In this article, the Metzner and Otto' s idea, the role of viscoelasticity on the Metzner and Otto coefficient, ks, effects of flow regime on ks and the determination of ks for Rushton turbine impeller have been studied using the direct method of the laser Doppler anemometry (LDA) velocity measurement for the case of viscoelastic liquids. The normalized mean tangential velocity profiles are independent of Rushton turbine impeller speeds. Contrary to literature findings, it is shown that the variation of local shear rate against the impeller speed is better correlated by the power equation, i.e. γ= ks' · Nb' , in the transition region, i. e. ～ 30 < Re <～ 2000. Also, a correlation between improved coefficient, ks', and the elasticity number of viscoelastic liquids is given which is very helpful in designing of the mixing of both viscoelastic and inelastic non-Newtonian fluids t     

Controlled aggregation of colloidal particles for toner applications

Micrometer‐sized particles were formed by controlled aggregation of carboxylated polystyrene colloidal spheres having a mean diameter of about 200 nm with a commercial cationic coagulant. To identify the parameters governing the size and structure of the aggregates, the aggregate size distribution was studied over a period of time with dynamic light scattering. The effect of the particle concentration, pH, and ionic strength on the aggregation behavior was investigated. The coagulant concentration used for present studies was 5 parts per hundred on the basis of the polystyrene particles and the particle concentrations used were 10–15%. The particle size distribution for the latex suspensions was also investigated with a 10% aluminum sulfate [Al₂(SO4)₃·14H₂O] solution as a model coagulant. With the commercial coagulant, aggregation was found to be slower at lower pH than at neutral pH. At pH 6, the particles started to aggregate within minutes and form aggregates of about 1000 nm. We expected that lowering the pH would reduce interparticle repulsive forces and enhance the collision efficiency. However, at a lower pH of 2, the aggregation process slowed down. Increasing the ionic strength at neutral pH led to a broader aggregate size distribution, and the population of larger aggregates increased. The suspensions with the model coagulant showed similar behavior. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

A Unified Model for the Mixing of Non‐Newtonian Fluids in the Laminar,Transition, and Turbulent Region

Summary: Non‐Newtonian fluid behavior has significant influence on quantities in chemical engineering like power input, mixing time, heat transfer etc. In the laminar flow region, the concept of effective viscosity by Metzner and Otto is well established. In the transition region between laminar and turbulent flow, the existing concepts use three and even more empirical parameters to determine the specific power input. Here, a unified and general but simple approach is introduced to calculate the power input for shear thinning fluids over the whole flow region using just one empirical parameter. The Metzner‐Otto relation is obtained as a limiting case for the laminar region. The empirical parameter of the new approach is related to the Metzner‐Otto constant. The concept is validated for eight different stirrer systems. Mixing time and maximum shear rate and heat transfer can also be calculated using this approach. The new concept presented should also be applicable for other apparatuses, e.g., static mixers.

Comparison of experimental data and a curve calculated according to the new method (solid line).     

Effect of Volume Fraction on Transient Structural Behavior of Aerosol Particles Using Off-Lattice Kinetic Monte Carlo Simulation

Fractal-like aggregates exhibit interesting properties that determine their physicochemical advantages, and thus, the control and prediction of aggregation is critical for many applications. An off-lattice kinetic Monte Carlo (KMC) simulation was performed to investigate the aggregate evolution from primary particles to three-dimensional fractal aggregates, at three different volume fractions. We have found that at low volume fraction, aggregation kinetics is slow, and aggregate morphology is widely open and stringy, with fractal dimension of (D_f) 1.8, in which the system is constantly preserved in the dilute regime. In denser volume fractions, however, the aggregation kinetics appears to be accelerated and aggregate morphology is more compact and less stringy due to the transition from dilute to dense regimes. Moreover, the volume fractions determine what kind of coagulation mechanism may occur to produce aggregates with different morphologies. At low volume fraction, coagulation is predominated by coagulation between aggregates in which the maximum probability of interpenetration event is only 18%. This suggests that aggregates at low volume fraction can maintain their self-similarity behavior. While at high volume fraction, coagulation is predominated by two subsequent coagulation mechanisms, namely, primary particle–aggregate and aggregate–aggregate interaction. The probability of interpenetration event increases up to 40%. In addition, the interpenetration process as well as the primary particle–aggregate coagulation, particularly in the dense regime, could produce superaggregates with a hybrid structure with a high fractal dimension at large size scales and a low fractal dimension at small scales. A detail mechanism for the formation of superaggregates was discussed.

Copyright © 2015 American Association for Aerosol Research     

Dynamics of cells attachment, aggregation, growth and detachment in trickle-bed bioreactors

Excessive biomass formation in two-phase flow trickle-bed bioreactors induces biological clogging and leads to the progressive obstruction of the bed that is accompanied with a build-up in pressure drop and flow channeling. One of the important aspects during biological clogging in trickle-bed bioreactors is the aggregation of cells and the detachment of cells and aggregates from pore bodies within the porous bed. Current theoretical models describing the transient behaviour of biomass accumulation and the biological clogging in trickle-bed bioreactors for wastewater treatment neglect the cell aggregation process and the aggregates detachment. An attempt has been made with this contribution in which the authors strived to develop an Euler-Euler two-fluid dynamic model based on the volume-average mass, momentum equations, species balance equations, biomass dynamics equation, filtration equations for the cells and the aggregates and discrete population balance equations for the cells agglomeration to describe two-phase flow and space-time evolution of biological clogging in trickle-bed bioreactors for wastewater treatment. Phenol biodegradation by Pseudomonas putida as the predominant species immobilized on activated carbon was chosen as a case study to illustrate the consequences of formation of excessive amounts of biomass. Cells aggregation was described by the rate at which a certain size aggregate is being formed by smaller aggregates minus the rate at which the aggregate combines to form a larger aggregate. The detachment of the cells or aggregates from the collector surface was supposed to be induced by the colloidal forces in the case of Brownian cells/aggregates or by the hydrodynamic forces in the case of non-Brownian aggregates.     

Spinning wheel powder feeding device — fundamentals and applications

A spinning wheel powder feeding system has been developed as a conveying mechanism to feed fine particle aggregates on a laboratory scale. An example of a use of this conveying mechanism is with a transport tube reactor, since the reactor only provides a few seconds residence time to react the powder. Methods to shear the powder mechanically, as opposed to using a high gas velocity, are developed as to not reduce the available residence time in the reactor. The objective is to feed a powder at the smallest particle aggregate size possible rather than a large particle aggregate size generated by an upstream feeding device, and to achieve such dispersion using minimized gas flow. Statistical results show that the spinning wheel alone is able to reduce the mean aggregate size of the Particle Size Distribution (PSD) and when a minimal amount of gas is added to the system the PSD is reduced further. In addition, a fundamental model employing a discrete particle aggregate breakage equation combined with a Monte Carlo method has shown that the spinning wheel feeding system is able to consistently reduce particle aggregate size.     

Dependence of initial cluster aggregation kinetics on shear rate for particles of different sizes under turbulence

Initial aggregation kinetics for three particle sizes and broad range of Péclet numbers were investigated under turbulent conditions in stirred tank. This allowed us to observe the transition from diffusion‐controlled to purely shear‐induced aggregation. The evolution of the root‐mean‐square radius of gyration, zero‐angle intensity of scattered light, and obscuration was obtained by small‐angle static light scattering. For a given particle size the measured evolution of all integral quantities obtained for various volume average shear rates 〈G〉, scales with a dimensionless time, τ_exp = α_exp × 〈G〉 × ? × t. The experimentally obtained aggregation efficiency α_exp, follows the power law α_exp = Pe^?n, where Pe is the primary particle Péclet number. With increasing particle size a decrease in n is observed in accordance with theory and literature data. As previously predicted by population balance equation simulations three aggregation regimes were observed experimentally. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Effects of Titanium Dioxide Nanoparticle Aggregate Size on Gene Expression

Titanium dioxide (titania) nanoparticle aggregation is an important factor in understanding cytotoxicity. However, the effect of the aggregate size of nanoparticles on cells is unclear. We prepared two sizes of titania aggregate particles and investigated their biological activity by analyzing biomarker expression based on mRNA expression analysis. The aggregate particle sizes of small and large aggregated titania were 166 nm (PDI = 0.291) and 596 nm (PDI = 0.417), respectively. These two size groups were separated by centrifugation from the same initial nanoparticle sample. We analyzed the gene expression of biomarkers focused on stress, inflammation, and cytotoxicity. Large titania aggregates show a larger effect on cell viability and gene expression when compared with the small aggregates. This suggests that particle aggregate size is related to cellular effects.     

DEM simulation of aggregation of suspended nanoparticles

A DEM-based model was developed and examined for simulation of aggregation in suspensions of α-alumina nanoparticles. In the model, the random Brownian diffusion and the externally induced dielectrophoresis (DEP) motion were considered as the driving mechanisms for the transport of particles in colloidal suspension. To simulate particle interactions, the non-contact surface force and the contact force were taken into account using the well-known Derjaguin-Landau-Verway-Overbeek (DLVO) theory and the soft-sphere model, respectively.Specifically, the model was used to study the effects of pH, solid volume fraction and external AC electric field on α-alumina aggregate growth which was expressed in terms of coordination number, longest dimension, and fractal dimension. The simulations were carried out over a pH range of 4-10, solid volume fraction of 0.02-0.4, and a variety of AC electric fields. In relatively dilute suspensions, the aggregates predominantly exhibited chainlike structures, whereas at high solid volume fraction, aggregates with complex netlike structures were formed. It was also evident that, in concentrated colloidal suspensions, DEP had a negligible influence on aggregate growth over the examined conditions. The effect of DEP however, was found to be more noticeable on aggregate structure leading to the formation of more compact aggregates with a greater particle number density. The break-up and reattachment of sub-aggregates as well as the rearrangement of nanoparticles in the particle assemblies and subsequent curling of the loose network promoted by a strong AC electric field was deemed to be responsible for this structural transformation. Finally, the DEM-based model was used to predict the size of α-alumina aggregates over a range of pH. The predictions were found to be in good agreement with the published experimental data, particularly around the isoelectric point.     

Some Characteristics of Stirred Vessel Flows of Dilute Polymer Solutions Powered by a Hyperboloid Impeller

Measurements of the power consumption and mean and turbulent velocities in the wall jet of a stirred vessel flow, powered by a hyperboloid impeller, were carried out. The fluids were aqueous solutions of tylose, CMC and xanthan gum (XG), at weight concentrations ranging from 0.1% to 0.6%, which exhibited varying degrees of shear‐thinning and viscoelasticity. The hyperboloid impeller parameter k of Metzner and Otto (1957) was found to be equal to 27.2 ±4. In the Reynolds number range of 10³ to 3 × 10⁴ the mixing power was reduced for all non‐Newtonian fluids, but never by more than 13%. The flows of the 0.2% CMC and 0.2% XG solutions were found to be less turbulent than those of water, especially for the latter fluid where a reduction in axial rms in excess of 50% was found in the wall jet. This was attributed to elasticity effects and especially to the high zero shear viscosity of the latter fluid.     

Stability of particle suspensions after fine grinding

The objective of this work was to investigate the physical stability of sub-micron particle suspensions of organic crystalline food compounds after grinding. A Dynomill ball mill was used in combination with zirconium oxide grinding medium beads. The organic product was a poor water soluble product. During grinding the average particle diameter of the particulate product was reduced to a minimum value in the sub-micron range. Forward light scattering was used to analyze the particle size distribution. Dynamic light scattering measurements, on the other hand, showed that there were aggregates present after grinding. The difference in the obtained particle size distributions using both techniques was related to the shear in the measurement device, i.e. in the laser diffraction measurement the shear was higher than in the dynamic light scattering device. Thus in the laser diffraction measurement the aggregates were broken up by shear, while this was not the case in the dynamic light scattering measurements. The difference in the measurements showed that the particles formed aggregates at low to zero shear.The aggregation behaviour of the particles was studied by measuring the sedimentation behaviour of the particles suspension at various pH values. The impact of the pH on the aggregation rate was explained by the zeta potential of the particles. The suspensions were less stable near the iso-electric point of the particles.     

Numerical simulation of aggregate dispersion in different flow fields using discrete element method

An attempt was made to study the aggregate dispersion process in three different flow fields namely; steady shear, elongation flow, and combined shear and elongational flows using the discrete element method. The simulation was performed on two aggregate structures characterized by their fractal dimensions. The predicted results showed that the aggregate break‐up process evaluated in terms of weighted average fragment size 〈w〉 follows a power–law type relation as 〈w〉 = kt^?m in all the three flow fields. The dispersion performance of different flow fields evaluated by dispersing rate and a final steady‐state fragment size was found to be dependent upon the extent of applied stress and flow fields such that at low applied stress levels much smaller steady state values of 〈w〉 could be obtained for the elongational flow. The aggregate structure, characterized by its fractal dimension, was found to have different effects on the aggregate dispersion process depending on the flow field and applied stress level. The results predicted from this simulation could be explained in terms of ability of flow fields in rotating the aggregates and fragments in appropriate position to be broken up and the fractal dimensions of aggregates. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Particle features of poly(vinyl chloride) resins prepared by a new heterogeneous polymerization process

The heterogeneous polymerization of vinyl chloride monomer (VCM), with n‐butane as the reaction medium, was used to prepare poly(vinyl chloride) (PVC) resins. The particle features of the resulting resins and the particle formation mechanism of the polymerization process were investigated. The PVC resins prepared by the new polymerization process had a volume‐average particle size comparable to that of suspension PVC resins and a lower number‐average particle size. From scanning electron micrographs, it could be seen that the new PVC resins had a regular particle shape and a smooth surface with no obvious skin. They also had a high porosity. The new PVC resins were composed of individual and loosely aggregated primary particles. The diameter of the primary particles in the top layer of the grains was smaller than that of the primary particles in the center part of the grains. On the basis of the particle features of these PVC resins, a particle formation mechanism for the new polymerization process was proposed. PVC chains precipitate from a VCM/n‐butane mixed medium to form primary aggregates at a very low conversion, and the primary aggregates of the PVC chains aggregate to form primary particles, which further aggregate to form grains. The primary particles and grains grow by the capture of newly formed PVC chains and their primary aggregates and by polymerization occurring inside the aggregates. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 954–958, 2003     

Relative shear stability of mini- and macroemulsion latexes

The shear stability of mini- and macroemulsion latexes is compared and quantitatively evaluated with respect to their particle-size distributions. The effect of a few externally added large particles on the shear stability of these two types of latexes was also investigated. All the latexes selected were in the colloidal size range (less than 1 micron). The original particle sizes for the macroemulsion latexes ranged from 141 to 241 nm, and those for the miniemulsion latexes ranged from 96 to 209 nm. The miniemulsion latexes were found to be more shear stable than were their macroemulsion latex counterparts over the particle-size range investigated. This trend was repeated even in the presence of a few large particles. Additionally, seeding experiments suggest that mini- and macroemulsion latexes incur different levels of shear aggregation due to inherent differences in their particle-size distributions. The shear rate used along with the particle size and number were quantitatively shown to significantly influence the aggregation process. Finally, a quantitative method for evaluating relative shear stability in emulsion polymerization was demonstrated, which, although not very rigorous, could serve as a starting point for further quantitative isolation and investigation of the various parameters that affect the shear aggregation process. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 1317–1324, 1997     

Mixing of a lignin‐based slurry fuel

Lignin‐based slurry fuels are a potential alternative to fossil fuels in kraft pulp mills. Lignogels — mixtures of lignin, fuel oil, water and surfactant — are non‐Newtonian fluids, with shear‐thinning and thixotropic behaviour. Their mixing was investigated in tanks with volumes of 3 and 30 L. An A310 hydrofoil impeller was used in all experiments. Results were compared with measurements in Newtonian fluids, used to characterize the impeller over a broad range of Reynolds numbers (1–500 000). An aqueous CMC solution was also used for characterization of the impeller and estimation of the Metzner‐Otto constant. Results in the transition region were corrected by introduction of two empirical parameters.     

Using CFD to predict the behavior of power law fluids near axial-flow impellers operating in the transitional flow regime

A computational fluid dynamics (CFD) model of flow in a mixing tank with a single axial-flow impeller was developed with the Fluent^TM software. The model consists of an unstructured hexagonal mesh (158,000 total cells), dense in the region from the surface of the impeller. The flow was modeled as laminar and a multiple reference frame approach was used to solve the discretized equations of motion in one-quarter of a baffled tank. A solution of 0.1% Carbopol in water, a shear-thinning fluid, was found to be clear enough to measure impeller discharge angles using laser Doppler velocimetry. This is the first time that impeller discharge angles have been reported in the literature for a shear-thinning fluid with a hydrofoil impeller. Rheological measurements indicated that the Carbopol solution can be characterized by the power law (K=9,n=0.2) under the range of shear conditions (0.1- expected near the impeller in the mixing tank. The CFD model accurately predicted the dependence of power number and discharge angle on Reynolds number (as predicted by Metzner and Otto), for an A200 (pitched blade turbine or PBT) and an A315 (Hydrofoil) impeller operating in the transitional flow regime (Reynolds numbers: 25-400) with glycerin and 0.1% Carbopol solutions. Subsequently, the results of a systematic CFD study with power law fluids indicated that the power number and discharge angle of an axial-flow impeller in the transitional flow regime depends not only on the Reynolds number (as determined by Metzner and Otto's method) but also on the flow behavior index n. Consequently, an alternative to Metzner and Otto's method was pursued. The results of converged CFD simulations indicate that the near-impeller “average shear rate” increases not only with increasing RPM (as proposed by Metzner and Otto), but also with decreasing flow behavior index (n) and discharge angle in the transitional flow regime. Considering this result, an improved method of estimating the power number and discharge angle for power law fluids in the transitional flow regime is proposed.     

Aggregation in Organic Solutions of Malonamides: Consequences for Water Extraction

The molecular organization of N,N′‐dimethyl‐N,N′‐dioctylhexylethoxymalonamide (DMDOHEMA), the current reference extractant for the DIAMEX (DIAMide EXtraction) process, is correlated with its water extraction properties from neutral media. The aggregation of DMDOHEMA in n‐heptane was investigated by vapor pressure osmometry (VPO) and the aggregate speciation characterized by combined small‐angle neutron and X‐ray scattering (SANS and SAXS, respectively). Two approaches were taken to model the aggregation of the diamide and the water extraction as a function of the diamide concentration by taking into account a single aggregation equilibrium with an average aggregation number N equal to 4.28 ± 0.05; and a competition between two types of aggregates in the organic phase, namely, aggregates of the reverse micelle type with 4 diamides per aggregate, and an oligomeric structure composed of about 10 diamide molecules which appears at high extractant concentration (>1 mol/L). In both cases, the supramolecular speciation representing the monomers/aggregates distribution was determined, and for each supramolecular organization, a solubilization parameter was calculated using the Sergievskii‐Dannus relationship. Thus, the correlation between the two types of micellization of the diamide and the extraction of water into the organic phase was demonstrated. The larger aggregates can extract about five times more water than monomers.