Aggregate size distribution evolution for Brownian coagulation-sensitivity to an improved rate constant

Brownian motion causes small aggregates to encounter one another and grow in gaseous environments, often under conditions in which the coalescence rate (say, spheroidization by "sintering") cannot compete. The polydisperse nature of the aerosol population formed by this mechanism is typically accounted for by formulating an evolution equation for the joint PDF of the state variables needed for describing individual particles. In the simple case of fractal-like aggregates (prescribed morphology and state, characterized just by the number of aggregated spherules, or total aggregate volume), we use the quadrature method of moments and Monte Carlo simulations to show that recent improvements in the laws governing free molecule regime coagulation frequency (rate "constant") of these aggregates cause systematic changes in the shape of the asymptotic aggregate size distribution, with significant implications for the light-scattering power and inertial impaction behavior of such aggregate populations.     

Deposition efficiency of fractal-like aggregates in fibrous filters calculated using Brownian dynamics method

Nonspherical particles, such as fractal-like aggregates emitted by diesel engines, are commonly met in the ambient air. Some of them are believed to be carcinogenic to humans, thus their efficient removal is of crucial practical importance. A fibrous filter is the device commonly used for aerosol purification but the literature lacks experimental data concerning aggregates filtration. Effect of aggregates' parameters (fractal dimension, primary particle radius) as well as fiber diameter and air velocity on the filtration efficiency is investigated theoretically using the modified Brownian dynamics method. Three different expressions for the friction coefficient evaluation for the aggregates were examined. The results obtained indicate that structure of an aggregate, filter structure and process conditions strongly influence the aggregates deposition efficiency, which significantly differs from the values determined for mass-equivalent spherical particles. The results determined using the Brownian dynamics approach were compared with the values calculated using classical single fiber theory and noticeable discrepancy was observed for the most penetrating particles, while both approaches agree for the limiting cases of small or large particles. Peclet number based on the mobility radius and the interception parameter based on the outer radius are the proper criteria to describe diffusional and deterministic deposition of aggregates.     

Viscosity of liquid suspensions with fractal aggregates: Magnetic nanoparticles in petroleum colloidal structures

New physical model is presented resulting in a simple formula for the dependence of viscosity η of colloidal liquid solution on the shear rate G applicable to a wide variety of systems including complex natural liquids like petroleum. The principal point of the model is the fractal nature of colloid particle aggregates present in the liquid. Such aggregates are experimentally detected now in non-Newtonian liquids. The model is based on calculation of energy loss on colloidal particle aggregate of fractal structure localized in the flow of liquid with shear rate. We have performed the viscosity measurement experiments which confirmed successfully the developed physical model. Also, we demonstrate experimentally that petroleum colloidal particles and magnetic iron oxide nanoparticles can form composite fractal-like aggregates in natural petroleum materials. Our model can explain both the non-Newtonian properties of petroleum and sensitivity of petroleum viscosity to external magnetic fields.     

Molecular dynamics simulations of laser-induced incandescence of soot using an extended ReaxFF reactive force field

Laser-induced incandescence (LII) of soot has developed into a popular method for making in situ measurements of soot volume fraction and primary particle sizes. However, there is still a lack of understanding regarding the generation and interpretation of the cooling signals. To model heat transfer from the heated soot particles to the surrounding gas, knowledge of the collision-based cooling as well as reactive events, including oxidation (exothermic) and evaporation (endothermic) is essential. We have simulated LII of soot using the ReaxFF reactive force field for hydrocarbon combustion. Soot was modeled as a stack of four graphene sheets linked together using sp(3) hybridized carbon atoms. To calculate the thermal accommodation coefficient of various gases with soot, graphene sheets of diameter 40 ? were used to create a soot particle containing 2691 atoms, and these simulations were carried out using the ReaxFF version incorporated into the Amsterdam Density Functional program. The reactive force field enables us to simulate the effects of conduction, evaporation, and oxidation of the soot particle on the cooling signal. Simulations were carried out for both reactive and nonreactive gas species at various pressures, and the subsequent cooling signals of soot were compared and analyzed. To correctly model N(2)-soot interactions, optimization of N-N and N-C-H force field parameters against DFT and experimental values was performed and is described in this paper. Subsequently, simulations were performed in order to find the thermal accommodation coefficients of soot with various monatomic and polyatomic gas molecules like He, Ne, Ar, N(2), CO(2), and CH(4). For all these species we find good agreement between our ReaxFF results and previously published accommodation coefficients. We thus believe that Molecular Dynamics using the ReaxFF reactive force field is a promising approach to simulate the physical and chemical aspects of soot LII.     

Impact of FRET between Molecular Aggregates and Quantum Dots

Energy transfer has been employed in third‐generation solar cells for the conversion of light into electrical energy. Long‐range nonradiative energy transfer from semiconductor quantum dots (QDs) to fluorophores has been demonstrated by using CdS QDs and thiophene?BODIPY (boron dipyrromethene, abbreviated as TG2). TG2 shows a broad photoluminescence (PL) spectrum, which varies with concentration. At very low concentrations, monomeric units are present; then, upon increasing the concentration, these monomers form a mixed (J‐/H‐)aggregated state. Energy transfer between the CdS QDs and TG2 was confirmed by separately investigating the interactions between CdS and the monomer of TG2 and between CdS and the aggregated states of TG2. Size‐dependent PL quenching confirmed that nonradiative Förster resonance energy transfer (FRET) from photoexcited CdS QDs to the J‐aggregate state of TG2 was the major energy‐relaxation channel, which occurred on the timescale of hundreds of fs. These results have broad applications in the field of light harvesting based on the assembly of molecular aggregates.     

Drag and Torque on Clusters of N Arbitrary Spheres at Low Reynolds Number

Hydrodynamics of particle clusters suspended in viscous fluids is a subject of considerable theoretical and practical importance. Using a multipole expansion of the flow velocity in a series of spherical harmonics, Lamb's fundamental solution of the Stokes flow outside a single sphere is generalized in this work to the case of N nonoverlapping spheres of arbitrary size with slip boundary conditions. The expansion coefficients are found by transforming the boundary conditions to the Lamb form and by transforming the spherical coordinates and solid spherical harmonics centered at different spheres. The problem is reduced to the solution of the linear system of equations for the expansion coefficients, which is carried out numerically. Based on the developed theory, the relation between the hydrodynamic and gyration radius of fractal-like aggregates with different structure is established. In another application, an asymptotic slip-regime dependence of the aggregate hydrodynamic radius on the Knudsen number and the number of particles is found by performing calculations of drag forces acting on the gas-borne fractal-like and straight chain aggregates. A good agreement is shown in comparing predictions of the described theory with available experimental and theoretical results on motion of various small sphere clusters in viscous fluid. Copyright 2000 Academic Press.     

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.     

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

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

Deposition of spherical particles onto cylindrical solid surfaces. I. Numerical simulations

The permeability of fractal porous aggregates with realistic three-dimensional structure is investigated theoretically using model aggregates composed of identical spherical primary particles. Synthetic aggregates are generated by several techniques, including a lattice-based method, simulation of aggregation by differential settling and turbulent shear, and the specification of simple cubic structures, resulting in aggregates characterized by the number of primary particles, solid fraction, characteristic radius, and fractal dimension. Stokesian dynamics is used to determine the total hydrodynamic force on and the distribution of velocity within an aggregate exposed to a uniform flow. The aggregate permeability is calculated by comparing these values with the total force and velocity distribution calculated from the Brinkman equation applied locally and to the entire aggregate using permeability expressions from the literature. The relationship between the aggregate permeability and solid fraction is found to be best predicted by permeability expressions based on cylindrical rather than spherical geometrical elements, the latter tending to underestimate the aggregate permeability significantly. The permeability expressions of Jackson and James or Davies provide good estimates of the force on and flow through porous aggregates of known structure. These relationships are used to identify a number of general characteristics of fractal aggregates.     

Fragmentation and erosion of two-dimensional aggregates in shear flow

We consider single two-dimensional aggregates containing glass particles trapped at a water/oil or water/air interface. Two modes for aggregate break-up are observed: break-up by fragmentation into a few parts and break-up by erosion of single particles. We have studied the critical shear rate for these modes as a function of the aggregate size. Two different particle sizes were used. The smaller particles, with a radius of 65 microm, form aggregates that break up predominantly by erosion at a shear rate between 0.5 and 0.7 s(-1). This value hardly depends on the size of the aggregates. The larger particles, with a radius of 115 microm, form aggregates that break by erosion or by fragmentation. In both modes, the critical shear rate again depends only weakly on the size of the aggregates and ranges between 1.6 and 2.2 s(-1). Also the structural changes inside the aggregate before break-up were studied. The aggregate behavior at the water/air and water/oil interfaces is quite similar. The critical shear rate for break up was also modeled. The model shows in both modes a weak dependence of the critical shear rate on the aggregate size, which is consistent with the experimental observations. The kinetics of the erosion process was also modeled and compared with the experimentally obtained time dependence of the aggregate size. The differences in the large and small particle systems can be attributed to the occurrence of friction forces between the particles, which one expects to be much larger for the large particle system, due to the stronger two-particle interaction.     

Ceria–Zirconia Particles Wrapped in a 2D Carbon Envelope: Improved Low‐Temperature Oxygen Transfer and Oxidation Activity

Engineering the interface between different components of heterogeneous catalysts at nanometer level can radically alter their performances. This is particularly true for ceria‐based catalysts where the interactions are critical for obtaining materials with enhanced properties. Here we show that mechanical contact achieved by high‐energy milling of CeO₂–ZrO₂ powders and carbon soot results in the formation of a core of oxide particles wrapped in a thin carbon envelope. This 2D nanoscale carbon arrangement greatly increases the number and quality of contact points between the oxide and carbon. Consequently, the temperatures of activation and transfer of the oxygen in ceria are shifted to exceptionally low temperatures and the soot combustion rate is boosted. The study confirms the importance of the redox behavior of ceria‐zirconia particles in the mechanism of soot oxidation and shows that the organization of contact points at the nanoscale can significantly modify the reactivity resulting in unexpected properties and functionalities.     

利用激光诱导炽光法定量测量柴油机缸内燃烧过程碳烟体积分数

激光诱导炽光(LII)法是一种用于测量火焰中碳烟体积分数的光学测试方法. 本文介绍了LII 的基本原理以及LII 实现定量测量的常见标定方法, 建立了一套基于双色法-激光诱导炽光法(2C-LII)的用于柴油机缸内燃烧过程碳烟体积分数定量测量的测试系统, 该测试系统采用双成像原理, 可以实现多点标定和全视场范围内的碳烟体积分数测量. 在一台工作在1200 r·min^-1、喷油量21 mg的光学单缸柴油机上, 研究了60、100 和140MPa三个不同喷油压力下, 缸内燃烧过程碳烟的分布情况, 结果表明, 碳烟自发光出现在燃烧放热率峰值之后, 且随着喷油压力提高, 碳烟发光持续期缩短, 碳烟发光强度降低. 测试区域内火焰中的碳烟体积分数范围约为0-50×10^-6. 不同喷油压力下, 碳烟生成初期、碳烟峰值和碳烟氧化三个阶段内平均碳烟体积分数的范围分别是: 5×10^-6-9×10^-6, 15×10^-6-20×10^-6和14×10^-6-16×10^-6. 喷油压力提高后火焰中的碳烟分布区域面积增大, 平均碳烟体积分数减小, 碳烟体积分数的空间分布趋于均匀.     

The controlled flocculation of submicron emulsion particles. I. A three-step synthetic route to supermicron polymer particles

The basic features of a three-step experimental process to produce supermicron polymer particles are described. First, a submicron emulsifier-free latex is prepared by a well-known technique. Second, the latex is aggregated by destabilizing with cetyl pyridinium chloride under constant stirring conditions, to yield roughly spherical clusters of 6-12 μ diameter. Third, the aggregates are stabilized with poly(vinyl alcohol) and internally coalesced by heating at or above the glass transition temperature. The final product particles have relatively smooth surfaces. Results are qualitatively interpreted in terms of a dynamic equilibrium where the aggregate size is determined by a balance between attractive interparticle potentials and stirring shear forces. Bimodal aggregate size distributions suggest the aggregate break-up mechanism may involve the erosion of individual latex particles and small fragments from the surface of aggregates. © 1996 John Wiley & Sons, Inc.     

Characterization of superlighting polymer-DNA aggregates: a fluorescence and light scattering study

The massive amplification of fluorescence signal observed upon hybridization of as few as five DNA molecules into self-assembled structures formed between a cationic polymer and DNA oligonucleotides is investigated. These superlighting polymer-DNA aggregates were studied by fluorescence spectroscopy, static and dynamic light scattering, and zeta potential measurements in order to characterize the aggregation behavior and to understand the processes involved during DNA detection. Multi-angle laser light scattering was also used to obtain the weight-average aggregate mass (AM), the aggregation number (Nagg), the radius of gyration (Rg), and the dissymmetry ratio (z). These results have been used, together with TEM imaging, to propose a suitable physical model for the aggregates.     

A simple model for the structure of fractal aggregates

Structural properties of small aggregates containing up to 100 particles have been studied through detailed Monte Carlo cluster-cluster aggregation simulations in both diffusion-limited and reaction-limited conditions. First, the radius of gyration, the radius of the smallest sphere encompassing the cluster, and the particle-particle correlation function, g(r), have been computed based on the positions of all the particles in the cluster, and their fractal scaling has been analyzed. Then, an empirical model has been developed to simulate the g(r) function for aggregates of any size and used to determine the corresponding structural properties and scattering structure factors. Finally, in order to illustrate the application of the structural properties thus computed, two experiments on diffusion-limited aggregation have been performed, and the average scattering structure factors have been measured as a function of time using a small-angle light-scattering device. The obtained average scattering structure factors have been simulated using the Smoluchowski population balance equations, using the single aggregate structural properties and scattering structure factor predicted by the developed empirical g(r) model.     

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.     

Study of deposition offset in plasma spray of zirconia

Numerical modeling and experimental measurements have been performed to study the effects of powder carrier gas flow rates and powder sizes on the deposition offset in a plasma spray of yttria-stablized zirconia. The mathematical model involved simultaneous solution of the continuity, momentum and energy equations of the plasma gas, the dynamics and heat transfer of powder particles in the plasma, and the coupling effects between the plasma and panicles. Experiments included measurement of particle velocities by laser strobe technique and measurement of deposition offset. Calculated plasma temperatures and velocities are greater than 13,000 K and 2,000 m/s, respectively, in the vicinity of nozzle exit. For the plasma-particle momentum transfer, the drag coefficient was computed in two ways- with corrections accounting for the strongly varying plasma properties, and without these corrections. Calculated and experimental results, in respect to deposition offset, are in agreement to within 25% when calculated without varying properties corrections, and within about 40% with corrections; agreement in respect to average particle velocities is within 20% when calculated without varying properties corrections, and within the range 30–50% with corrections.     

Solvation and aggregation of polyphenylethynylene based anionic polyelectrolytes in dilute solutions

The absorption and fluorescence properties of a polyphenylethynylene based conjugated polyelectrolyte with sulfonate solubilizing groups (PP2) are shown to change dramatically with solution conditions because of the equilibrium between unaggregated and aggregated forms of the polymer. The fluorescence of PP2 is strongly quenched on addition of counterions such as Na+, K+, Li+, and TBA+, an effect which arises from the creation of salt stabilized aggregates. The formation of aggregates has been further corroborated by concentration and temperature studies in water and comparisons to dimethylsulfoxide solvent, in which the polymer does not aggregate. In aqueous solutions, the addition of the cationic surfactant, octadecyltrimethyl ammonium, causes the polymer aggregates to dissociate and creates polymer/surfactant aggregates that have spectral properties like that of the unaggregated polymer.     

Redispersion of Highly Disperse Powder of Titanium Dioxide in Aqueous Medium

Based on an analysis of interparticle interaction in highly disperse powders, a parameter is suggested allowing one to evaluate the tendency of dispersed particles to the formation of aggregates, the aggregation coefficient. It was shown that the particles of metal oxide powders with radius smaller than 10 m are present in their aggregated state. It was found that redispersion of highly disperse titanium dioxide powder in the aqueous medium is incomplete. The incomplete redispersion may be caused by the roughness of particles and/or the formation of the regions of entrapped air that are not destroyed by capillary pressure.     

EXCITATION ENERGY TRANSFER IN BILIRUBIN-CHLOROPHYLL AGGREGATES

Abstract— Solutions of chlorophyll a (chl a ) with different concentrations of bilirubin (blr) were used as a model system for studying the mechanism of energy transfer between bili-proteins and chl in blue-green algae. Several optical properties such as the absorption spectra, emission spectra for different wavelengths of excitation, degree of polarization and lifetime of fluorescence were measured. The measurements were carried out in several solvents (of different hydrogen bond-forming capacities) and at various dye concentrations.
The results indicate that aggregates of chl with blr are formed. Energy absorbed by blr in the aggregates is emitted as chlorophyll fluorescence, indicating energy transfer from blr to chl within the aggregate. The fluorescence yield and fluorescence polarization of aggregates are lower than those of isolated chl.