Cluster-cluster Agglomeration Research Articles

Fractal cometary dust – a window into the early Solar system

The properties of dust in the protoplanetary disk are key to understanding the formation of planets in our Solar System. Many models of dust growth predict the development of fractal structures that evolve into non-fractal, porous dust pebbles representing the main component for planetesimal accretion. In order to understand comets and their origins, the Rosetta orbiter followed comet 67P/Churyumov-Gerasimenko for over two years and carried a dedicated instrument suite for dust analysis. One of these instruments, the MIDAS atomic force microscope, recorded the 3D topography of micro- to nanometre sized dust. All particles analysed to date have been found to be hierarchical agglomerates. Most show compact packing, however, one is extremely porous. This paper contains a structural description of a compact aggregate and the outstanding porous one. Both particles are tens of micrometres in size and show rather narrow subunit size distributions with noticeably similar mean values of 1.48+0.13−0.59 μm for the porous particle and 1.36+0.15−0.59 μm for the compact. ompact. The porous particle allows a fractal analysis, where a density-density correlation function yields a fractal dimension of Df = 1.70 ± 0.1. GIADA, another dust analysis instrument on-board Rosetta, confirms the existence of a dust population with a similar fractal dimension. The fractal particles are interpreted as pristine agglomerates built in the protoplanetary disk and preserved in the comet. The similar subunits of both fractal and compact dust indicate a common origin which is, given the properties of the fractal, dominated by slow agglomeration of equally sized aggregates known as cluster-cluster agglomeration.

Coagulation-agglomeration of fractal-like particles: structure and self-preserving size distribution.

Agglomeration occurs in environmental and industrial processes, especially at low temperatures where particle sintering or coalescence is rather slow. Here, the growth and structure of particles undergoing agglomeration (coagulation in the absence of coalescence, condensation, or surface growth) are investigated from the free molecular to the continuum regime by discrete element modeling (DEM). Particles coagulating in the free molecular regime follow ballistic trajectories described by an event-driven method, whereas in the near-continuum (gas-slip) and continuum regimes, Langevin dynamics describe their diffusive motion. Agglomerates containing about 10-30 primary particles, on the average, attain their asymptotic fractal dimension, D(f), of 1.91 or 1.78 by ballistic or diffusion-limited cluster-cluster agglomeration, corresponding to coagulation in the free molecular or continuum regimes, respectively. A correlation is proposed for the asymptotic evolution of agglomerate D(f) as a function of the average number of constituent primary particles, n̅(p). Agglomerates exhibit considerably broader self-preserving size distribution (SPSD) by coagulation than spherical particles: the number-based geometric standard deviations of the SPSD agglomerate radius of gyration in the free molecular and continuum regimes are 2.27 and 1.95, respectively, compared to ∼1.45 for spheres. In the transition regime, agglomerates exhibit a quasi-SPSD whose geometric standard deviation passes through a minimum at Knudsen number Kn ≈ 0.2. In contrast, the asymptotic D(f) shifts linearly from 1.91 in the free molecular regime to 1.78 in the continuum regime. Population balance models using the radius of gyration as collision radius underestimate (up to about 80%) the small tail of the SPSD and slightly overpredict the overall agglomerate coagulation rate, as they do not account for cluster interpenetration during coagulation. In the continuum regime, when a recently developed agglomeration rate is used in population balance equations, the resulting SPSD is in excellent agreement with that obtained by DEM.

CHARGING AND COAGULATION OF DUST IN PROTOPLANETARY PLASMA ENVIRONMENTS

Combining a particle-particle, particle-cluster and cluster-cluster agglomeration model with an aggregate charging model, the coagulation and charging of dust particles in various plasma environments relevant for proto-planetary disks have been investigated. The results show that charged aggregates tend to grow by adding small particles and clusters to larger particles and clusters, leading to greater sizes and masses as compared to neutral aggregates, for the same number of monomers in the aggregate. In addition, aggregates coagulating in a Lorentzian plasma (containing a larger fraction of high-energy plasma particles) are more massive and larger than aggregates coagulating in a Maxwellian plasma, for the same plasma densities and characteristic temperature. Comparisons of the grain structure, utilizing the compactness factor, {\phi}{\sigma}, demonstrate that a Lorentzian plasma environment results in fluffier aggregates, with small {\phi}{\sigma}, which exhibit a narrow compactness factor distribution. Neutral aggregates are more compact, with larger {\phi}{\sigma}, and exhibit a larger variation in fluffiness. Measurement of the compactness factor of large populations of aggregates is shown to provide information on the disk parameters that were present during aggregation.

Langevin agglomeration of nanoparticles interacting via a central potential

Nanoparticle agglomeration in a quiescent fluid is simulated by solving the Langevin equations of motion of a set of interacting monomers in the continuum regime. Monomers interact via a radial rapidly decaying intermonomer potential. The morphology of generated clusters is analyzed through their fractal dimension df and the cluster coordination number. The time evolution of the cluster fractal dimension is linked to the dynamics of two populations: small (k≤ 15) and large (k>15) clusters. At early times monomer-cluster agglomeration is the dominant agglomeration mechanism (d(f)=2.25) , whereas at late times cluster-cluster agglomeration dominates (d(f)=1.56). Clusters are found to be compact (mean coordination number of ∼5), tubular, and elongated. The local compact structure of the aggregates is attributed to the isotropy of the interaction potential, which allows rearrangement of bonded monomers, whereas the large-scale tubular structure is attributed to its relatively short attractive range. The cluster translational diffusion coefficient is determined to be inversely proportional to the cluster mass and the (per-unit-mass) friction coefficient of an isolated monomer, a consequence of the neglect of monomer shielding in a cluster. Clusters generated by unshielded Langevin equations are referred to as ideal clusters because the surface area accessible to the underlying fluid is found to be the sum of the accessible surface areas of the isolated monomers. Similarly, ideal clusters do not have, on average, a preferential orientation. The decrease in the numbers of clusters with time and a few collision kernel elements are evaluated and compared to analytical expressions.

Effects of Driving Conditions on Diesel Exhaust Particulates

Four driving conditions were examined to characterize how speeds and loads of a medium-duty diesel engine affect resultant diesel exhaust particulates (DEPs) in terms of number concentrations (≤400 nm), size distribution, persistent free radicals, elemental carbon (EC), and organic carbon (OC). At the medium engine load (60%), DEPs surged in number concentrations at around 40–70 nm, whereas DEPs from the full engine load (100%) showed a distinctive bimodal distribution with a large population of 30–50 nm and 100–400 nm. Under the full engine load, engine speeds insignificantly affected resultant DEP number concentrations. When the engine load decreased from 100% to the medium level (60%), DEPs of ultrafine size and 100–400 nm decreased at least 1.4 times (from 5.6 × 108 to 4 × 108 #/cm3) and more than 3 times (from 2.7 × 108 to 0.8 × 108 #/cm3), respectively. The same reduction in the engine load significantly decreased persistent free radicals in DEPs up to approximately 30 times (from 123 × 1016 to 4 × 1016 #spin/g). Decreasing the engine load from 100 to 60% also concurrently reduced both EC and OC in total DEPs around 2 times, from 27.3 to 13.9 mg/m3, and from 17.6 to 9.2 mg/m3, respectively. For DEPs smaller than 1 µm, under the full engine load, EC and OC consistently peaked at 170–330 nm under an engine speed of 1800 rpm or 94–170 nm under an engine speed of 3000 rpm, reflecting processes of nucleation, cluster-cluster agglomeration, and condensation. Decreasing the engine load from 100 to 60% reduced EC and OC in DEPs (smaller than 1 μm) at least 3 times (0.6 to 0.2 mg/m3) and 2 times (0.4 to 0.2 mg/m3), respectively. Taken together, decreasing the full engine load to a medium (60%) level effectively reduced the number concentrations (≤400 nm), persistent free radicals, EC, and OC of total DEPs, as well as the concentration of EC and OC in ultrafine and accumulation-mode DEPs.

Agglomeration Simulation of Chain-like Inclusions in Molten Steel Based on Fractal Cluster-Cluster Agglomeration Model

Based on the fractal cluster-cluster agglomeration (CCA) model, two-dimensional simulations of cluster aggregation process have beencarried out by varying initial particle number, particle size and sticking probability between clusters. Particle size and amount of seed particleshave small effects on the shape of clusters. Actual alumina clusters observed in tundish show the chain-like appearance and are very similar tothe simulatedagglomerated clusters with highstickingprobability.The agglomeration process of alumina chain-like clusters aroundimmersionnozzle in the tundish and RH process are plausibly controlled by the random collision process with high sticking probabilityvalues. [doi:10.2320/matertrans.MRA2007037](Received February 15, 2007; Accepted May 18, 2007; Published July 19, 2007)Keywords: fractal, fractal dimension, inclusion, chain-like inclusion, deoxidation, cluster-cluster aggregation

Soot measurements at the axis of an ethylene/air non-premixed turbulent jet flame

The size, morphology, and volume fraction of soot particles within the fuel-rich regions of a non-premixed turbulent jet flame fueled by ethylene/air at atmospheric pressure were investigated. Experiments involved thermophoretic sampling followed by transmission electron microscopy and laser extinction techniques to determine mean soot properties of principal interest at various heights along the flame axis. Similar to numerous past studies, soot in this turbulent flame consisted of nearly uniform spherical particles that collected into aggregates of different shapes and sizes. Soot spherule (primary particle) diameters were 19 to 35 nm, in agreement with the narrow size range reported in many combustion environments. With fractal dimensions and prefactors in the range 1.74 ± 0.11 and 2.2 ± 0.4, respectively, aggregate morphology was also found to be almost identical to soot formed in various laminar flames and emitted from turbulent flames. These universal parameters apparently resulted from the dominant cluster-cluster agglomeration mechanism, which was also responsible for the monotonic increase in the average aggregate size with height above the burner. The mean soot volume fraction reached a maximum of 1.1 ppm at a height lower than the peak axial location of the spherule size, while the particle number density varied in the range of 10 10–10 11 particles/cm 3 with a similar trend. The peak value of the actual specific surface area was 2.5 cm 2/cm 3, which was about a factor of three larger than the value estimated by a volume-equivalent spherical model. The results clearly identified various axial zones of prevailing soot nucleation, surface growth, oxidation, and agglomeration processes in the non-premixed turbulent flame considered here.

Investigations on the fracturing of nanoparticle agglomerates—first results

The mechanical properties of nanoparticle agglomerates have been addressed in many studies. Agglomerates of nanoparticles grown by stochastic processes such as diffusion-limited cluster-cluster agglomeration represent fractal-like objects. These agglomerates are not in the most stable state, and delivering a certain minimum energy, i.e. the activation energy for restructuring, can induce rearrangement. However, in many applications of nanoparticles a high degree of dispersion in the carrier medium (gas or liquid) is desired. Thus, the fragmentation of the aggregates down to the primary particles would be optimal. Depending on the production process, the bond strength between the primary particles will exhibit a distribution that may range from weak van der Waals bonds to strong solid state necking. In the present study, the degree of fracturing as indicated by image analysis of electron micrographs from impacted agglomerates of nanoparticles of Ag and TiO2 was investigated. The influence of kinetic energy on fracturing was studied.

Optical Properties of Fluffy Particles

AbstractFor particles grown in the two limiting cases of coagulation (ballistic particle-cluster agglomeration and ballistic cluster-cluster agglomeration), lower and upper limits of the extinction at wavelengths from 1 μm to 1 mm are derived. The particle sizes are in the Rayleigh limit and the number of constituent grains in each particle is constant. Effective medium theories, the discrete dipole approximation and the discrete multipole method are applied to compute the optical behaviour of the coagulated particles. The spectral representation for inhomogeneous media is employed to investigate topology effects systematically.

Optical spectra of size-selected matrix-isolated silicon clusters

Size selected silicon clusters have been isolated in rare gas matrices and studied by optical absorption spectroscopy. The clusters were produced in a pulsed laser vaporization source, size selected with a quadrupole mass spectrometer and deposited at low energies into a cocondensed krypton matrix held at T<20 K. A comparison of the optical spectra of ten atom wide bands (Si25-Si35, Si35-Si45 and Si45-Si55) shows the general size evolution of the optical properties. Single cluster sizes have also been isolated and show somewhat sharper spectra than the bands. The measured spectra show similarities to spectra calculated using Mie theory and bulk optical constants. Cluster-cluster agglomeration was studied by evaporating the inert gas matrix. The results suggest that the clusters agglomerate into larger particles even under the mildest "soft landing" conditions.

The general dynamic equation for aerosols. Theory and application to aerosol formation and growth

Conservation equations for aerosol size distribution dynamics are derived and compared. A new discrete-continuous conservation equation is derived that overcomes the limitations of the purely discrete or continuous equations in simulating aerosol dynamics over a broad particle size spectrum. Several issues related to aerosol formation and growth not previously amenable to exact analysis are studied in detail using the discrete-continuous equation: (1) the establishment of a steady state concentration profile of molecular clusters in the presence of a preexisting aerosol; (2) the relative importance of nucleation, condensation, and scavenging in gas-to-particle conversion; and (3) the importance of cluster-cluster agglomeration relative to other processes. The formation and growth of a sulfuric acid/water aerosol in a smog chamber is simulated using the discrete-continuous equation, and the results are compared with recent experimental data. The above issues related to aerosol formation and growth are investigated for the simulated experiment.