Cluster-cluster Aggregation Model Research Articles

Numerical investigation of the coalescence behavior of carbon nanoparticle based on the cluster-cluster aggregation model considering the experimental coalescence characteristic time

The coalescence behavior of carbon nanoparticle, such as soot and carbon black, has not been so much discussed. This study delves into the intricate behavior of nanoparticle aggregates, with a keen emphasis on the variations in their shape and size based on coalescence dynamics. The coalescence rate obtained from previous experimental results was implemented in an aggregate mean free path cluster–cluster aggregation model. The effect of coalescence on morphology was examined by classifying the aggregates obtained using the cluster–cluster aggregation model in terms of their complexity. We contrasted the results of cluster–cluster aggregation simulation with experimental aggregate shape analyzing electron microscopy images and experimental primary particle size distribution. When neglecting coalescence, proportion of branched-shape aggregates was higher, whereas accounting for coalescence resulted in predominantly ellipsoidal or spherical particles. Contrasting simulations with experimental data reveals that filter-sampling methods may overemphasize aggregate complexity. Contrarily, thermophoretic sampling provided a closer match to simulation predictions. A pivotal finding was that the coalescence model, when coupled with accurate experimental sampling techniques, aligns closely with the experimental observations.

Code for the cluster dichotomy model

The stability of colloid is closely related to the aggregation of colloidal particles and the dispersion of clusters in the system. Because aggregation changes the original state of the sol, previous studies have paid more attention to the aggregation process of the colloid. In fact, aggregation process and dispersion process coexist. The Cluster-Cluster Aggregation model has been widely used to simulate the process of colloidal agglomeration. In the aspect of cluster dispersion, people pay more attention to the simulation of cluster dispersion caused by external forces (such as shear force). In the actual system, the sudden decrease of electrolyte concentration leads to the increase of electrostatic repulsion between colloidal particles, resulting in the disintegration of the clusters. Inspired by the dimerization process of the traditional Cluster-Cluster Aggregation model, we previously proposed a dichotomy model to simulate the dispersion process of colloidal clusters. Here, we provide Java code for the dichotomy model, which can simulate dispersion caused by external forces and internal forces. This paper further elaborates the key points of the dichotomy model, mainly including: the definitions of the relevant probabilities involved in the dichotomy model, the data structures of particle, cluster and cube, and the functions of the relevant parameters related to the dichotomy model. Furthermore, the cluster's characteristics of erosion dispersion and collapse dispersion are studied respectively. Program summaryProgram Title: Dichotomy modelCPC Library link to program files:https://doi.org/10.17632/my9xzpm8xg.1Licensing provisions: Apache-2.0Programming language: JavaNature of problem: Many scholars focus on the research of cluster aggregation, but ignore the cluster dispersion, and there are few programs for the simulation of cluster dispersion. The program provided in this paper can well simulate the dynamic process of cluster dispersion.Solution method: Inspiring by the idea of dimerization in the classical CCA model, the process of dispersing a larger cluster into multiple smaller clusters is transformed into the superposition of several times of one-to-two processes. The three-dimensional on-lattice model is used to simulate the process of cluster dispersion. We use the Java language to write programs, and dynamically display the simulation results through the Java3D technology.

A stochastic model, simulation, and application to aggregation of cadmium sulfide nanocrystals upon evaporation of the Langmuir–Blodgett matrix

Abstract A stochastic model of nanocrystals clusters formation is developed and applied to simulate an aggregation of cadmium sulfide nanocrystals upon evaporation of the Langmuir–Blodgett matrix. Simulations are compared with our experimental results. The stochastic model suggested governs mobilities both of individual nanocrystals and its clusters (arrays). We give a comprehensive analysis of the patterns simulated by the model, and study an influence of the surrounding medium (solvent) on the aggregation processes. In our model, monomers have a finite probability of separation from the cluster which depends on the temperature and binding energy between nanocrystals, and can also be redistributed in the composition of the cluster, leading to its compaction. The simulation results obtained in this work are compared with the experimental data on the aggregation of CdS nanocrystals upon evaporation of the Langmuir–Blodgett matrix. This system is a typical example from real life and is noteworthy in that the morphology of nanocrystals after evaporation of the matrix cannot be described exactly by a model based only on the motion of individual nanocrystals or by a cluster-cluster aggregation model.

A novel dichotomy model based on the traditional CCA

The Cluster-Cluster Aggregation model (CCA) was often used to simulate the aggregation of colloids, in which the rapid and slow aggregation processes of colloids can be well characterized. In practical system, the movement of particles or clusters occurs in parallel. In the CCA model, in order to facilitate computer simulation, the movement of particles or clusters is processed serially by the method of Metropolis sampling. That is, randomly selecting one particle or cluster to move randomly, colliding with other cluster in the movement, and aggregating according to certain conditions, such aggregation would usually occur between a moving cluster and a static cluster, and this process is essentially a dimerization process. Based on this idea, this study proposes a cluster dichotomy model, in which the dispersion process can be regarded as the inverse process of cluster aggregation, that is, the randomly selected cluster always breaks up into two small clusters. This kind of dispersion is called dichotomy. Based on this model, the rapid and slow dispersion processes of colloidal clusters can be simulated by setting the relevant parameters. The dichotomy model proposed in this paper can be used to study colloidal stability by coupling with the traditional CCA model.

A Monte Carlo Simulation Study on: Deposition, Diffusion, and Aggregation

In this paper we present a Monte Carlo simulation program to implement a single model: deposition, diffusion, and aggregation (DDA). By using the simulation program, we show in the following that the DDA model generates a wide variety of fractal structures characteristic of different models such as diffusion-limited aggregation (DLA) or cluster-cluster aggregation (CCA), but such DLA and CCA models do not incorporate the possibility of cluster-mass dependent deposition. Starting from those kernels, aggregation laws to describe the interaction between free and deposited clusters were proposed and a simple cluster-mass dependent deposition law was employed. The simulation results are then discussed in the frame of the relative strength of parameters.

Effects of additives of organically modified montmorillonite and Octosilicate in a silica reinforced tire tread mixture

Dual filler networks of spherical and layered particles on the example of elastomer-reinforcement with silica, doped with a small quantity of organically-modified layered silicates (Octosilicate or montmorillonite) in the mass ratio of 80 to 3 were investigated, as well as the influence of the organic-modifier on the mechanical properties of the rubber composites. Synergies with interesting mechanical properties for technical rubber applications were found, but surprisingly only for the system that contains organically modified octosilicate, attributed to a higher extent of exfoliation/intercalation and related to a higher and more homogeneous surface modification than for organically modified montmoriilonite under the chosen experimental conditions. Shear modulus measurements on concentration series' allowed the determination of scaling exponents for the reinforcement that are well described by the cluster-cluster aggregation model. This also suggests integration of the relatively large layers of montmorillonite or Octosilicate during the early stages of the flocculation process because of the increased collision probability of particles of different sizes over particles of same size.

Three-dimensional tomography reveals distinct morphological and optical properties of soot aggregates from coal-fired residential stoves in China

Electron tomography (ET) is used to reconstruct the exact 3-dimensional morphologies of fractal-like soot aggregates sampled from a household heating stove commonly used in China. Conventional ET techniques suffer from “the missing wedge” problem caused by unreachable tilt angles, leading to noisy reconstructed tomograms. We overcame this problem by implementing a high-resolution object-edge identification method coupled with a novel voxel-filling algorithm to improve the reconstruction quality. Our reconstructed micron-length aggregates highlight the local non-idealities present throughout a particle's surface; these characteristics are almost impossible to account for in existing computational simulation exercises. Q-space analysis predicts the fractal dimension of our ET reconstructed aggregates to be in the range between 2.2 and 2.6, which deviates significantly from the universal value of 1.8 obtained using the widely adopted diffusion limited cluster-cluster aggregation (DLCA) model. The optical properties of our ET reconstructed aggregates are compared with those built with a DLCA model and equivalent spheres . The most striking optical characteristics of the ET reconstructed aggregates are their wavelength invariant mass absorption cross-sections of ~3.5 m2/g and single scattering albedo of ~0.5. The sample size investigated in this work is constrained by the extremely time-consuming object-edge identification process of electron tomography. This issue necessitates the development of more efficient computer vision algorithms for future research.

Process Description of an Unconventional Biofilm Formation by Bacterial Cells Autoagglutinating through Sticky, Long, and Peritrichate Nanofibers.

In this study, we elucidated the formation process of an unconventional biofilm formed by a bacterium autoagglutinating through sticky, long, and peritrichate nanofibers. Understanding the mechanisms of biofilm formation is essential to control microbial behavior and improve environmental biotechnologies. Acinetobacter sp. Tol 5 autoagglutinate through the interaction of the long, peritrichate nanofiber protein AtaA, a trimeric autotransporter adhesin. Using AtaA, without cell growth or extracellular polymeric substances production, Tol 5 cells quickly form an unconventional biofilm. The process forming this unconventional biofilm started with cell-cell interactions, proceeded to cell clumping, and led to the formation of large cell aggregates. The cell-cell interaction was described by Derjaguin-Landau-Verwey-Overbeek (DLVO) theory based on a new concept, which considers two independent interactions between two cell bodies and between two AtaA fiber tips forming a discontinuous surface. If cell bodies cannot collide owing to an energy barrier at low ionic strengths but approach within the interactive distance of AtaA fibers, cells can agglutinate through their contact. Cell clumping proceeds following the cluster-cluster aggregation model, and an unconventional biofilm containing void spaces and a fractal nature develops. Understanding its formation process would extend the utilization of various types of biofilms, enhancing environmental biotechnologies.

Physical limitation of pesticides (chlordecone) decontamination in volcanic soils: fractal approach and numerical simulation.

In the French West Indies, the chlordecone (organochloride pesticide) pollution is now diffuse becoming new contamination source for crops and environment (water, trophic chain). Decontamination by bioremediation and chemical degradation are still under development but the physical limitations of these approaches are generally not taken into account. These physical limitations are related to the poor physical accessibility to the pesticides in soils because of the peculiar structural properties of the contaminated clays (pore volume, transport properties, permeability, and diffusion). Some volcanic soils (andosols), which represent the half of the contaminated soils in Martinique, contain nanoclay (allophane) with a unique structure and porous properties. Andosols are characterized by pore size distribution in the mesoporous range, a high specific surface area, a large pore volume, and a fractal structure. Our hypothesis is that the clay microstructure characteristics are crucial physico-chemical factors strongly limiting the remediation of the pesticide. Our results show that allophane microstructure (small pore size, hierarchical microstructure, and tortuosity) favors accumulation of chlordecone, in andosols. Moreover, the clay microporosity limits the accessibility of microorganisms and chemical species able to decontaminate because of poor transport properties (permeability and diffusion). We model the transport properties by two approaches: (1) we use a numerical model to simulate the structure of allophane aggregates. The algorithm is based on a cluster-cluster aggregation model. From the simulated data, we derived the pore volume, specific surface area, tortuosity, permeability, and diffusion. We show that transport properties strongly decrease because of the presence of allophane. (2) The fractal approach. We characterize the fractal features (size of the fractal aggregate, fractal dimension, tortuosity inside allophane aggregates) and we calculate that transport properties decrease of several order ranges inside the clay aggregates. These poor transport properties are important parameters to explain the poor accessibility to pollutants in volcanic soils and should be taken into account by future decontamination process. We conclude that for andosols, this inaccessibility could render inefficient some of the methods proposed in the literature.

Aggregation-driven reductions in the mass extinction coefficient of bioaerosols

When bioaerosols float in the atmosphere, due to static electricity generated by collisions and friction, particles agglomerate. By using the cluster-cluster aggregation model, the structures of aggregated particles were established at different stages in the aggregation of bioaerosols. Moreover, extinction parameters of the aggregated particles were calculated by using the discrete dipole approximation method, thus obtaining the bioaerosol mass extinction coefficient. The results demonstrate that aggregation of bioaerosols can decrease the mass extinction coefficient. When there are three, or four, original particles in each of the aggregated particles, the mass extinction coefficients of bioaerosols decrease to 50% and 25% of those before aggregation. Porosity of aggregated particles is a key factor affecting the mass extinction coefficient: the greater the porosity, the smaller the mass extinction coefficient a bioaerosol.

Evolution of phase morphology in dispersed clay systems under the microwave irradiation

Abstract The results of a study of the microwave emission effect (power 700 W, frequency 2.45 GHz) on the structural changes in natural clay particles with effective diameters D≤630 μm are presented. The influence of the irradiation time (10 and 20 min) and the environment in the microwave chamber (atmospheric air and air saturated with water vapor) on the structural changes occurring in the particles were traced. During the first 10 min, capillary water was completely removed and agglomeration was carried out by attaching single dispersed particles (diffusion limited aggregation model). At the second stage (10-20 min), the already formed agglomerates grew (cluster-cluster aggregation model). A complex of independent optical-physical methods was used to analyze weak structural changes, including X-ray diffraction analysis, colorimetry and wavelet analysis. This approach increased the information content and reliability of measurements, quantitatively characterizing the structural responses in disperse clay systems. In the air, the removal of capillary water was accompanied by agglomerations of particles and polymorphic transformations of oxides: montmorillonite was completely decomposed and amorphous phases, in particular CaCO3, crystallized. The composition of the environment in the microwave chamber affected the type of phase transformations in iron compounds: iron-aluminum silicate (Fe2Al4Si5O18) was formed in the air; magnetite Fe.Fe2O4 (Fe3O4) appeared in the water vapor medium. The carried-out studies with the developed set of experimental methods indicated the possibility of regulating the processes of structure formation in dispersed clay systems by optimizing the regimes of exposure to microwave radiation.

ELECTRON SPIN RESONANCEON HYBRID NANOCOMPOSITES BASED ON NATURAL RUBBER

Electron spin resonance (ESR) was used as a new method to analyze the synergy between two nanofillers dif-ferent by nature, form and rigidity dispersed in natural rubber matrix. Natural rubber (NR) nanocomposites loaded with fixed amount of carbon nanotubes (2 parts per hundred of rubber parts; phr) and various amounts of expanded organically modified montmorillonite (EOMt, 4–20 phr) were investigated. The dependence of the double integral of the resonance spectra on the amount of EOMt present in the natural rubber was established. Its decrease with an in-creaseof the amount of EOMt confirmed the synergy between these two nanofillers. Also DMA temperature sweep measurements were performed and the cluster-cluster aggregation (CCA) model was used to assess the apparent filler networking energy. The obtained results suggest that the presence of the EOMt above a critical amount strengthens the hybrid-filler networking.

Modeling the Breakup of Clusters Induced by Internal Repulsion

In nanoparticles system, particles (or clusters) can aggregate into big-scale clusters, which also can break into small ones by the change of internal conditions. For this purpose, a breakup model was proposed and a JAVA program was developed to simulate the process based on the classic Cluster-Cluster Aggregation (CCA) model. In the simulation, a single cluster, which is gotten from the CCA, breaks into small ones firstly, and then these break into smaller and smaller ones sequentially abiding by specified rules. It is found that clusters present various structure under different parameters in the cube system. Meanwhile, the process visualization can be well displayed by JAVA 3D figures dynamically, and some data analysis can be performed spontaneously based on the data files recorded by the program.

Version 4.0 of code Java for 3D simulation of the CCA model

This paper presents a new version Java code for the three-dimensional simulation of Cluster–Cluster Aggregation (CCA) model to replace the previous version. Many redundant traverses of clusters-list in the program were totally avoided, so that the consumed simulation time is significantly reduced. In order to show the aggregation process in a more intuitive way, we have labeled different clusters with varied colors. Besides, a new function is added for outputting the particle’s coordinates of aggregates in file to benefit coupling our model with other models. New version program summaryProgram Title: CCA v04Program Files doi:http://dx.doi.org10.17632/zwz37tvjny.1Licensing provisions: Apache-2.0Programming language: JavaJournal reference of previous version: Computer Physics Communications 207 (2016) 547–548Does the new version supersede the previous version?: YesNature of problem: The previous program for CCA model can be optimized for yielding better operation efficiency and visualization effects. Besides, it can be extended for coupling with other models by adding some new functions.Solution method: Some redundant traverses of the clusters-list for updating an important variable were removed technically. Furthermore, displaying different clusters with distinct colors can benefit to the effectiveness of visualization. We have also introduced a new function for outputting the aggregated clusters, so that this model can be easily coupled with other models.Reasons for the new version:1. In the previous versions [1–3], the global variable of Dmax, which means the maximum diffusion coefficient of clusters, is supposed to be calculated when aggregation occurs. In fact, this variable is critical to determine whether the currently selected cluster carries out diffusion or not. In the previous version, we had to traverse the clusters-list to update Dmax, even though it may keep unchanged after a round of aggregation. But, we have explored that it is not necessary to traverse all clusters, if we compare the previous variable of Dmax with the diffusion coefficient of the new cluster, which is formed by aggregating two clusters. In the case of the new one is larger, Dmax will be updated to it; otherwise, Dmax keep unchanged. Obviously, removing redundant traverses can enhance algorithm efficiency, and the time complexity of the algorithm is closely related to the loop in it. As a result, the new version of code can greatly cut down the simulation time, in contrast to the previous codes.2. The old versions paint all particles with same color, which does not help to identify different clusters. In order to show the visualization of the 3D aggregate process in different states intuitively, we introduce labeling different clusters with different colors. Consequently, the particles belong to one cluster are painted with the same color.3. A new function is added to record intermediate or final state of clusters so that it can be used for further research when using other relevant models.Summary of revisions:1. Reduce unnecessary traverses of the clusters-list for speeding up simulation.2. Paint clusters with different colors to pursuit better visualization effects.3. Add a new function of exporting the coordinates of clusters to a text file for benefiting other models.Additional comments:To test the optimization effects offered by the new version of code, we have carried out a comparison experimentto measure the simulation time with different initial particles, by using the new and the previous version 3.0 of code. In the experiments, we set concentration C to 0.01, diffusion exponent γ to 0, sticking probability exponent σ to 1, the sticking probability P1 to 0.1, absolute temperature T to 298 K, and the side length L of cube was respectively set to 30, 40, 50, 60, 70 and 80 to yield different initial particles, as the number of particles N can be calculated by the formula N=C∗L3 [1]. To avoid the influences of hardware and software, we use Monte Carlo steps (MCS) as our simulation time [4–6]. As shown in Fig. 1, the slope coefficient caused by this new version of code is about 1.3813, it is close to line complexity, as for the previous version, it is 1.5703, larger than the new one. It is obvious the new one has a faster running speed than the previous one. More importantly, the reduction of simulation time becomes more obvious when the number of simulated particles is getting larger.The changed visualization of our program is shownin Fig. 2. We can clearly see how much clusters in simulation system, and how they distribute. And the button “save” marked red in Fig. 2 can help realize our new function by exporting the particle coordinates to a text file, which also store the related initial conditions.AcknowledgmentsThis work was partially supported by “National Natural Science Foundation of China (Nos. 41271292, 61303038)”.

A Tribute to Marian Smoluchowski's Legacy on Soft Grains Assembly and Hydrogel Formation

The paper compares the statistical description of physical-metallurgical processes and ceramic-polycrystalline evolutions, termed the normal grain growth (NGG), as adopted to soft- and chemically-reactive grains, with a Smoluchowski's population-constant kernel cluster-cluster aggregation (CCA) model, concerning irreversible chemical reaction kinetics. The former aiming at comprehending, in a semi-quantitative way, the volume-conservative (pressure-drifted) grain-growth process which we propose to adopt for hydrogel systems at quite low temperature (near a gel point). It has been noticed, that by identifying the mean cluster size $<k>$ from the Smoluchowski CCA description with the mean cluster radius' size $R_D$, from the NGG approach of proximate grains, one is able to embark on equivalence of both frameworks, but only under certain conditions. For great enough, close-packed clusters, the equivalence can be obtained by rearranging the time domain with rescaled time variable, where the scaling function originates from the dispersive (long-tail, or fractal) kinetics, with a single exponent equal to $d+1$ (in $d$-dimensional (Euclidean) space). This can be of interest for experimenters, working in the field of thermoresponsive gels formation, where crystalline structural predispositions overwhelm.

RHEOMETRIC AND DYNAMIC MECHANICAL ANALYSIS OF COMPLEX NATURAL RUBBER BASED COMPOSITES

This work describes the preparation and characterization of complex natural rubber (NR) based composites containing hybrid nano- and conventional fillers intended for base seismic application. Thorough rheometric and dy-namic mechanical analyses in strain sweep mode at 2 Hz and 10 Hz (two frequencies laying in the range 0 – 15 Hz in which most of the earthquakes have the dominant frequencies) were performed on complex natural rubber (NR) based composites containing hybrid nanofiller (carbon nanotubes, expanded montmorillonite) and different amounts of con-ventional fillers like carbon black (CB) and silica. The rheometric studies showed that the influence of the combina-tion of the different fillers on curing parameters is quite complex, but mainly the introduction of the fillers reduces the scorch and optimum cure time of the compounds. The dynamic mechanical analysis showed a pronounced non-linear strain dependence of the storage modulus and a remarkable increase of the loss factor tanδ for all composites, espe-cially for those containing high CB content, compared to the NR-gum. To describe this strain-dependency of the stor-age modulus the cluster-cluster aggregation (CCA) model was used. The values of the fitting parameters ΔE’0, γc, and E’∞ calculated by this model show that they are affected by the type of the fillers present in the NR matrix and also by the applied frequency.

Benefits of hybrid nano-filler networking between organically modified Montmorillonite and carbon nanotubes in natural rubber: Experiments and theoretical interpretations

In this paper some new aspects to the hybrid nano-filler networking in elastomer matrix under dynamic mechanical loading conditions and some new methods to reveal a hybrid nano-filler synergy are applied and discussed. Electron spin resonance (ESR) spectra of the multi-walled carbon nanotubes (MWCNT) present in the natural rubber (NR) based nanocomposites were investigated and the dependence of the double integral of resonance spectra on the amount of expanded organically modified montmorillonite (EOMt) present in the NR was established. Its decrease with an increasing amount of EOMt confirmed the synergy between these two nano-fillers. DMA temperature sweep measurements were performed and the cluster-cluster aggregation (CCA) model was used to assess the apparent filler networking energy. The obtained results suggest that the presence of the EOMt above a critical amount strengthens the hybrid-filler networking. In order to investigate how different ratios of these two nano-fillers influence the strain dependency of the storage modulus, strain sweep measurements were performed in tensile mode, and the CCA-model was used to describe the Payne effect.

Pollution of soils and ecosystems by a permanent toxic organochlorine pesticide: chlordecone—numerical simulation of allophane nanoclay microstructure and calculation of its transport properties

Pest control technology was introduced into the tropics without considering the specificity of their ecosystems and the risk of pollution was underestimated. Some volcanic soils (andosols) contain nanoclay (allophane) with a unique structure and porous properties compared to crystalline clays. Andosols are characterized by large pore volume and pore size distribution, a high specific surface area, and a fractal structure. These soils are more polluted than the other kinds of tropical soils but release less pollutants (chlordecone) to water and plants. The literature shows that the allophane microstructure favors accumulation and sequestration of chlordecone, an organochlorine pesticide, in andosols. We used a numerical model to simulate the structure of allophane aggregates. The algorithm is based on a cluster-cluster aggregation model. From the simulated data, we derived the structural features, pore volume and tortuosity, and its transport properties, hydraulic conductivity and diffusion. We show that transport properties decrease because of the presence of allophane. We propose that low hydraulic conductivity and diffusion are important parameters to explain the high concentrations and trapping of pollutants in andosols.

3D simulation of the Cluster–Cluster Aggregation model

We write a program to implement the Cluster–Cluster Aggregation (CCA) model with java programming language. By using the simulation program, the fractal aggregation growth process can be displayed dynamically in the form of a three-dimensional (3D) figure. Meanwhile, the related kinetics data of aggregation simulation can be also recorded dynamically. Compared to the traditional programs, the program has better real-time performance and is more helpful to observe the fractal growth process, which contributes to the scientific study in fractal aggregation. Besides, because of adopting java programming language, the program has very good cross-platform performance. Program summaryProgram title: CCACatalogue identifier: AEUK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUK_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 390649No. of bytes in distributed program, including test data, etc.: 83881850Distribution format: tar.gzProgramming language: Java.Computer: Any computer with Windows, java jdk and java3d jdk installed.Operating system: Windows.RAM: Determined by the number of the initial particles in the simulation testClassification: 14, 16.12.Nature of problem:The programs for the CCA model published are very rare, and are mostly in the form of a 2D figure. So, existing computer simulation programs cannot well simulate the fractal aggregation. Compared to the existing programs, our simulation program for the CCA model in the form of a 3D figure can better simulate the process dynamically.Solution method:A program is provided that well simulates CCA model in the form of a 3D figure. The program implementation is based on the java programming language. Especially, we use the java3d technology to display the simulative graphics in form of 3D.Restrictions:In order to show the process of fractal aggregation growth dynamically, this program needs to refresh the graphics of aggregation of colloidal particle frequently. So this program takes up a lot of computer memory. The storage capacity of the computer memory used to run the program will limit the number of single particles which the program can simulate.Unusual features:The program simulates the CCA model in the form of a 3D figure using the java3d technology.Additional comments:!!!!Due to the large file size, CCA is not delivered directly when download or Email is requested. Instead an html file giving details of how the program can be obtained is sent.!!!!Running time:Determined by the size of the problem.

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.