•Modified DLA model has been used to simulate the co-precipitation of wax/asphaltene particle.•Fractal dimension is adopted to explore the geometric property of the aggregates.•The changing law of ...fractal dimension with concentration and size ratio has been explored.
Diffusion-limited aggregation (DLA) model has been widely used to simulate the aggregation processes. In this work, the aggregation of wax and asphaltene particles in crude oil is studied with a modified DLA model. Assuming both wax and asphaltene particles are sphere, the co-precipitating process could be regarded as a simple aggregation process containing two kinds of particles. Three important parameters are discussed, as the sticking coefficient between particles, the ratio of particle size, and the particle concentration. Via analyzing the fractal dimension of the formed aggregates, the aggregation mechanism of wax and asphaltene particles could be explained, and help to further reveal the nature of the disordered growth.
The modeling of the fractal-like adsorption systems, such as the sludge-, algae-, and nanoparticle aggregation-pollutants systems, is of vital significance to understand the mechanisms involved and ...to connect the mechanisms with the isotherms. But it has not been studied yet. In this paper, a three-dimensional DLA (diffusion limited aggregation) model was modified and used to investigate the fractal-like adsorption systems which were dominated by the physical, chemical, ion exchange and multi-mechanisms. The connection between the adsorption isotherms and the adsorption mechanisms was established. The results showed that the shape and filling degree of the modified DLA model was improved. The adsorption capacity of the fractal-like adsorption system increases with the increase of the fractional dimension of the DLA model. The chemical adsorption capacity is directly proportional to the adsorption active sites. In the ion exchange system, the structure of the DLA model did not change before and after adsorption. The BET, Sips, and ion exchange isotherms could adequately represent the physical, chemical, and ion exchange adsorption. For the multi-system, the adsorption isotherm was C-shaped with the fractal dimensions of the DLA model of 2.28 and 2.42. When the fractal dimensions increase, the isotherm was S-shaped and linear.
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•The improved 3-dimensional DLA model was developed.•The fractal-like adsorption systems were modeled based on the DLA model.•The adsorption amount increased with the increase of the fractional dimension.•The isotherms can adequately describe the fractal-like adsorption systems.
In this study a 3D multi-particle diffusion limited aggregation method is employed to simulate growth of rough surfaces with fractal behavior in electrodeposition process. A deposition model is used ...in which the radial motion of the particles with probability P, competes with random motions with probability 1−P. Thin films growth is simulated for different values of probability P (related to the electric field) and thickness of the layer(related to the number of deposited particles). The influence of these parameters on morphology, kinetic of roughening and the fractal dimension of the simulated surfaces has been investigated. The results show that the surface roughness increases with increasing the deposition time and scaling exponents exhibit a complex behavior which is called as anomalous scaling. It seems that in electrodeposition process, radial motion of the particles toward the growing seeds may be an important mechanism leading to anomalous scaling.
The results also indicate that the larger values of probability P, results in smoother topography with more densely packed structure. We have suggested a dynamic scaling ansatz for interface width has a function of deposition time, scan length and probability. Two different methods are employed to evaluate the fractal dimension of the simulated surfaces which are “cube counting” and “roughness” methods. The results of both methods show that by increasing the probability P or decreasing the deposition time, the fractal dimension of the simulated surfaces is increased. All gained values for fractal dimensions are close to 2.5 in the diffusion limited aggregation model.
•A 3D multi-particle diffusion limited aggregation method is employed to simulate growth of rough surfaces in electrodeposition process.•The simulated surfaces exhibit a complex behavior which is called as anomalous scaling.•The values of H and β that have been measured by this model are close to KPZ universality class.•A dynamic scaling ansatz is suggested for interface width as a function of thickness, scan length and probability P.•The values of H=0.45,βloc=0.46,β=0.35,(H∕β)=1.29,δ=0.16,γ=0.14 and y=0.05 are found for characteristic scaling exponents.
BORDER AGGREGATION MODEL Thacker, Debleena; Volkov, Stanislav
The Annals of applied probability,
06/2018, Letnik:
28, Številka:
3
Journal Article
Recenzirano
Odprti dostop
Start with a graph with a subset of vertices called the border. A particle released from the origin performs a random walk on the graph until it comes to the immediate neighbourhood of the border, at ...which point it joins this subset thus increasing the border by one point. Then a new particle is released from the origin and the process repeats until the origin becomes a part of the border itself. We are interested in the total number ξ of particles to be released by this final moment.
We show that this model covers the OK Corral model as well as the erosion model, and obtain distributions and bounds for ξ in cases where the graph is star graph, regular tree and a d-dimensional lattice.
Flocculation plays an important role in the immobilized fermentation of biofuels and biochemicals. It is essential to understand the flocculation phenomenon at physical and molecular scale; however, ...flocs cannot be studied directly due to fragile nature. Hence, the present study is focused on the morphological specificities of yeast flocs formation and sedimentation via the computer simulation by a single floc growth model, based on Diffusion‐Limited Aggregation (DLA) model. The impact of shear force, adsorption, and cell propagation on porosity and floc size is systematically illustrated. Strong shear force and weak adsorption reduced floc size but have little impact on porosity. Besides, cell propagation concreted the compactness of flocs enabling them to gain a larger size. Later, a multiple flocs growth model is developed to explain sedimentation at various initial floc sizes. Both models exhibited qualitative agreements with available experimental data. By regulating the operation constraints during fermentation, the present study will lead to finding optimal conditions to control the floc size distribution for efficient fermentation and harvesting.
Flocculation plays an important role in the immobilized production of biofuels and biochemicals. In this study, the authors perform the computer simulation for flocs formation and sedimentation by modified DLA models, which shows the impact of shear force, adsorption, and cell propagation on porosity and floc size systematically. This work will lead to the optimal conditions with proper floc size distribution for efficient fermentation and harvesting.
This article reviews recent advances in the shape-controlled synthesis routes of hierarchical Ag dendritic nanostructures. Various fabricated techniques, with or without templates or surfactants, ...electrochemical method and sonochemical, microwave or photochemical assisted synthesis method, can be amazingly effective in the dendritic Ag nanostructures synthesis, if synthetic parameters are carefully selected. The involved synthesis mechanism are discussed in order to control the limited factors along the fabricated progress efficiently and then to find new synthetic means. Also, the blemish of the above synthesis routes that hinders the practical application is pointed out to inspire the future research.
The formation, breakage, and re-growth of flocs were investigated by using modified flocculation tests and numerical simulation to explore the evolution of floc morphology for different hydraulic ...retention times. The shorter the aggregation time was, the smaller the flocs produced for the same hydraulic conditions were. Another interesting discovery was that broken flocs that formed in shorter aggregation time had the capacity to completely recover, whereas those formed in a longer amount of time had rather worse reversibility of broken flocs. With the addition of the maximum motion step in the representative two-dimensional diffusion-limited aggregation (DLA) model, there was a transition for flocs from isotropic to anisotropic as the maximum motion step increased. The strength of flocs was mainly affected by the distribution of particles near the aggregated core rather than distant particles. A simplified breakage model, which found that broken flocs provided more chances for diffused particles to access the inner parts of flocs and to be uniformly packed around the aggregated core, was first proposed. Moreover, an important result showed that the floc fragments formed with a larger value of the maximum motion step had more growing sites than did those with a smaller msa value, which was a benefit of following the re-forming procedure.
Polymer electrolyte membranes containing various weight percent of salt have been prepared in the authors’ laboratory for the study of their potential applications in solid state electrochemical ...devices; however, the polymer electrolyte membranes were found to become sort of media for fractal growth, months after they were prepared. Fractal growth patterns in polymer membranes of poly (ethylene oxide) and chitosan membranes have been analyzed, and their fractal dimensions were determined. A diffusion-limited aggregate model which is based on the Brownian motion theory is applied to simulate the experimentally obtained fractal patterns. The approach was extended by performing computer simulations with computing resources available. The fractal dimension values of the simulated and the experimentally obtained original fractal patterns were marginally close. This indicates that the simulation work has successfully produced fractal patterns that are in fairly acceptable conformity with the fractal patterns observed in the polymer membranes.
Using fractal theory simulation of dendrite crystal DLA growth model of pure substance, the undercooling during solidification process of crystal nucleation is simulated; and then in the crystal ...nuclei are formed on the basis of a pure substance, the phase field model and combined with the finite difference method further differentiation simulation of dendrite crystal growth. According to MATLAB programming, the simulation results obtained by field and temperature field can be seen in the DLA growth, growth model with random premise, for the same kind of material simulated dendrite crystal have both similarities and differences exist. Then, we can get the conclusion, through fractal growth of DLA model with phase field model of dendrite nucleation, growth process is carried out the simulation results, a simple by phase field model is more accord with the dendrite crystal in the experiment.
This paper reports a new route for the preparation of conducting network in insulating polymer matrix. In existing techniques solubility of conducting component is an essential condition. Reported ...technique facilitates making composite of conducting polymer, which is insoluble in normal solvents, with percolation threshold of 0.5 wt%. Mechanism of formation of the three component hybrid may be described as when silica which acted as seed is dispersed in insulating polymer, the in-situ polymerized conducting polymer having high aspect ratio is grown over the silica surface connecting each other and making a continuous network. The star like growth of the conducting polymer can be seen under optical microscope.
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