Research On Fractal-Aggregation During Coagulation Process: Computer Simulation

Fractal theory and Monte-Carlo method have been applied to research on particle aggregation during coagulation or flocculation since the phenomenon is a non-linear and chaotic process, in which particle aggregates are formed with complicated shape and random structure. The computer has played a quite important role in calculation and simulation of aggregation. Most models, which are accessible to a good understanding of the dynamics process, have been established and applied by means of computer simulation. A computer language: VB is employed in this work to make a set of application procedure for a poly-dispersed cluster-cluster aggregation model. Several numerical simulations of DLCA and RLCA are performed to obtain the morphological characteristic and the concentration and the sticking probability dependence of the fractal dimension of the small-sized clusters. And the dynamics process is concerned for a primary rule of the fractal cluster growth. A more innovative method self-similar iteration is developed to produce larger-sized fractal aggregates by incorporating self-similar property of regular fractal with the Monte-Carlo simulation. It is tested by a simple analysis of the two-dimensional iterative aggregates. It is expected to provide groundwork for study on fractal-aggregation and exploring the significance of application to coagulation or flocculation. Main conclusions are as follows:Small-sized DLCA aggregates containing 100~500 primary particles clearly show fractal features. Their fractal dimensions depend strongly on the initial particle concentration. A departure from fractal scale occurs at the concentrations over 0.03 (particle/lattice). Values of fractal dimension obtained from the power-law relationship of Rg-N vary from 1.45 to 1.52 for two-dimensional aggregates and from 1.80 to 1.99 for three-dimensional aggregates, respectively. A stretched exponential form of particle-particle correlation function can fit well the simulation values, which educes a little lower fractal dimensions than those from Rg-N fitting.For a long initial stage of DLCA, the average cluster size has performed a behavior of exponential growth. It shows a trend of steady power-law growth at a later time, and then a sharp increase to the maximum size near to the end point of aggregation.The structures of aggregates formed in RLCA simulations behave a strong dependence on the sticking probability. The enclosing radii and the radii of gyration show a trend of power-law growth as the sticking probability varies from 0.1 to 1, and the ratio of both falls with a light fluctuation. The time of aggregation decrease according to a power-law relationship with the sticking probability increasing.The results obtained from the self-similar iteration of DLCA aggregates contained Nn primary particles. As a result of the anisotropy of the random particle aggregate, the primary particles of a single aggregate exhibit scattering to some extend, and the fractal dimensions lower a little.