ISSN:
1089-7690
Quelle:
AIP Digital Archive
Thema:
Physik
,
Chemie und Pharmazie
Notizen:
Smoluchowski's equation is widely applied to describe the time evolution of the cluster-size distribution during aggregation processes. Analytical solutions for this equation, however, are known only for a very limited number of kernels. Therefore, numerical methods have to be used for describing the time evolution of the cluster-size distribution. In this work, we present a novel self-consistent method for solving Smoluchowski's equation for any homogeneous kernel. The method considers dynamic scaling to be valid but does not need to assume a given form for the scaling distribution Φ(x). Moreover, the scaling distribution Φ(x) is obtained as a natural result of the algorithm. Due to the implementation of dynamic scaling concepts, the algorithm converges almost immediately with a minimal calculation effort. Comparing calculated size distributions with the corresponding analytical solutions shows the validity of the method. The method is then used to fit experimental data for diffusion limited aggregation. For this purpose, a fitting procedure is developed which allows us to fit the corresponding parameters for any given homogeneous kernel. As an application, a full comparison between the experimental data and the numerically obtained cluster-size distributions for the constant and the Brownian kernel was carried out. © 1999 American Institute of Physics.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1063/1.480092
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