科研之友
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摘要
Aggregation is a non-equilibrium process of fundamental importance for all dispersed particulate systems, and the aggregates so produced are common in nature and technology. The resulting aggregates show fractal morphology with a universal, quantifiable fractal dimension. Current quantitative explanations for the fractal aggregate structure are based on simulation models that successfully describe experimental findings and have the key feature that as aggregates form, they continue to move and eventually connect with other aggregates. If the motion between meetings is diffusive, which is very typical, the process is called diffusion limited cluster aggregation (DLCA). We have shown previously that a three-parameter description, including the fractal dimension, the scaling prefactor, and the shape of these aggregates, is both necessary and sufficient to completely describe their morphology. Here we define a new shape description and find geometric relations between the dimensions of the aggregates. Moreover, we show that with this new shape description the aggregate shape is described by the Divine Proportion and its generalization to any dimension. Finally, we recall a simple, analytical theory for DLCA aggregate structure, the Restricted Hierarchical Model, to find that it accurately predicts shape, fractal dimension, and scaling prefactor to yield a necessary and sufficient three-parameter description of aggregate structure.
- 出版日期2015
