Scale-invariant growth of fractal aggregates

The fractal dimension of a formed aggregate depends on the masses and fractal dimensions of approaching clusters as well as on the degree of their mutual penetration. The relations are described by the aggregation act equation. Aggregation act equation is used to analyze the structure of growing fractal aggregates. If the coagulating aggregates have the same fractal dimension, the appropriate choice of the ratio of their radii makes it possible to save fractal dimension for the resultant aggregate. The more close to unity the ratio, the lower is the value of fractal dimension. Especially, if the aggregating clusters have the same mass, they grow by the hierarchical cluster–cluster mechanism, for which the constant fractal dimension has the lowest value possible. Some experimental data are quoted to support the obtained dependences. Using these data, the aggregation act equation is verified to provide the reliable values of fractal dimension of some aggregates formed by two clusters of comparable aerodynamic diameters.