Aggregation fractal-type

Humic materials have been shown to be mass fractal aggregates in solution or in suspension, and surface fractals in the solid state. The fractal dimensions of both fractal types are generally between 2 and 3. But there has been no systematic study of how the fractal dimension varies with environmental variables (pH, ionic strength, humic concentration, sample source, identity and concentration of multivalent cations, aggregate size, etc.). 

In more rigorous terms of fractal geometry, earlier formulations about filler aggregates can be understood as multi-fractal object definitions and prefactor [ as lacunarity of corresponding fractal part of the system [38,39]. For thin fractal types V(0) 0 and... 

Fig. 42. Distribution of the fractal dimensions of the clusters generated by aggregation in the journal bearing flow for different flow types (Hansen and Ottino, 1996b).

Fractal dimension of clusters formed by flow-induced aggregation is independent of local flow type. 

M. Carpineti and M. Giglio Spinodal-Type Dynamics in Fractal Aggregation of Colloidal Clusters. Phys. Rev. Lett 68, 3327 (1992). 

In the context of particle aggregation, the particular fractal structures called mass fractals are usually considered. Mass fractals correlate the location of mass with radius, as opposed to other types of fractal constructs such as boundary fractals, surface fractals, and pore fractals (see Ref. 17). The power law which correlates the size of an aggregate with the number of primary particles in the aggregate is given by... 

Simulations may be grouped according to the general uses for which they were developed. As such, the first to be developed, and the simplest simulation techniques, are those investigating the structure of aggregates. These models first appeared in 1963 [18], and after Mandelbrot s seminal work on fractal geometry [45], development of these types of simulations increased dramatically, spurred by the well-known Witten-Sander model [46]. 

From the discussion of various simulation methods, it is clear that they will continue to play an important role in further development of aggregation theories as they have advanced the state of knowledge over the last 20 years. The major limitation of the precise methods of Molecular and Brownian Dynamics continues to be difficulty associated with treatment of aggregates with complex geometry the same topic that limits the ability to model these systems using von Smoluchowski s approach. Research needs to be conducted on the hydrodynamics of interactions between fractal aggregates of increasing complexity in order to advance the current ability to describe these types of systems. 

Figure 12. Different types of aggregation geometries, df refers to the fractal dimension of the aggregates. From Hiemenz and Rajagopalan (1997) with permission from Marcel-Dekker.

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