Diffusion-limited clustering

Transport control of flocculation is realized in an especially direct way in the process known as diffusion-limited cluster-cluster aggregation5 (aggregation as used in this term means flocculation in the present chapter). In this process, which is straightforward to simulate and visualize on a computer, particles undergo Brownian motion (i.e., diffusion) until they come together in close proximity, after which they coalesce instantaneously and irreversibly to form floccules (or clusters ). The clusters then diffuse until they contact one another and combine to form larger clusters, and so on, until gravitational... 

Fig. 6.1. Visualization sequence of diffusion limited cluster cluster flocculation, based on a two dimensional computer simulation of the random encounter and instantaneous combination of 2(XX)...

Clusters that are build in a diffusion limited cluster-cluster aggregation... 

Kolb M. Reversible diffusion-limited cluster aggregation. J Phys A Math Gen 1986 19 L263-L268. 

Figure 3.9 Box-counting analysis of a projection of a computer-generated diffusion-limited cluster aggregate of 10 000 particles with mass fractal dimension of 1.88. The images have box sizes L of (top left to bottom right) 1, 2,4,8,16, 32 and 64 pixels and require 205 245,59519, 17 062, 4895,1436, 462 and 135 squares respectively to cover the image.

Computer simulations have shown that the value of fractal dimension largely depends on whether the aggregation process is controlled by the diffusion rate of the clusters and single particles or by their chemical reactivity at the time of collision, the latter being mainly controlled by the DLVO forces. This observation, in agreement with experimental work on aerosols and colloids, has led to a new classification of aggregation processes the reaction-limited and diffusion-limited cluster aggregation (RLCA and DLCA respectively) processes. 

Meakin, P. (1985). The effects of random bond breaking on diffusion limited cluster-cluster aggregation. J. Chem. Phys., 83, 3645-3649. 

Ldpez-Lopez, J.M., Moncho-Jorda, A., Schmitt and Hidalgo-Alvarez, R. (2005). Formation and structure of stable aggregates in binary diffusion-limited cluster-cluster aggregation processes. Phys. Rev. E, 72, 31 401-31 409. 

In summary, the typical final restructured value A 2.0-2.2 for laboratory results may be compared with a value Df l.2 for simulations [72, 113], In this model, diffusion-limited cluster-cluster aggregates restructured in discrete steps to A 2.2, after which further increase was not possible. The situation in the atmosphere is more complex, and there probably exists a spectrum of A values in the range 1.8 to 2.0-2.2, dependent mainly on aggregate age and meteorological conditions encountered. 

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