Smokes, fractal dimension

Certain real systems seem to be described by OLA, notably electrodeposition on a sharp point (39) and dielectric breakdown (33,40). The second class involves cluster formation by the homogeneous aggregation of a collection of two clusters of comparable size (37, ) (cluster-cluster aggregation, CA) and the resultant aggregate has a more open structure and lower fractal dimension, D = 1.4 ( d = 2) and 1.8 (d = 3). Real smoke ( ) and colloids (41) seem to have D = 1.8 this is a satisfying verification of the model. A process that has not, however, been included in the simulations is rearrangement within the clusters. This would lead to denser structures with higher Hausdorff dimensions ( ). 

Colbeck et al. [88] analysed various smokes and found textural fractal dimensions in the range 1.12-1.27 for petrol, diesel, fuel, oil, paraffin, butane and wood (Table 9.2), whilst the mass fractal dimensions were 2.04, 1.88, 1.97 and 2.35 for diesel, fuel oil, butane and wood respectively. This wide range represents a... 

Table 9.2 Fractal dimensions of different smokes [88]. Reprinted from J. Aerosol Sci., Vol. 28, Colbeck, L, Atkinson, B. and Johar, Y., The morphology and optical properties of soot produced by different fuels, 715-723. Copyright (1997), with permission from Elsevier.

Figure 9.6 Mean values of the fractal dimension for butane smoke aged for 4 h and then subject to various relative humidities and supersaturations (data from [115]).

Liquid aerosol particles are nearly always spherical. Solid aerosol particles usually have complex shapes, as shown in Figs. 1.1—1.5. In the development of the theory of aerosol properties, it is usually necessary to assume that the particles are spherical. Correction factors and the use of equivalent diameters enable these theories to be applied to nonspherical particles. An equivalent diameter is the diameter of the sphere that has the same value of a particular physical property as that of an irregular particle. For approximate analysis, shape can usually be ignored, as it seldom produces more than a twofold change in any property. Particles with extreme shapes, such as long, thin fibers, are treated as simplified nonspherical shapes in different orientations. The complex shape of some fiime and smoke particles can be characterized by their fractal dimension. (See Section 20.2.)... 

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