Processes that Generate Fractal Distributions

Two types of chemical behavior of fractal surfaces must be considered how the fractal surfaces are formed by reaction with fluids (morphogenesis) and how the fractal surfaces of solids react with fluid reactants. The first will be addressed here, the second in the following section. 

Surface reactions, agglomeration, and spinodal decomposition are known to yield fractal mass distributions but other processes, such as fracture, milling or etching, also form scale-invariant surfaces.  

Another example of a fractal surface is anodically etched p-type silicon. It has a fractal porosity and shows photoluminescence and even electroluminescence, which would be impossible in compact bulk silicon. Electrons behave differently in fractally distributed solids than in three-dimensional extended lattices they are supposed to be more localized. The density of states p in a three-dimensional box is 

There are two fundamentally different ways that a solid can precipitate from a homogeneous fluid (gas or liquid) or in a homogeneous bulk solid by spinodal decomposition or as a nucleation and growth process. The morphologies of the products of these two processes are very different, as described in Section 4.2. 

Spinodal decomposition occurs when the free energy curve in the graph vs. the composition x is convex or, in other words, if the second derivative is negative  

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The concept of fractals has been applied to describe aqueous droplet size distributions generated from an air blast atomizer. A critical fractal dimension, Dc (value of 3), was used as an indicator to show whether liquid breakup or aggregation of droplets dominates during atomization. If the fractal dimension D = Dc, then the number of droplets in the spray stays constant D > Dq implies that aggregation governs the process, whereas D < Dq implies that the breakup process dominates and the number of droplets increases. The fractal dimension, D, is obtained from ... 

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