Fractal dimension of percolation cluster

Table 7.3 gives the predicted exponents n, for microbial invasion (j8 = 1) and enzyme diffusion P = V2) for two and three dimensions and fractal dimensions of percolation clusters at, above and below the percolation threshold, using equation 7.12. The fractal dimension in each case increases with p with > = at/7 = 1. The initial exponents are independent of p since the fractal pathways have not yet been developed and the starch is immediately accessible on the surface. Thus, the initial slope reflects the intrinsic behaviour A The major exponent is dominated by the fractal dimension existing near p. For the poly-disperse samples, a fractal dimension of Z) = 1.59 better describes the data for both invasion and diffusion compared to Z) 1.8 for the monodisperse samples. The difference in fractal dimension is due to the coarseness of the poly-disperse pathways (average diameter 10 im) compared to the monodisperse blend (diameter = 1 pm). In general, the theoretical exponents in Table 7.3 are in agreement with the simulation exponents. 

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