Scaling properties of diffusion-limited reactions

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Abstract
A simple scaling argument for diffusion-limited reactions for both A+A→0 and A+B→0 is developed. Temporally asymptotic behavior of species densities in the absence of sources and reaction orders in the steady state in the presence of sources are discussed. We specifically address the effect of the spatial distributions of reactants on the reaction rates. For the A+A→0 reaction we recover existing results found by other methods. For A+B→0 in the absence of sources we find that the asymptotic behavior depends not only on the spectral dimension (as commonly believed) but also on the fractal dimension. In the presence of sources we agree with previous results when the steady-state density is not too low, but argue that a modification of these results may occur at very low densities.