The effect of fluctuations on diffusion-limited reactions

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Abstract
We discuss the effect of various sources of fluctuations on the kinetics of diffusion-limited reaction processes. The diffusion mechanism for the motion of the reactants plays the most essential role and its effect is apparent in all of the reaction processes presented. Spatial fluctuations in the concentrations of the reactants are another source of fluctuations that have a dramatic effect on the kinetics of the system. The example of two-species annihilation, A + B→Inert, is recalled and analysed to demonstrate this effect. Finally, we show that discrete fluctuations, i.e. fluctuations arising from the discrete nature of the particles, are also of great importance and influence the kinetics. We present a formalism for the study of discrete fluctuations. This formalism is based on the Van Kampen Ω-expansion of a master equation representing the process in question. Various reaction processes are analysed and their kinetics is predicted in view of the different sources of fluctuations. Our theoretical scaling predictions are backed by extensive Monte Carlo simulations.

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