Diffusion –limited reaction processes are those for which the transport time (the typical time until reactants meet) is much larger than the reaction time (the typical time until reactants react, when they are constrained to be within their reactionrange distance). The transport properties of the reactants largely determine the kinetics of diffusion –limited reactions. One then naturally wonders how the (often anomalous) diffusion of particles discussed so far may affect such processes. This, and the need to account for the effects of fluctuations in the concentration of the reactants at all length scales, as well as other sources of fluctuations, make the study of diffusion –limited reactions notoriously difficult. The topic is discussed in the next four chapters.

In Chapter 11, we begin with the far simple case of reaction –limited processes. In their case the system may be assumed to be homogeneous at all times: the transport mechanism and fluctuations play no significant role. The kinetics of reaction –limited processes is well understood, since they may be successfully analyzed by means of classical rate equations. We also touch upon the important subject of reaction –diffusion equations, but only at the mean –field level, without the addition of noise terms.

Chapter 12 discusses the Smoluchowski model for binary reactions, and trapping. It is instructive to see how diffusion –limited processes depart from their reaction –limited counterpart, even for such elementary reaction schemes.