Dynamics of diffusion-controlled reactions among stationary sinks: Scaling expansion approach

Diffusion-controlled reactions in a nondilute sink system are rigorously studied with the aid of a scaling expansion method. A space-time coarse graining is carried out in a manner consistent with an expansion in sink concentration to obtain macroscopic transport equations from microscopic equations. It is shown that, beyond the lowest order in sink concentration, the macroscopic transport equation for the reaction–diffusion process cannot be written in a conventional local form in space and time since a nonlocal contribution in space becomes important. Properties of the fluctuations around the macroscopic motion are also explicitly explored, and they are shown to be small in comparison with the macroscopic motion for three-dimensional systems with an appropriate choice for the size of a sink radius and obey a Gaussian process. An absorption process whose characteristic length is much longer than that of the reaction–diffusion process is also investigated, and a local damping equation in space and time is derived.