The diffusive interaction in diffusion-limited reactions: the time-dependent case Original Research Article

The time-dependent diffusive interaction in some finite and infinite systems of immobile neutral three-dimensional sinks is treated. We have shown that in large but finite arrays the bulk concentration of diffusing particles decays slower than predicted by the classical kinetics law. Moreover, we have found for finite systems that the relaxation rate changes in the course of time due to the competition between sinks. It is further shown that the classical kinetics law is caused by the diffusive interaction of sinks. An explanation for the difference in concentration dependence of the rate constant in random and periodic infinite arrays of sinks is put forward. For these arrays a general kinetic equation describing the local concentration field in a vicinity of a test sink is proposed and investigated. Using this equation we have obtained the rate constant as a function of time and sink concentration.