Viscosity expansions in reactive diffusion processes

Properties of chemical reactions in systems undergoing diffusional motion depend on the ratio of chemical to diffusional rates. The present work deals with perturbation expansions in this quantity. For bounded diffusion, the Laplace transformed survival probability, mean lifetime, eigenvalues, and eigenfunctions are expanded in this ratio. The theory is developed mainly in the fast diffusion limit. In this limit, the survival probability for an initial equilibrium state is shown to be exponential up to linear order. For unbounded diffusion, expansions are derived for the steady-state concentration profile and rate coefficient. By inverting the series one obtains Padé-like approximations for rate coefficients with much improved convergence. Several examples are worked out in detail. These include the "radiation" boundary condition, barrierless isomerization, steady-state binding, and Förster quenching.