Fluctuation and rotation in diffusion-influenced monomolecular reactions

Abstract

Different methods of modeling partially absorbing boundaries in diffusion–reaction processes are examined. If the partially absorbing nature of the boundary arises from fluctuations between absorbing and nonabsorbing states, an important parameter is τr, the relaxation time associated with the fluctuations. If τr is much less than the thermal mean free time, a diffusion equation with a radiation boundary condition (RBC) in which the thermal mean free length plays a key role can be used. For the case where τr is much greater than the thermal mean free time, a stochastically switching absorber (SSA) model is presented. For a one-dimensional case it is shown that if τr is much less than the time required for diffusion across the diffusion domain, the RBC model can be made equivalent to the SSA model. A first passage time is calculated for an anisotropic three-dimensional model: two spherical particles connected by a flexible link with one of the particle’s reactivity confined to a circular patch. An approximate analogy is found between the effects of rotation and fluctuation on the first passage time.