Dimensional crossovers in A+B -> 0 reaction in tubular geometries

Diffusion-controlled A + B --> O reactions in constrained geometries are we ll-known to obey nonconventional dimension-dependent kinetics. We investiga te these kinetics in narrow d-dimensional tubes to study the crossovers fro m early time d-dimensional kinetics to eventual one-dimensional kinetics. W e rely on a reaction-diffusion model that leads to analytically verifiable quantitative results. The crossover times are identified as those times at which the kinetic exponent exhibits maximum curvature and are shown to be u niversally given by t(c) = 0.034W(2)/D where W is the width of the tube alo ng a narrow direction and D is the diffusion coefficient of both species. O ur procedure overcomes many of the statistical difficulties inherent in:Mon te Carlo simulations of this problem [Ahn, J.; Kopelman, R.; Argyrakis,. J. Chem. Phys. 1999, 110, 2116].