Scalings of A + B Reaction Kinetics due to Anisotropic Confinements

Abstract

We report on the diffusion-limited A + B reaction in highly anisotropic spaces. In addition to the highly non-classical behavior of the density of reactants predicted for isotropic spaces, we observe a dimensional crossover in A + B → 0 reactions due to the geometrical compactness of the tubular 2- and 3-dimensional spaces (baguettelike structures). For slabs, we find the crossover time T_c. = Wα, which scales as $\alpha = \frac{\beta }{{a - b}}$, where a, b and β are given by the earlier and the late time inverse density scalings of ρ^{− 1} ˜-, t^a and ρ⁻¹ - t^bW^β, respectively. We also obtain a critical width W, below which the chemical reaction progresses without traversing a 2- or 3-dimensional Ovchinnikov-Zeldovich reaction regime. We find that there exist different hierarchies of dimensionally forced crossovers, depending on the initial conditions and geometric restrictions. Kinetic phase diagrams are employed and exponents are given for the A + B elementary reactions in various euclidean geometries. Monte-Carlo simulations illustrate some of the kinetic hierarchies.