Hierarchies of nonclassical reaction kinetics due to anisotropic confinements

In contrast to classical chemical reaction kinetics, for diffusion limited chemical reactions the anisotropy of the geometry has far reaching effects. We use tubular two and three-dimensional spaces to illustrate and discuss the dimensional crossover in A1B→0 reactions due to dimensional compactification. We find that the crossover time tc5W a scales as a5b/(a2b), where a, b, and b are given by the earlier and the late time inverse density scaling of r;t and r;tW, respectively. We also obtain a critical width Wc below ~above! which the chemical reaction progresses without ~with! traversing a two or three-dimensional Ovchinnikov–Zeldovich ~OZ! reaction regime. As a result 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 various Euclidean and fractal compactified geometries, for the A1B and A1A elementary reactions. Monte Carlo simulations illustrate some of the kinetic hierarchies. © 1999 American Institute of Physics. @S0021-9606~99!00504-8#