Non-classical kinetics and reactant segregation in d-dimensional tubular spaces

For the diffusion-controlled A + B --> products reaction in d-dimensional tubular spaces, with length L and width W, where L >> W, we show that the Ovchinnikov-Zeldovich reactant segregation has no upper critical dimension and that the reciprocal density rho(-1) scales asymptotically with W(d-1/2)t(1/4). This is consistent with Li's scaling ansatz for d = 2, 3 and with Monte Carlo simulations. For the crossover time t(c) this gives a scaling relation t(c) similar to W-alpha provided that W is wide enough to allow segregation at t < t(c). Similar scaling arguments are used to derive the scaling relations between rho(-1) and W and between t(c) and W for the A + A --> 0 and A + C --> C reactions in d-dimensional tubular lattices. We also extend these scaling relations to square slab spaces of volume L-2 X Wd-2 and to tubular or square-slab spaces with fractal cross sections. (C) 1997 Elsevier Science B.V.