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

Abstract

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 ϱ −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 ∼ W α provided that W is wi enough to allow segregation at t < t c. Similar scaling arguments are used to derive the scaling relations between ϱ −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 × W d − 2 and to tubular or square-slab spaces with fractal cross sect