Shear flows and segregation in the reaction A+B→ circ/

We study theoretically and numerically the effects of the linear velocity field v=v0yx' on the irreversible reaction A+B→ circ/. Assuming homogeneous initial conditions for the two species, with equal initial densities, we demonstrate the presence of a crossover time tc∼v0-1. For tv0-1, the critical dimension for anomalous kinetics is reduced to dc=2, with the density decay rate Bt-1 holding for d≥2. Bounds are calculated for the amplitude B in d=2, which depend on the velocity gradient v0 and the (equal) diffusion constants D. We also briefly consider the case of a nonlinear shear flow, where we give a more general form for the crossover time tc. Finally, we perform numerical simulations for a linear shear flow in d=2 with results in agreement with theoretical predictions. copyright 1996 The American Physical Society