SHEAR FLOWS AND SEGREGATION IN THE REACTION A-]0(B)

We study theoretically and numerically the effects of the linear veloc ity field v=upsilon(0)yx on the irreversible reaction A+B-->O. Assumin g homogeneous initial conditions for the two species, with equal initi al densities, we demonstrate the presence of a crossover time t(c)-ups ilon(0)(-1). For t much less than upsilon(0)(-1), the kinetics are una ffected by the shear and we retain both the effect of species segregat ion (for d<4) and the density decay rate At--alpha, where alpha=min(d/ 4,1). We calculate the amplitude A to leading order in a small density expansion for 2 less than or equal to d<4, and the critical dimension for anomalous kinetics is reduced to give bounds in d=4. However, for t much greater than upsilon(0)(-1), d(c)=2, with the density decay ra te Bt(-1) holding for d greater than or equal to 2. Bounds are calcula ted for the amplitude B in d=2, which depend on the velocity gradient upsilon(0) and the (equal) diffusion constants D. We also briefly cons ider the case of a nonlinear shear flow, where we give a more general form for the crossover time t(c). Finally, we perform numerical simula tions for a linear shear flow in d=2 with results in agreement with th eoretical predictions.