Dynamics of a lamellar system with diffusion and reaction: Scaling analysis and global kinetics

The evolution of a one-dimensional array of reactive lamellae with distributed striation thickness is studied by means of simulations, scaling analysis, and space-averaged kinetics. An infinitely fast, diffusion-controlled reaction A+B{→}2P occurs at the interfaces between striations. As time increases, thin striations are eaten by thicker neighbors resulting in a modification of the striation thickness distribution (STD). Scaling analysis suggests that the STD evolves into a universal form and that the behavior of the system at short and long times is characterized by two different kinetic regimes. These predictions are confirmed by means of a novel numerical algorithm.