Boundary Effects on Chaotic Advection-Diffusion Chemical Reactions

A theory of a fast binary chemical reaction, $\mathcal{A}+\mathcal{B}\to \mathcal{C}$, in a statistically stationary bounded chaotic flow at large Peclet number Pe and large Damköhler number Da is described. The first stage correspondent to formation of the developed lamellar structure in the bulk part of the flow is terminated by an exponential decay, $\propto \exp (-\lambda t)$ (where $\lambda$ is the Lyapunov exponent of the flow), of the chemicals in the bulk. The second and the third stages are due to the chemicals remaining in the boundary region. During the second stage, the amounts of $\mathcal{A}$ and $\mathcal{B}$ decay $\propto 1/\sqrt{t}$, whereas the decay law during the third stage is exponential, $\propto \exp (-\gamma t)$, where $\gamma \sim \lambda /\sqrt{\mathrm{P}\mathrm{e}}$.