Acceleration of chemical reaction by chaotic mixing

Abstract

Theory of fast binary chemical reaction, ${\cal A}+{\cal B}\to{\cal C}$, in a statistically stationary chaotic flow at large Schmidt number ${Sc}$ and large Damk\"ohler number ${Da}$ is developed. For stoichiometric condition we identify subsequent stages of the chemical reaction. The first stage corresponds to the exponential decay, $\propto\exp(-\lambda t)$ (where $\lambda$ is the Lyapunov exponent of the flow), of the chemicals in the bulk part of the flow. The second and the third stages are related to the chemicals remaining in the boundary region. During the second stage the amounts of ${\cal A}$ and ${\cal B}$ decay $\propto 1/\sqrt{t}$, whereas the decay law during the third stage is exponential, $\propto\exp(-\gamma t)$, where $\gamma\sim\lambda/\sqrt{Sc}$.