Quantitative analysis of mixing structures in chaotic flows generated by infinitely fast reactions in the presence of diffusion

The interplay between diffusive and convective mixing processes may have a strong, impact upon apparent reaction rates. This paper analyzes the interaction of convection and diffusion mechanisms by considering an infinitely fast irreversible reaction A + B --> products, occurring in a two-dimensional chaotic flow. Attention is focused on the aeometric properties of mixing patterns and on the overall reactant consumption. We show that the length of the reaction interface undergoes a transition from a kinematics-dominated exponential growth to a persistent oscillatory regime. This regime results from two competing mechanisms, namely, recursive stretching and folding of the interface caused by chaotic advection and merging of contiguous striations patterns owed to diffusive transport. In the case of globally chaotic flows, a singular transition is observed in the scaling of the dominant eigenvalue with the Peclet number. The geometric information arising from the analysis of the reaction interface is also exploited for deriving a simple one-dimensional model that predicts the apparent rates over a wide range of Peclet numbers.