Predicting the evolution of fast chemical reactions in chaotic flows.

We study the fast irreversible bimolecular reaction in a two-dimensional chaotic flow. The reactants are initially segregated and together fill the whole domain. Simulations show that the reactant concentration decays exponentially with rate lambda and then crosses over to the algebraic law of chemical kinetics in the final stage of the reaction. We estimate the crossover time from the reaction rate constant and the flow parameters. The exponential decay phase of the reaction can be described in terms of an equivalent passive scalar problem, allowing us to predict lambda using the theory of passive scalar advection. Depending on the relative length scale between the velocity and the concentration fields, lambda is either related to the distribution of the finite-time Lyapunov exponent of the flow or given in terms of an effective diffusivity which is independent of the small-scale stretching properties of the flow. For the former case, we suggest an optimal choice of flow parameters at which lambda is maximum.