Efficiency of a stirred chemical reaction in a closed vessel

We perform a numerical study of the reaction efficiency in a closed vessel. Starting with a little spot of product, we compute the time needed to complete the reaction in the container following an advection-reaction-diffusion process. Inside the vessel it is present a cellular velocity field that transports the reactants. If the size of the container is not very large compared with the typical length of the velocity field one has a plateau of the reaction time as a function of the strength of the velocity field, $U$. This plateau appears both in the stationary and in the time-dependent flow. A comparison of the results for the finite system with the infinite case (for which the front speed, $v_f$, gives a simple estimate of the reacting time) shows the dramatic effect of the finite size.