Efficiency of a stirred chemical reaction in a closed vessel

Abstract:

We perform a numerical study of the burning efficiency in a closed vessel. Starting with a little spot of product, we compute the time needed to complete the reaction in the container. Inside the vessel there is a cellular flow that transports the reactants. Our main result is that 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 burning time as a function of the strength of the velocity field, U. This means that, once the plateau is reached, a further increase of U does not reduce the time needed to complete the reaction. This plateau arises when we consider both a stationary and a time-dependent cellular flow, and we give analytical and numerical arguments that try to explain why it appears. Also a comparison of the results for the finite system with the infinite case shows the dramatic effect of the finite size.