A simple model for a two-stage chemical reaction with diffusion

We analyse the evolution of a two-stage chemical reaction between two neigh bouring plumes of reactants. Under the assumption that the plumes are appro ximately Gaussian we derive a system of ordinary differential equations for the total amount, the centroid and the variance of each reactant. We compa re the solution of these equations with full numerical simulation of the re action. Excellent agreement is obtained, with solution of the near-Gaussian model requiring considerably less computational effort than the full simul ations. Of key importance is the yield of the reaction, and we discuss this feature in particular.