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

We analyse the evolution of a two-stage chemical reaction betweentwo neighbouring plumes of reactants. Under the assumption thatthe plumes are approximately Gaussian we derive a system ofordinary differential equations for the total amount, the centroidand the variance of each reactant. We compare the solution ofthese equations with full numerical simulation of the reaction.Excellent agreement is obtained, with solution of the near-Gaussianmodel requiring considerably less computational effort thanthe full simulations. Of key importance is the yield of thereaction, and we discuss this feature in particular.