A Gaussian model for reaction and diffusion in a lamellar structure

We develop a novel model of a two-stage chemical reaction between alternating lamellae of reactants. Under the assumption that the lamellae are approximately Gaussian, we derive a system of ordinary differential equations for the amount, the centroid and the variance of each lamella of the reactants and of the desired product. Good agreement, and considerable savings of computational time are found when solutions are compared with full numerical simulation of the reaction. We demonstrate the effect of lamellar arrangement on the yield of the reaction using the Gaussian model for systems with large numbers of lamellae.