A two-stage reaction with initially separated reactants

A two-stage reaction (A+B→R,B+R→S) is studied, where the reactants A and B lie initially in an array of alternating striations. The product R is desired, and S is an unwanted by-product. A corresponding reaction–diffusion system in one spatial dimension is analysed in two special cases, and comparison is made with numerical simulations of the reaction and diffusion in a periodic array of lamellae for realistic parameter values. For lamellar widths of the order of 1μm or less, diffusion rapidly smears out the lamellar structure, and the yields of R and S are nearly equal to those in a spatially homogeneous, well-mixed system. For thicker lamellae, of around one millimetre in width, the yields are significantly different in the lamellar case from the well-mixed case. The differences are quantified and discussed.