Interface diffusion controlled reactions in multilayers

We consider the reaction α + β → ω where ω is either a solid solution or a stoichiometric compound. We consider this reaction inside multilayers to occur at a single interface, and at a temperature low enough that volume diffusion is frozen and surface diffusion is controlling. We compute both the reaction front velocity and its morphology. It is shown that depending on the conditions of the experiment, two classes of solutions are possible: a single propagating front sweeping the multilayer, or a fingering solution propagating along the original α/β interfaces.