Fast-reaction asymptotics for a two-scale reaction-diffusion system

We investigate a reaction–diffusion process in a two-phase medium with microscopic length scale ε. The diffusion coefficients in the two phases are highly different (d1/D = ε2) and the reaction constant k is large. First, the homogenisation limit ε → 0 is taken, which leads to a two-scale model. Afterwards, we pass to the fast-reaction limit k → ∞ and obtain a two-scale reaction-diffusion system with a moving boundary traveling within the microstructure