We conider the evolution of an advection-diffusion equation coupled to a Stokes flow in an evolving perforated domain. This models for instance a partially desolved, partially mineralized substance. For simplicity, the solid phase is assumed to consist of the union of balls with centers that do not evolve in time. The evolution of their radii is coupled to the advection-diffusion equation through a mass exchange term at the interface. The complete microscopic system is therefore a parabolic-elliptic free boundary problem.

We study the homogenization limit $\epsilon \to 0$ when the number of the particles is of order $\epsilon^3$ and their size is of order $\epsilon^\alpha$. We prove (optimal) quantitative convergence results to the solution of an effective limit system both in the critical case $\alpha =3$ and in the superciritical case $\alpha \in (1,3)$.
In the critical case, the effective fluid velocity is governed by the Brinkman equation. The effective advection-diffusion includes a new exchange term that is coupled to a transport equation for the evolution of the solid phase. In the supercritical case, the effective fluid velocity is governed by the Brinkman equation and the exchange term between dissolved and mineralized substance does not change in the homogenization limit.