  In this work we present the homogenization of a reaction-diffusion model that
includes an evolving microstructure. Such type of problems model, for example,
mineral dissolution and precipitation in a porous medium. Hence, we are dealing
with a multi-scale problem with free boundaries on the pore scale. In the
initial state the microscopic geometry is given by a periodically perforated
domain, including spherical solid grains. The radius of each grain is of order
$\epsilon$ and depends on the unknown (the solute concentration) at its
surface. Therefore the radii of the grains change in time, leading to a
nonlinear, free boundary problem. In a first step, we transform the evolving
micro domain to a fixed, periodically domain. Using the Rothe-method we prove
the existence of a weak solution and obtain a priori estimates that are uniform
with respect to $\epsilon$. Finally, letting $\epsilon \to 0$, we derive a
macroscopic model, the solution of which approximates the micro-scale solution.
For this, we use the method of two-scale convergence, and obtain strong
compactness results enabling to pass to the limit in the nonlinear terms.
