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

Homogenization of a mineral dissolution and precipitation model involving free boundaries at the micro scale