Darcy's law for evolving microstructure

A Darcy law for evolving microstructure is derived by homogenisation of Stokes flow. We transform the Stokes equations from the locally evolving domain onto a periodic reference domain. There, we pass to the homogenisation limit by employing the method of two‐scale convergence. After transforming the limit back to its original two‐scale domain, we obtain a Darcy Law for evolving microstructure. This Darcy Law does not only capture the space‐ and time‐dependent permeability, but also includes how the change of the porosity induces pressure. In order to give uniform a priori estimates, we derive a Korn‐type inequality for this two‐scale transformation method as well as a family of ϵ‐scaled operators div−1ϵ.