  We consider the homogenisation of a coupled Stokes flow and
advection-reaction-diffusion problem in a perforated domain with an evolving
microstructure of size $\varepsilon$. Reactions at the boundaries of the
microscopic interfaces lead to the formation of a solid layer having a
variable, a priori unknown thickness. This results in a growth or shrinkage of
the solid phase and, thus, the domain evolution is not known a priori but
induced by the advection-reaction-diffusion process. The achievements of this
work are the existence and uniqueness of a weak microscopic solution and the
rigorous derivation of an effective model for $\varepsilon \to 0$, based on
$\varepsilon$-uniform a priori estimates. As a result of the limit passage, the
processes on the macroscale are described by an advection-reaction-diffusion
problem coupled to Darcy's equation with effective coefficients (porosity,
diffusivity and permeability) depending on local cell problems. These local
problems are formulated on cells, which depend on the macroscopic position and
evolve in time. In particular, the evolution of these cells depends on the
macroscopic concentration. Thus, the cell problems (respectively the effective
coefficients) are coupled to the macroscopic unknowns and vice versa, leading
to a strongly coupled micro-macro model. For pure reactive-diffusive transport
coupled with microscopic domain evolution but without advective transport,
homogenisation results have recently been presented. We extend these models by
advective transport which is driven by the Stokes equation in the a priori
unknown evolving pore domain.
