Rigorous upscaling of rough boundaries for reactive flows

We consider a mathematical model for reactive flow in a channel having a rough (periodically oscillating) boundary with both period and amplitude e. The ions are being transported by the convection and diffusion processes. These ions can react at the rough boundaries and get attached to form the crystal (precipitation) and become immobile. The reverse process of dissolution is also possible. The model involves non-linear and multi-valued rates and is posed in a fixed geometry with rough boundaries. We provide a rigorous justification for the upscaling process in which we define an upscaled problem defined in a simpler domain with flat boundaries. To this aim, we use periodic unfolding techniques combined with translation estimates. Numerical experiments confirm the theoretical predictions and illustrate a practical application of this upscaling process. Keywords: Reactive flows; rough boundaries; homogenization.