Rigorous upscaling of rough boundaries for reactive flows

We consider a mathematical model for reactive ¿ow 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. We provide a rigorous justi¿cation for the upscaling process in which we de¿ne an upscaled problem de¿ned in a simpler domain with ¿at boundaries. To this aim, we use periodic unfolding techniques combined with translation estimates. Numerical experiments con¿rm the theoretical predictions and illustrate a practical application of this upscaling process.