Upscaling Evolving Microstructures and its Applications

Reactive flows are of great importance in porous media, bio-medical, and industrial applications. In a porous medium, solid grains (forming the solid matrix) are surrounded by void spaces (the pores) in which fluids or gases are flowing and transporting chemical species. The two groups at Bergen and Erlangen have been working on a variety of applications, which, however, have a common theme: The chemical species are possibly interacting with the grain boundaries, which may lead to non-negligible geometry changes. This forces the flow to create new pathways and affects the flow and transport characteristics of the medium. An extreme case, but quite common in practice, is the clogging of the flow channels. The proposed project aims at tackling the following challenges: 1. How to properly incorporate geometrical changes into the macroscale equations? In particular, how to obtain reliable macroscale models for convection dominated regimes? 2. What are the governing equations for the processes leading to clogging and what are the models post-clogging? In particular, how should one rigorously derive these models at least in the thin 2D channel? 3. How to access these coupled problems numerically? There is quite a variety of applications for such problems including subsurface processes including hydrocarbon extraction, ground water contamination, biomedical applications, carbon sequestration, concrete carbonation, and preservation of monuments etc. The scientific challenges cut through disciplines and several important questions from different points of view such as modelling, numerical simulations and mathematical analysis remain unaddressed. This project aims at starting a collaboration to address some of these challenges. A strong component of education and training for the PhD students is planned. Moreover, we will also exchange the educational material and course descriptions at the two institutions.