Upscaling of coupled processes with evolving interfaces

Porous media have highly oscillatory characteristics, with rapid pore-scale changes between the solid matrix and the fluid-filled void space. The pore-scale characteristics affect the fluid flow and transport through the porous domain, but one is generally interested in the average (Darcy-scale) behavior of these processes. Hence, upscaling is important to connect the pore scale with the Darcy scale, deriving effective quantities allowing simulations on the Darcy scale. This is particularly important when evolving interfaces are present; that is, either a solid-fluid interface due to a chemical reaction or a fluid-fluid interface due to the void space being filled by two immiscible fluids. Then the pore-scale characteristics change dynamically with time, and the effective quantities depend on time.