Anomalous and effective transport models in heterogeneous systems

Many real-world engineering, geological, and biological applications involve the motion of (fluid or solid) particles through heterogeneous environments. This includes porous media flows such as the ones present in filtration, osmosis, catalysis, subsurface reservoirs, or other transport phenomena in stochastic (e.g., turbulent) flows or heterogeneous (e.g. composite) materials. Even under strongly simplifying assumptions, that allows a full analytical or numerical description, anomalous and complex emerging transport phenomena can arise. We will show, for example, how a simple model describing the motion of Brownian particles in steady random flow fields or porous media have to be described with non-standard non-Fickian dispersion models (based on Continuous Time Random Walks) to describe accurately the transport characteristics such as arrival time distributions. When also reactions are present, other closure (mixing) problems arise. Here we will present a PDE model based on homogenisation to compute effective reaction and transport model for particle filtration, adsorption or shear-induced breakage.