A homogenised model for flow, transport and sorption in a heterogeneous porous medium

A major challenge in flow through porous media is to better understand the link between microstructure and macroscale transport. For idealised microstructures, mathematical framework of homogenisation theory can be used for this purpose. Here, we consider a two-dimensional comprising an array obstacles smooth but arbitrary shape, size spacing which vary along length medium. We use via method multiple scales systematically upscale novel problem involving cells varying area obtain effective continuum equations The are characterised by local porosity, anisotropic permeability, solute diffusivity adsorption rate. These properties depend non-trivially on two degrees microstructural geometric freedom our problem: obstacle spacing. exploit dependence construct compare scenarios where same porosity profile results from different combinations focus simple example geometry circular rectangular lattice, numerically determine permeability diffusivity. investigate spatially uniform not. Our may useful design filters or studying impact deformation transport soft media.