Intrinsic permeability of porous systems: models and microfludiic experiments for heterogeneous structures

Understanding the relationship between flow (Q) and pressure drop (ΔP) for porous media is a long-standing challenge affecting a wide variety of environmental, societal and industrial issues, from soil remediation to enhanced oil recovery. While for homogeneous media such dependence is well represented by the Kozeny-Carman formula,  the fundamental nature of such a relationship (Q vs ΔP) within heterogeneous systems, characterized by a broad range of pore sizes, is still not understood. We design a set of controlled and complex porous structures that we use to conduct microfluidics experiments to measure their intrinsic permeability. We synthesize the results upon deriving an analytical formulation relating the overall intrinsic permeability and key features of the porous structure. We propose to embed the spatial variability of pore sizes into the medium permeability by upscaling the flow through each pore, via the Hagen Poiseuille Law. Our prediction fits well the collected data, highlighting the role played by the micro-structure on the overall medium permeability. Furthermore, beside the theoretical understanding of this important relationship, we also extend our set-up to novel experiments focusing on the paradigmatic case study of biofilm growth that affects the system permeability by obstructing the pore spaces.