Inertial effects on tortuosity in porous media flows*

Porous media are ubiquitous and play a crucial role in various fields, such as the extraction industry and medical applications. The transport of mass and energy through these complex and multiscale materials primarily occurs at the pore level, characterized by interconnected and tortuous structures. Tortuosity is often treated as the third pillar of porous media description, next to porosity and permeability. This parameter quantifies the elongation of transport paths in phenomena like fluid flow, diffusion, and electric current transport. When considering fluid dynamics within porous media, researchers typically assume a slow-creeping regime. However, there are situations where the flow is faster, introducing deviations from basic linear models and subsequently influencing tortuosity.

Here, we present our latest observations on tortuosity in a three-dimensional porous media model under relatively high Reynolds numbers (Re). We aimed to examine tortuosity during the transition from the Darcy to the non-Darcy (inertial) regime. Unexpectedly, we found that tortuosity does not follow a natural monotonous decrease with increasing flux. To shed light on this, we first provide an overview of the method and algorithm employed to compute tortuosity. We then attempt to understand the physical flow mechanisms causing this observed ambiguity. In analyzing our findings, we highlight the significance of inertial effects and the kinetic energy confinement within the vortices emerging in the flow.