InterPore2025

On the relation between the streamline- and volume-integrated tortuosity

22 May 2025, 12:35

15m

Oral Presentation (MS21) Non-linear effects in flow and transport through porous media MS21

Speaker

Dawid Strzelczyk

Description

Tortuosity is one of the fundamental effective parameters describing hydrodynamic properties of porous media. However, the fact it can be defined in several different ways, e.g. via the length of the streamlines [1] or as a statistic of the pore-scale velocity field [2], may cause inconsistency between the results. For example, the equivalence between the weighted streamline-based tortuosity and easier to calculate volume-integrated tortuosity was analytically proven by Duda and others [2] for Stokes flows, with the latter being larger then the former when inertial effects show up. In the present work we study the sources of this inequality. In particular, we investigate the contributions to the tortuosity from the recirculation zones and the percolating part of the flow separately. We do so in terms of the volume of the recirculation zones and the kinetic energy/momentum contained therein, as well as the viscous momentum transfer from the percolating to the recirculation zones. We relate the changes of those quantities to the known regimes of inertial flows [3]. Our results explain the observations on the deviation from each other of the values of variously defined tortuosities, presented in previous works. They deepen the understanding of the pore-scale mechanisms of the onset of inertial effects in porous media and can serve as the theoretical baseline for the formulation of reduced models of inertial transport therein.

The picture shows the percolating volume of the flow through a periodic array of spheres for low (left) and high (right) Reynolds number. The flow is driven by a body force aligned with the x-direction.