Hydraulic tortuosity in arbitrary porous media flow

TL;DR

This paper introduces a new method to calculate hydraulic tortuosity directly from fluid velocity fields, simplifying analysis in complex porous media and revealing specific relationships with porosity and percolation properties.

Contribution

It proposes an alternative, streamline-independent method for calculating tortuosity from velocity data, applicable to complex geometries and experimental data.

Findings

Tortuosity in fibrous media follows T = 1 + p√(1-φ).

The divergence exponent of T relates to percolation scaling.

The method simplifies tortuosity measurement in complex systems.

Abstract

Tortuosity ($T$) is a parameter describing an average elongation of fluid streamlines in a porous medium as compared to free flow. In this paper several methods of calculating this quantity from lengths of individual streamlines are compared and their weak and strong features are discussed. An alternative method is proposed, which enables one to calculate $T$ directly from the fluid velocity field, without the need of determining streamlines, which greatly simplifies determination of tortuosity in complex geometries, including those found in experiments or 3D computer models. Numerical results obtained with this method suggest that (a) the hydraulic tortuosity of an isotropic fibrous medium takes on the form $T = 1 + p\sqrt{1-\phi}$, where $\phi$ is the porosity and $p$ is a constant and (b) the exponent controlling the divergence of $T$ with the system size at percolation threshold is related to an exponent describing the scaling of the most probable traveling length at bond percolation.