Failure of the Conventional Expression of Tortuosity in Granular Porous Solids

The tortuosity of porous solids has been widely used as a basic concept in understanding the fluid flow capacity of these media. Starting from a geometric expression of the tortuosity, different relationships have been developed over time to estimate it from different perspectives as hydraulic, electrical, and molecular diffusion, making necessary an exhaustive analysis of these developments. In this study, evidences for the lack of the true hydrodynamic sense of the conventional expression of tortuosity are shown. As a first sign of its failures, the disparity of results between the different relationships of tortuosity-porosity derived from this conventional expression is shown. Next, the presentation of several examples directly shows that the value obtained with that conventional expression is the same in cases where the actual tortuosity is obviously different. Likewise, a routine physical analysis of the flow in this study shows that the use of the capillary analogue is erroneous for one-dimensional flow analyses. Another inconsistency has been encountered in the widely used equality between the volumetric porosity and the product of free cross-sectional area by the length representing the path of the fluid through the pores. The last key showing the deficiencies of these estimations of the tortuosity is the constraint of the use of constant section ducts in the electrical analogy. As a new expression of tortuosity, an alternative ratio is proposed which can be included in known hydraulic and electrical relationships, in the same way than the conventional tortuosity. This tortuosity ratio constitutes a rethinking of the knowledge and understanding of flow in granular porous media.