The tortuosity of a porous material quantifies how straight or tortuous paths taken through the porous material are in average. A value of 1 means that all paths are straight, and higher values denote that paths are more tortuous. There have been several attempts to quantify this property, and each definition delivers (slightly) different results.

The tortuosity factor describes how strongly the diffusivity is reduced due to pore shape. The tortuosity factor in a particular direction (X, Y or Z) is defined through equation (194) . In this expression, the terms “diffusivity” and “tortuosity factor” should be understood as “diffusivity in X (Y or Z) direction” and “tortuosity factor in X (Y or Z) direction”. Diffusivities in X, Y and Z directions are the diagonal entries of the computed diffusivity tensor .

Following the notation of Epstein, the geometric tortuosity is the square root of the tortuosity factor .

Consider two structures with the same porosity of 50.01%. In one case, the pores are straight cylinders, and in the other, the pores are strongly curved, and have no preferred orientation. The structures are shown in 3D view and in a 2D cut, parallel to YZ-plane. Observe the effect of the shape and orientation of the pore space on the calculated diffusivity and tortuosity factor in Z-direction.

 

For the structure on the left (A), the relative diffusivity in Z-direction is very close to the porosity value (50.01%) and the tortuosity factor is close to the minimal possible value of 1.

For the structure on the right (B), where the pores are curved, the relative diffusivity in Z-direction is smaller (22.835%) for the same porosity value (50.01%) and the tortuosity factor is two times higher.