The Compute Tortuosity GeoApp uses different approaches, as described in Holzer et al., 2023, to calculate the tortuosity of the pore space in a chosen computation direction. Additionally, a geometric analysis can be performed and effective transport properties on the macroscale can be predicted based on Holzer et al., 2013.
Modules needed to run this GeoApp (depending on the selected options):
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Generally, three different kinds of tortuosity can be computed:
Geometric Tortuosity, which is directly derived from the microstructure,
Physical Tortuosity or physics-based tortuosity, which is indirectly derived by transport mechanisms,
Mixed Tortuosity, which uses a mixture of determinations based on geometric analysis and physical transportation phenomena.
Click Edit to open the Compute Tortuosity parameter dialog.
Select a Result File Name and the Computation Direction in the General Settings panel. Also, the Boundary ConditionsinComputation Direction and in Tangential Direction must be defined.
After activating Use Advanced Settings you can define the Parallelization, the Bin Sizes for Streamlines and Porosimetry & Granulometry, the In- / Outlet Length for Stokes Flow, and Dense Sampling of Streamlines.
In the Tortuosity Calculation panel, select the properties to be computed.
There are two options available for the Geometric Tortuosity. These tortuosity values are derived directly from the morphological characteristics of the analyzed structure and are defined solely by the structure.
The general definition of the Geometric Tortuosity is the comparison of the effective geometric path length to the shortest geometric path length :
(295) Geometric Tortuosity
The geometric tortuosity options are:
Geodesic Tortuosity in PoroDict: Computing the mean geodesic tortuosity from the percolation pathway starting from every voxel in the inlet, i.e., the shortest path in pore space is compared to the direct path.
Percolation Path Tortuosity in PoroDict: Computing the mean value of the percolation pathways with the 50 largest diameters, i.e., the length of the path of large particles (largest possible diameters) through the structure (median axis) is compared to the direct path.
There are four options available for the Physical Tortuosity. These tortuosities are indirectly derived and do not use the geometric path lengths:
(296)
Physical tortuosities are determined using effective properties to deduce a tortuosity value indirectly. Therefore, the effects of microstructure such as bottleneck effects are included. A physical tortuosity is only meaningful if it is based on a transport phenomenon that is relevant to the simulated material. Thus, different tortuosities can be determined depending on the dominating transport mechanism: diffusion of molecules or ions, conductivity of electrons, etc.
Consider, for example, the effective diffusion of gas through a porous membrane compared to the gas's self-diffusion. In this case, the diffusion tortuosity is of interest, as described in the DiffuDict user guide. GeoDict can output both, the value for the tortuosity and the value of the tortuosity factor by comparing the effective diffusion to self-diffusion:
(297)
where is the porosity and the relative diffusivity due to the porous-media dependent part of the effective diffusion. The numbers and can be converted in each other by the general relation between them:
(298)
The available physical tortuosities are:
Diffusional Tortuosity in DiffuDict: Diffusion as indirect, physical approach (see also Epstein, 1989). The tortuosity will be extracted from the DiffuDict Laplace or Knudsen Diffusion result files, respectively.
Conduction Tortuosity in ConductoDict: Electrical or Thermal conductivity as indirect, physical approach (see also Ullman et al., 1982). The tortuosity will be extracted from the respective ConductoDict result file.
There are five options available for the Mixed Tortuosity. The mixed tortuosities are derived from a mixed determination including the geometrical analysis of streamlines and pathways from simulations of diffusion, flow, advection, etc. The available mixed tortuosities are:
Tortuosity from Laplace Diffusion Flux in DiffuDict (see also Tye, 1983): The mean value of the DiffuDict Laplace diffusion flux streamlines and/or the tortuosity is calculated based on the volume average of the DiffuDict Laplace diffusion flux.
Tortuosity from Electrical Current Density and Thermal Heat Flux in ConductoDict: The mean value of the streamline length of the ConductoDict streamlines and/or the tortuosity is calculated based on the volume average of the electrical current density and thermal heat flux.
Tortuosity from Stokes Flow Velocity in FlowDict (see also Duda et al., 2011): The mean value of the streamline length of FlowDict Stokes flow velocity streamlines and/or the tortuosity is calculated based on the volume average of FlowDict Stokes flow velocity.
Tortuosity from Advection Particle Path Length in AddiDict: Computes the mean value of the particle path length for advection.
Tortuosity from Particle Diffusion Path Length in AddiDict: The mean value is calculated based on effective isotropic diffusivity.
In addition to the different tortuosities, the Compute Tortuosity GeoApp can calculate Microstructure characteristics. Three options are available:
Characteristic Diameters from Granulometry in PoroDict: Computing D10, D50, and D90.
Characteristic Diameters from Porosimetry in PoroDict: Computing D10, D50, and D90.
Surface Area in MatDict: Specific surface area between pore space and solid materials.
Results
Below the exemplary results for the following structure are shown.
The result file’s Result Viewer opens automatically when the Compute Tortuosity app finishes. The result file provides detailed information about the formulas used to calculate the different tortuosities, the microstructure characteristics, the pore phase and transport properties, as well as those used to predict effective transport properties.
Depending on the selection in the Compute Tortuosity parameter dialog, the respective results are given in tables. If the calculation of the tortuosity based on streamlines was selected, the evaluation of streamline length is shown as a Streamline Tortuosity plot.
Additionally, the corresponding result folder contains the detailed GeoDict results for all selected tortuosity computations.
Microstructure Characteristics
