What about using the fractal dimension (box-counting) as a measure? Here is a paper on tortuosity.

Article Transport Properties of Saturated and Unsaturated Porous Fra...

Regards,

Joachim

I was working on a team to clean up a huge toxic mess in fractured media (a karst formation). We were unable to directly measure tortuosity; however, I adapted an existing model to handle tortuosity, then validated it against an analytical solution, then adjusted the tortuosity until the model agreed with the measured data that we were able to collect. The result was sufficiently accurate and the remediation was successful. Here is one of the animations I created during the validation phase: http://dudleybenton.altervista.org/projects/Fractures/2DF2_R.gif

Determining the tortuosity factor in a porous material can be challenging, and it often requires more advanced techniques such as image analysis or computational modeling. However, some simplified mathematical formulas can provide an estimation of the tortuosity factor in certain cases.

One common approach is to use the porosity (ϕ) and the permeability (k) of the porous material to calculate an approximate tortuosity factor (τ). The formula is as follows:

τ ≈ (ϕ^2) / (1 - ϕ) * (k / k0)

Where:

• ϕ is the porosity of the material, which represents the ratio of the void space (pores) to the total volume of the material.
• k is the permeability of the material, which describes how easily fluids can flow through the porous structure.
• k0 is a reference permeability value, often taken as the permeability of a fully saturated material or a reference material.

It's important to note that this formula provides an approximation of the tortuosity factor and assumes certain simplifications. It assumes a relationship between porosity, permeability, and tortuosity, which may not hold in all porous materials or for complex pore structures.

For more accurate determinations of tortuosity, techniques such as micro-computed tomography (micro-CT) imaging or numerical simulations using computational fluid dynamics (CFD) models can be employed. These methods provide a more detailed and precise characterization of the pore structure and fluid flow patterns, allowing for more accurate calculations of tortuosity.

If you are working with a specific porous material, it's recommended to consult relevant literature or seek guidance from experts in the field who have experience with characterizing tortuosity in similar materials.

Hello Dr.Ma'Mon Abu Hammad

Thank you for answer.Your recomended in use of CFD is best. I need to learn this software. I hope it solves my problem.