Numerical approximation to the scaling law describing the geometrical tortuosity in porous media

Abstract

When studying porous media transport properties, it is crucial to ascertain tortuosity (τ) and its variation with porosity (𝜙𝜙). In this work, numerical methods were used to investigate this relationship. First, a digital representation of media was derived, and thereby implement an algorithm for calculating tortuosity. The program allows deriving several statistics of the paths present within the pores. The results complement the theoretical studies that suggest the existence of a scaling law in disordered media. However, this paper proposes that the relationship between τ and 𝜙𝜙 depends on the average fractal dimension instead of the fractal dimensionality of the optimal path. It was also confirmed that the geometry of the latter can be considered in the same universality class as those described by loopless compressible invasion percolation

Keywords

• tortuosity
• porous media
• percolation
• numeric simulation
• scaling law
• fractal dimension