Tortuosity Model in Porous Media

Tortuosity is an important factor which affects water and solute transport in porous media. Although numerous methods have been developed to model tortuosity in unsaturated porous media based on specific immiscible fluid interfacial area, pore size, water content, as well as others, they are generally empirical and include unknown parameters. Perhaps the most physical definition of tortuosity T in the literature is as a ratio of an effective length to a straight line distance, making T>1. However, it is sometimes given as the inverse of this definition, therefore, its value would be less than 1. In this study, we use the first approach because it is completely compatible with the definition of the corresponding quantity in percolation theory. Our result, expressed for systems of variable saturation, is a power function of water content and the critical water content, and all model parameters e.g., fractal dimension of the shortest path, have physical meaning. The results can also be combined with percolation scaling results for the hydraulic or electrical conductivity to make an inference regarding the appropriate form to represent connectivity as a function of water content.