Transport Properties of Saturated and Unsaturated Porous Fractal Materials

Inviscid, irrotational flow through fractal porous materials is studied. The key parameter is the variation of tortuosity with the filling fraction φ of fluid in the porous material. Altering the filling fraction provides a way of probing the effect of the fractal structure over all its length scales. The variation of tortuosity with φ is found to follow a power law of the form α~φ^-ϵ for deterministic and stochastic fractals in two and three dimensions. A phenomenological argument for the scaling of tortuosity α with filling fraction φ is presented and is given by α~φ^Dw-2/Df-dE, where Df is the fractal dimension, Dw is the random walk dimension, and dE is the Euclidean dimension. Numerically calculated values of the exponents show good agreement with those predicted from the phenomenological argument for both the saturated and the unsaturated model.