Tortuosity of Flow Paths through a Sierpinski Carpet

Sierpinski carpet is an exactly self-similar fractal, which is often used to simulate fractal porous media. A simple recursive model for the tortuosity of flow path in Sierpinski carpet is derived based on the self-similarity of the carpet. The proposed model is related to the stage of the carpet, and there is no empirical constant in this model. The model predictions are compared with those from available correlations by both numerical and experimental methods as well as analysis. Good agreement is found between the present model predictions and those from the available correlations. The present model may have the potential in analysis of transport properties in self-similar fractals.