Tortuosity of unsaturated porous fractal materials

The tortuosity of a capillary-condensed film of inviscid fluid adsorbed onto fractal substrates as a function of the filling fraction of the fluid has been calculated numerically. This acts as a way of probing the multiscale structure of the objects. It is found that the variation of tortuosity alpha with filling fraction phi is found to follow a power law of the form alpha similar to phi(-epsilon) for both deterministic and stochastic fractals. These numerically calculated exponents are compared to exponents obtained from a phenomenological scaling and good agreement is found, particularly for the stochastic fractals.