Dynamic permeability of fractal porous media

This work is devoted to theoretical and experimental studies of acoustic waves in air-saturated fractal porous media. The theoretical model of oscillatory flow through a porous medium is based on the concept of a fractal continuum in a non-integer dimensional space. This model allows us to obtain analytical solutions for the velocity field and frequency-dependent permeability. Accordingly, static and dynamic permeability are expressed as functions of fractal dimension numbers and characteristic length scales. To validate theoretical findings, we conducted two independent acoustic experiments with polyurethane open-cell foams having a fractal pore structure. High-frequency ultrasound measurements (in the range of tens to hundreds of kHz) were used to evaluate the fractal properties of the studied foams. The fractal parameters were determined by fitting the signals transmitted from the foam to theoretical output signals. These parameters were then used to predict the static permeability k0. We found that the predicted values of k0 are in good agreement with the experimental values obtained in low-frequency long acoustic waveguide (a few hundred Hz range) experiments. Thus, this work provides a robust and physically meaningful framework for describing acoustic wave propagation in fractal porous materials.