Dynamic permeability and tortuosity of a porous material saturated by a Maxwell fluid

This study derives the asymptotic behavior of dynamic tortuosity for arbitrary pore geometries filled with non-Newtonian fluid in both high- and low-frequency regimens. This derivation leads to the formulation of a general model of dynamic tortuosity through the use of a simple transition function. The analytical model can be applied to complex shapes of pores filled with a non-Newtonian fluids, which so far not has been reported in the literature. Applied to the porelastic Biot theory, the model predicts the influence of non-Newtonian fluids on the modal dispersion of the dilatational waves. This integration provides insights into wave dynamics within the most general context of porous materials with complex pore geometries, offering a robust theoretical foundation for various practical applications.