Acoustic waves in gas-filled structured porous media: Asymptotic tortuosity/compliability and characteristic-lengths reevaluated to incorporate the influence of spatial dispersion

This study extends efforts to incorporate spatial dispersion into Biot-Allard’s theory, with a focus on poroelastic media with intricate microgeometries where spatial dispersion effects play a significant role. While preserving Biot’s small-scale quasi-“en-bloc” frame motion to keep the structure of Biot-Allard’s theory intact, the paper challenges Biot’s quasi-incompressibility of fluid motion at that scale by introducing structurations in the form of Helmholtz’s resonators. Consequently, Biot-Allard’s theory undergoes a significant augmentation, marked by the arising of non-local dynamic tortuosity and compliability, which are associated with potentially resonant fluid behavior. Building on an acoustic-electromagnetic analogy, the study defines these non-local responses and suggests simplifying them into pseudo-local ones, now potentially resonant and reminiscent of Veselago-type phenomena. In the high-frequency limit of small boundary layers and as an extension of the classical Johnson-Allard’s findings, simple field-averaged formulas are demonstrated for pseudo-local ideal-fluid tortuosity and compliability (complex frequency-dependent) and viscous and thermal characteristic lengths (positive frequency-dependent). These formulations are grounded in the Umov-Heaviside-Poynting thermodynamic macroscopic acoustic stress concept, suggested by the analogy. Future computational investigations, spanning various fundamental microgeometries, are planned to assess assumed pseudo-local simplifications, encompass low- and intermediate frequencies, and unveil potential behavioral outcomes resulting from the incorporation of spatial dispersion effects.