Abstract

This paper introduces a general theoretical framework for the modeling of long-wavelength acoustic wave prop agation in multiscale rigid-frame permeable sorptive metamaterials. This class of materials results from the combination of multiscale sorptive porous materials, which possess characteristic sizes ranging from nanometres up to millimetres, a mesopore fluid network, and local acoustic resonators. The two-scale asymptotic homogeni sation method is used to establish the macroscopic equations that describe sound propagation through the investigated class of materials. The upscaling process unveils the key role of internal mass sources, activated by pressure, on the macroscopic mass balance, while the macroscopic fluid flow constitutive law remains classi cal. Phenomena such as inner acoustic resonances, multiple types of diffusion, visco-thermal dissipation across scales, and sorption at the nanoscale, are shown to determine the atypical effective compressibility of the fluid equivalent to the metamaterial. The dynamic permeability behaves classically, however, and is determined by the most permeable local constituent. We develop an analytical model for a material with a specific microstructure and successfully validate it against numerical pore-scale simulations and experimental data from a prototype sample whose key building-block elements are granular activated carbon and 3D-printed acoustic resonators. This work paves the way for the bottom-up design of materials that can exploit multiphysics and multiscale phenomena for acoustic wave control applications.