Acoustics of permeable heterogeneous materials with local non-equilibrium pressure states

The key idea developed in this work is the enforcement of local non-equilibrium pressure states in permeable materials by means of introducing geometrical and/or material heterogeneities. The two-scale asymptotic method of homogenisation is used to derive the macroscopic equations that describe sound propagation in the investigated class of materials. This allowed us to conclude that, at the leading order, the macroscopic fluid flow is mostly determined by that occurring in the most permeable fluid network. In contrast, the effective compressibility of the saturating fluid is modified by the non-equilibrium pressure states occurring in the different much less permeable local heterogeneities of the materials. The theory is exemplified by introducing an analytical model for the acoustical properties of a perforated microporous matrix with cylindrical microporous inclusions co-axially inserted in the perforations. The experimental validation of the theory is also provided.