Acoustic non-local permittivities in rigid-framed porous metamaterials

What should be the most general macroscopic theory of sound propagation in a medium defined by a fluid in which rigid motionless solid inclusions are placed in periodic or stationary random manner? This, indeed, appears to be a very basic question of classical physics to which no complete answer has yet been provided. Based on considerations inspired by an apparently uncommon conception of the macroscopic electromagnetic theory, we suggest here what the general answer might be, in a special "slender fluid" case where the free-fluid bulk attenuation and the macroscopic fluid-solid shear reaction force are both neglected. In forthcoming work, our present conception of the macroscopic theories will be illustrated by the explicit construction of our two acoustical non-local "permittivities".