Nonlocal Maxwellian theory of sound propagation in fluid-saturated rigid-framed porous media

•We propose a macroscopic nonlocal theory of sound propagation in rigid-framed porous media saturated with a viscothermal fluid.•This theory takes not only temporal dispersion into account, but also spatial dispersion.•An alternative procedure for homogenization is expressed, taking advantage of an acoustics–electromagnetics analogy.•No explicit scale separation of type asymptotic approach is required to perform the upscaling procedure.

Following a deep electromagnetic–acoustic analogy and making use of an overlooked thermodynamic concept of acoustic part of the energy current density, which respectively shed light on the limitations of the near-equilibrium fluid-mechanics equations and the still elusive thermodynamics of electromagnetic fields in matter, we develop a new nonperturbative theory of longitudinal macroscopic acoustic wave propagation allowing for both temporal and spatial dispersion. In this manner, a definitive answer is supplied to the long-standing theoretical question of how the microgeometries of fluid-saturated rigid-framed porous materials determine the macroscopic acoustic properties of the latters, within Navier–Stokes–Fourier linear physics.