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.