Rayleigh scattering of acoustic waves in rigid porous media

This paper describes the long wave scattering effect in gas saturated porous media using the homogenization method. To investigate the deviation from the continuum description, the multiscale asymptotic expansions are developed up to the third order. The leading (zeroth) order leads to the Biot-Allard continuum description. The correction of first order induces nonlocal terms in the dynamic Darcy law and thermal behavior, without modifying the wave characteristics. The correction of second order introduces additional dispersion effects on the velocity and attenuation. This theoretical approach is illustrated by analytical results in the simple case of a periodic array of slits.