Relaxation-matched modeling of propagation through porous media, including fractal pore structure

The viscous and thermal dissipation of an acoustic wave propagating through a porous medium is shown to be characteristic of a relaxation process. Based on this interpretation, a new model for the complex density (dynamic permeability) and bulk modulus, which describe the viscous and thermal processes, respectively, is proposed. The model is based on approximating the relaxational characteristic, as opposed to previous models based on matching low- and high-frequency asymptotic behavior. An advantage of the relaxation model is that one fewer parameter is required. The relaxation model is also simpler than the commonly used Zwikker/Kosten/Attenborough or Biot/Allard models, in the sense that it contains no Bessel or Kelvin functions, and is not a modified form of the solution for uniform, circular pores. And unlike the Delany/Bazley empirical equations, the relaxation model is physically realistic for all frequencies. Extension of the relaxation model to fractal pore surfaces is also discussed.