Acoustical determination of the parameters governing viscous dissipation in porous media

Analytical solutions are derived to extract from dynamic density the macroscopic parameters governing viscous dissipation of sound waves in open-cell porous media. While dynamic density is obtained from acoustical techniques, the analytical solutions are derived from the model describing this dynamic density. Here, semiphenomenological models by Johnson et al. and by Wilson are investigated. Assuming dynamic density, open porosity, and static airflow resistivity known, analytical solutions derived from the Johnson et al. model yield geometrical tortuosity and viscous characteristic dimension. For the Wilson model, only dynamic density needs to be known. In this case, analytical solutions yield—for the first time—Wilson's density parameter and vorticity-mode relaxation time. To alleviate constraints on the Johnson et al. model, an extrapolation approach is proposed to avoid prior knowledge of static resistivity. This approach may also be used to determine this latter parameter. The characterization methods are tested on three materials covering a wide range of static airflow resistivities (2300–150100Ns∕m4), frame rigidities (soft and rigid), and pore geometries (cells and fibers). It is shown that the analytical solutions can be used to assess the validity of the descriptive models for a given material.