The number of "acoustical" parameters used in models to
predict the fluid phase behavior can vary from 1 to 8.
Three of these parameters: the static air flow resistivity, the open
porosity and the high frequency limit of the dynamic tortuosity can be
directly measured while characterization techniques are used to
estimate the others.
Schematic representation of the growing complexity of motionless skeleton models regarding the microstructure of the porous materials.
The tables reported below present, for a large number of models, the parameters they require to describe the visco-thermal dissipation effects when sound waves propagate through a porous medium.
Delany-Bazley model
This empirical model based on measurements results for fibrous materials should not be used without corrections proposed by Miki (see Delany-Bazley-Miki model below).
| Parameter(s) | Usual notation |
|---|---|
| Static air flow resistivity | $\sigma$ |
Delany-Bazley-Miki model
This empirical model may be used to described fibrous material behaviors.
| Parameter(s) | Usual notation |
|---|---|
| Static air flow resistivity | $\sigma$ |
Miki model
| Parameter(s) | Usual notation |
|---|---|
| Static air flow resistivity | $\sigma$ |
| Open porosity | $\phi$ |
| High frequency limit of the tortuosity | $\alpha_{\infty}$ |
| Parameter(s) | Usual notation |
|---|---|
| Static air flow resistivity | $\sigma$ |
| Open porosity | $\phi$ |
| High frequency limit of the tortuosity | $\alpha_{\infty}$ |
| Viscous characteristic length | $\Lambda$ |
| Thermal characteristic length | $\Lambda'$ |
Johnson-Champoux-Allard-Lafarge
This semi-phenomenological model may be used to described the dissipation behavior of materials with arbitrary pore shapes without important pore section variations.
| Parameter(s) | Usual notation |
|---|---|
| Static air flow resistivity | $\sigma$ |
| Open porosity | $\phi$ |
| High frequency limit of the tortuosity | $\alpha_{\infty}$ |
| Viscous characteristic length | $\Lambda$ |
| Thermal characteristic length | $\Lambda'$ |
| Static thermal permeability | $k'_{0}$ |
Johnson-Champoux-Allard-Pride-Lafarge
This semi-phenomenological model may be used to described the dissipation behavior of materials with arbitrary pore shapes and important pore section variations.
| Parameter(s) | Usual notation |
|---|---|
| Static air flow resistivity | $\sigma$ |
| Open porosity | $\phi$ |
| High frequency limit of the tortuosity | $\alpha_{\infty}$ |
| Viscous characteristic length | $\Lambda$ |
| Thermal characteristic length | $\Lambda'$ |
| Static thermal permeability | $k'_{0}$ |
| p | $p$ |
| p' | $p'$ |
Wilson model
This semi-phenomenological model may be used to described the dissipation behavior of fibrous materials or materials with arbitrary pore shapes with or without important pore section variations.
| Parameter(s) | Usual notation |
|---|---|
| High frequency limit of the dynamic density | $\rho_{\infty}$ |
| Vorticity-mode relaxation time | $\tau_{\textrm{vor}}$ |
| High frequency limit of the bulk modulus | $K_{\infty}$ |
| Entropy-mode relaxation time | $\tau_{\textrm{ent}}$ |
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