Lauriks, Walter

An acoustical transmission method is proposed for measuring permeability of porous materials having rigid frame. Permeability is one of the several parameters required by acoustical theory to characterize porous materials such as plastic foams and fibrous or granular materials. The proposed method is based on a temporal model of the direct and inverse scattering problem for the diffusion of transient low frequency waves in a homogeneous isotropic slab of porous material having a rigid frame. This time domain model of wave propagation was initially introduced by the authors [Z.E.A Fellah and C. Depollier, J. Acoust. Soc. Am. 107, 683 (2000)]. The viscous losses of the medium are described by the model devised by Johnson et al. [J. Fluid. Mech. 176, 379 (1987)]. Reflection and transmission scattering operators for a slab of porous material are derived from the responses of the medium to an incident acoustic pulse. The permeability is determined from the expressions of these operators. Experimental and numerical validation results of this method are presented. This method has the advantage of being simple, rapid, and efficient.

This paper provides a temporal model of the direct scattering problem for the propagation of transient low frequency waves in a homogeneous isotropic slab of porous material having a rigid frame. In this model, the inertial effects are described by the low frequency approximation of the tortuosity. The viscous and thermal losses of the medium are modeled by viscous and thermal permeabilities. The propagation equation is derived and solved analytically in the time domain. An original expression of Green’s function of the porous medium is obtained. The transmission scattering operator of the first transmitted wave is calculated and compared with experimental data.

This paper concerns the ultrasonic characterization of human cancellous bone samples by solving the inverse problem using experimental transmitted signals. The ultrasonic propagation in cancellous bone is modeled using the Biot theory modified by the Johnson et al. model for viscous exchange between fluid and structure. The sensitivity of the Young modulus and the Poisson ratio of the skeletal frame is studied showing their effect on the fast and slow wave forms. The inverse problem is solved numerically by the least squares method. Five parameters are inverted: the porosity, tortuosity, viscous characteristic length, Young modulus, and Poisson ratio of the skeletal frame. The minimization of the discrepancy between experiment and theory is made in the time domain. The inverse problem is shown to be well posed, and its solution to be unique. Experimental results for slow and fast waves transmitted through human cancellous bone samples are given and compared with theoretical predictions.