Measuring flow resistivity of porous material via acoustic reflected waves

Abstract

An acoustic reflectivity method is proposed for measuring flow resistivity of porous materials having rigid frame. The flow resistivity of porous material is defined as the ratio between the pressure difference across a sample and the velocity of flow of air through that sample per unit cube. It is important as one of the several parameters required by acoustical theory to characterize porous materials like 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 [D. L. Johnson, J. Koplik, and R. Dashen, 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 flow resistivity is determined from the expression of the reflection operator. Experimental and numerical validation results of this method are presented. A guide (pipe) is used in the experiment for obtaining a plane wave. This method has the advantage of being simple, rapid, and efficient. © 2005 American Institute of Physics.