Influence of dynamic tortuosity and compressibility on the propagation of transient waves in porous media

This paper provides an analytical solution in the time domain for the propagation of transient ultrasonic waves in a homogeneous, isotropic porous material with a rigid frame. The originality of this propagation equation is the use of the Pride et al. and Lafarge models, which give a better description of acoustic wave attenuation. Two parameters, p and p', are added to the description of losses in the porous material, given a modification of coefficients of the propagation equation in the time domain. The analytical solution to the wave equation has a different form as compared with that obtained from the Johnson-Allard model. This wave equation contains fractional derivative terms describing attenuation and dispersion in porous material. The Laplace transform method is used to solve the propagation equation. An experimental application to porous plastic foam is given to validate the mathematical solution to the propagation equation. One important result of this work is that the introduction of the two parameters p and p' corrects the Johnson-Allard model by increasing attenuation with no change in dispersion. This phenomenon is much more significant for resistive porous materials. (C) 2004 Elsevier B.V. All rights reserved.