A time-domain model of transient acoustic wave propagation in double-layered porous media

Z E A Fellah,C Depollier,A Wirgin,M Fellah,N Sebaa,W Lauriks

doi:10.1121/1.1953247

Abstract

This paper concerns a time-domain model of transient wave propagation in double-layered porous materials. An analytical derivation of reflection and transmission scattering operators is given in the time domain. These scattering kernels are the medium’s responses to an incident acoustic pulse. The expressions obtained take into account the multiple reflections occurring at the interfaces of the double-layered material. The double-layered porous media consist of two slabs of homogeneous isotropic porous materials with a rigid frame. Each porous slab is described by a temporal equivalent fluid model, in which the acoustic wave propagates only in the fluid saturating the material. In this model, the inertial effects are described by the tortuosity; the viscous and thermal losses of the medium are described by two susceptibility kernels which depend on the viscous and thermal characteristic lengths. Experimental and numerical results are given for waves transmitted and reflected by double-layered porous media formed by air-saturated plastic foam samples.

Highlights

The ultrasonic characterization of porous materials saturated by air1,2 is of great interest for a large class of industrial applications
Ultrasonic characterization of materials is often achieved by measuring the attenuation coefficient and phase velocity in the frequency domain,3,4 or by solving the direct and inverse problems directly in the time domain
Measurements of the attenuation coefficient may be more robust than measurements of phase velocity

Summary

INTRODUCTION

The ultrasonic characterization of porous materials saturated by air is of great interest for a large class of industrial applications. The application of the Kramers–Kronig dispersion relations may allow the determination of the phase velocity from the measured attenuation coefficient Many applications, such as medical imaging or inverse scattering, require a study of the behavior of pulses traveling into porous media.. An understanding of the interaction of ultrasound with a porous medium in both the time and frequency domains, and the ability to determine the change of waveform when propagating ultrasound pulses, should be useful in designing array transducers and in quantitative ultrasound tissue characterization.. An understanding of the interaction of ultrasound with a porous medium in both the time and frequency domains, and the ability to determine the change of waveform when propagating ultrasound pulses, should be useful in designing array transducers and in quantitative ultrasound tissue characterization.18,19 This time-domain model is an alternative to the classical frequency-domain approach.. V, experimental validation using ultrasonic measurement in transmission and reflection is discussed for air-saturated industrial plastic foams

TEMPORAL EQUIVALENT FLUID MODEL

FORMULATING THE PROBLEM

REFLECTION AND TRANSMISSION SCATTERING OPERATORS

EXPERIMENTAL VALIDATION

CONCLUSION