Asymptotic limits of some models for sound propagation in porous media and the assignment of the pore characteristic lengths.

Kirill V Horoshenkov,Jean-Philippe Groby,Olivier Dazel

doi:10.1121/1.4947540

Abstract

Modeling of sound propagation in porous media requires the knowledge of several intrinsic material parameters, some of which are difficult or impossible to measure directly, particularly in the case of a porous medium which is composed of pores with a wide range of scales and random interconnections. Four particular parameters which are rarely measured non-acoustically, but used extensively in a number of acoustical models, are the viscous and thermal characteristic lengths, thermal permeability, and Pride parameter. The main purpose of this work is to show how these parameters relate to the pore size distribution which is a routine characteristic measured non-acoustically. This is achieved through the analysis of the asymptotic behavior of four analytical models which have been developed previously to predict the dynamic density and/or compressibility of the equivalent fluid in a porous medium. In this work the models proposed by Johnson, Koplik, and Dashn [J. Fluid Mech. 176, 379-402 (1987)], Champoux and Allard [J. Appl. Phys. 70(4), 1975-1979 (1991)], Pride, Morgan, and Gangi [Phys. Rev. B 47, 4964-4978 (1993)], and Horoshenkov, Attenborough, and Chandler-Wilde [J. Acoust. Soc. Am. 104, 1198-1209 (1998)] are compared. The findings are then used to compare the behavior of the complex dynamic density and compressibility of the fluid in a material pore with uniform and variable cross-sections.

Highlights

The ability to accurately predict sound propagation in porous media is essential for many areas of science and engineering
A majority of models which are used for these purposes are equivalent fluid models in which the fluid trapped in the material pores is typically presented as a homogeneous, equivalent fluid with complex, frequency dependent acoustic characteristic impedance, zðxÞ, and complex wavenumber, kðxÞ
It is worth noting that the expression of the dynamic density we present in this paper [Eq (3)] is given for the bulk medium; it is normalized by the medium porosity /

Summary

Introduction

The ability to accurately predict sound propagation in porous media is essential for many areas of science and engineering. Typical examples include non-invasive inspection of porous bones, outdoor sound propagation in presence of porous ground, underwater sound propagation in the presence of porous sediments, and noise control. A majority of models which are used for these purposes are equivalent fluid models in which the fluid trapped in the material pores is typically presented as a homogeneous, equivalent fluid with complex, frequency dependent acoustic characteristic impedance, zðxÞ, and complex wavenumber, kðxÞ. The value of the characteristic impedance and the boundary conditions surrounding the porous layer determine the ability of sound waves to penetrate this layer. The value of the complex wavenumber relates to the speed of the sound wave in the porous space and the rate at which it attenuates

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Conclusion