Sound Propagation in Complex/Porous Materials

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*Acoustics of Materials*

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Chapter 4

Abstract

1. Introduction

plastic foams.

61

Tortuosity Perturbations Induced

In this chapter, we describe the effects of defects in a homogeneous saturated porous medium. Defects are modelized by inclusions which disturb the motion of the viscous fluid flowing in the pore space of the medium. The seepage rate of the fluid in the host medium and in the inclusion is given by the Darcy's law. Disturbances thus produced modify the shape of the stream lines from which we establish the tortuosity induced by the defects and its implications on the acoustic waves

Among the essential physical parameters to describe the microstructure of porous media, tortuosity is one of the most important parameters. For a review, we

> <sup>v</sup> ¼ � <sup>k</sup> η

is the pressure gradient applied to the medium, and k is its permeability. The Kozeny's model was developed in the framework of straight and parallel streamlines in porous media. Carman has generalized it to neither straight nor parallel stream-

<sup>τ</sup> <sup>¼</sup> <sup>&</sup>lt;λ<sup>&</sup>gt;

When a fluid flows through a porous medium from point A to point B distant from L (Euclidean distance) (Figure 1), it follows different paths whose mean length is < λ>, where λ is the length of the different paths connecting these two points. In isotropic media, the tortuosity is a scalar number greater than unit (<λ> ≥L), whereas for the low porous media, its values may be greater than 2; they range from 1 to 2 for high porosity media such as fibrous materials and some

lines by introducing the hydraulic tortuosity τ defined by:

Tortuosity was introduced as a correction to the permeability of Kozeny's model [2] of porous media defined by the Darcy's law relating the fluidic characteristics

where v is the seepage rate of the fluid, η the viscosity coefficient of the fluid, ∇p

∇p, (1)

<sup>L</sup> : (2)

by Defects in Porous Media

Keywords: tortuosity, defects, porous media, refractive index

Fatma Graja and Claude Depollier

propagation in saturated porous media.

can refer to the paper of Ghanbarian et al. [1].

and pore space of the medium [3]:
