Tortuosity Perturbations Induced by Defects in Porous Media

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 propagation in saturated porous media

Magnetic Field Produced by a Tile Permanent Magnet Whose Polarization is both Uniform and Tangential

pages 1-20International audienceThis paper presents the exact 3D calculation of the magnetic field produced by a tile permanent magnet whose polarization is both tangential and uniform. Such a calculation is useful for optimizing magnetic couplings or for calculating the magnetic field produced by alternate magnet structures. For example, our 3D expressions can be used for calculating the magnetic field produced by a Halbach structure. All our expressions are determined by using the coulombian model. This exact analytical approach has always proved its accuracy and its usefulness. As a consequence, the tile permanent magnet considered is represented by using the fictitious magnetic pole densities that are located on the faces of the magnet. In addition, no simplifying assumptions are taken into account for calculating the three magnetic field components. Consequently, the expressions obtained are valid inside and outside of the tile permanent magnet, whatever its dimensions. Such an approach allows us to realize easily parametric studies. To our knowledge, this calculation appears for the first time in the literature

Ultrasonic waves Reflected at Oblique Incidence by Porous Rigid Medium.

International audienceAn ultrasonic reflected wave at oblique incidence by porous medium with rigid frames is considered using equivalent fluid model. The viscous and thermal losses of the medium are described by two susceptibility kernels which depend on the viscous and thermal characteristic lengths. Analytical derivation of reflection coefficient is given in frequency domain. The simulated reflected wave is obtained at time domain by convolution between the reflected operator and the incident field. Experimental results for plastic foam samples of air-saturated porous media are given and compared with theoretical prediction

Transient Acoustic Wave Propagation in Porous Media

International audienceTransient Acoustic Wave Propagation in Porous Medi

Ultrasonic propagation of reflected waves in cancellous bone: Application of Biot theory.

International audienceAn ultrasonic propagation in cancellous bone is considered using the Biot theory modified by the Johnson et al. Numerical simulations of reflected waves in the time domain are worked out by varying the modified Biot parameters. The sensitivity of different mechanical parameters : Young modulus and the Poisson ratio of the skeletal frame and physical parameters , porosity , tortuosity and viscous characteristic length are studied showing their effect on the reflected ultrasonic waves of the bone sample. The sensitivity of the modified Biot parameters with respect to the reflected wave depends strongly on the coupling between the solid and fluid phases of the cancellous bone. We show from these simulations that some parameters such as porosity and tortuosity play an important role on reflected wave ; the remaining parameters have low sensitivity compared with the porosity and tortuosity. Experimental results for reflected waves by human cancellous bone samples are given and compared with theoretical predictions

Determination of the flow resistivity and thickness of porous materials with rigid frames via transmitted waves at Darcy's regime

International audienceAn acoustic method is proposed for measuring the flow resistivity and the thickness of air-saturated porous materials. The conventional methods [14, 16, 17] for the measurement of the flow resistivity (or the viscous permeability) require the prior knowledge of the porosity. The method presented in this work is based on a temporal model of the direct problem in which a simplified expression (independent of frequency and porosity) of the transmission coefficient at the Darcy’s regime (low frequency range) is established, this expression depends only on the viscous permeability (or the flow resistivity) and the thickness of a porous sample. The inverse problem is solved based on the leastsquare numerical method using experimental transmitted wave in time domain. Tests are performed using two samples of different thicknesses to same industrial plastic foam, thereby enabling the determination the thickness and flow resistivity of foam plastic. This method has the advantage of being simple, fast and efficient

Characterization of rigid porous medium via ultrasonic reflected waves at oblique incidence

International audienceIn this paper, an enhanced method is proposed for measuring porosity, tortuosity, viscous and thermal characteristic length of porous materials having a rigid frame via reflected ultrasonic waves at oblique incidence using the equivalent fluid model. The advantage of the proposed method is that the four parameters are determined simultaneously just using reflected experimental waves for a porous material saturated by air. The inverse problem is solved based on the least-square numerical method using experimental reflected waves in time domain. Tests are performed using industrial plastic foams. Experimental and numerical validation results of this method are presented

Verification of Kramers-Kronig relationship in porous materials having a rigid frame

The propagation of acoustic waves in porous materials having a rigid frame is well described by several models. A doubt about the causality of these models has been raised recently in the literature. A verification of the causality of these models is studied in this paper using the Kramers–Kronig dispersion relations adapted to the frequency power law dependence of the attenuation. It is shown that these models are causal in the high- and low-frequency range. A time domain wave equation and time-causal theory have been treated

Estimation des paramètres d'un sinus glissant par Transformé de Fourier Fractionnaire

- La Transformée de Fourier Fractionnaire (notée FRT), introduite par Namias en 1980, permet une analyse des signaux dans des domaines intermédiaires entre les domaines temporel et fréquentiel. Suivant un angle donné du plan temps fréquence, elle décompose le signal sur une base orthogonale de sinus glissants. Elle est donc adaptée à l'analyse de signaux multicomposantes formés de sinus glissants et permet une estimation robuste au bruit de la pente et de l'offset qui sont les deux paramètres essentiels des sinus glissants