Theory of dynamic permeability and tortuosity in fluid-saturated porous media

Johnson, David Linton; Koplik, Joel; Dashen, Roger

doi:10.1017/s0022112087000727

Cited by 1,820 publications

(1,519 citation statements)

References 34 publications

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“…The dynamic heat conduction phenomena in the open-cell porous media is described using the Champoux-Allard model modified by Lafarge et al 16 and the viscous dissipation from the Johnson et al model. 17 Note that these nonacoustic parameters are intercorrelated and morphology-dependent.…”

Section: A Microstructurementioning

confidence: 99%

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Effect of the microstructure closed pore content on the acoustic behavior of polyurethane foams

Doutres¹,

Atalla²,

Dong³

2011

Journal of Applied Physics

124

134

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The present paper proposes to investigate the links between the microstructure of polyurethane foams and their sound absorbing efficiency, and more specifically the effect of membranes closing the cells. This study is based on the complete characterization of 15 polyurethane foam with various cell sizes and reticulation rates (i.e., open pore content): (i) characterization of the microstructure properties (cell size C s , strut thickness t, reticulation rate R w …) from SEM pictures, (ii) characterization of nonacoustic parameters (porosity U, airflow resistivity r, tortuosity a 1 …) from direct and indirect methods. Existing analytical links between microstructure properties and nonacoustic parameters are first applied to fully reticulated materials. Then, they are improved empirically to account for the presence of the closed pore content. The proposed expressions associated to the Johnson-Champoux-Allard porous model allow a good estimation of the sound absorbing behavior of all polyurethane foams, fully reticulated or not. This paper also demonstrates the important effect of the presence of cell membranes: increase of the airflow resistivity, tortuosity, and the ratio between the thermal and viscous characteristic lengths while decreasing these two characteristic lengths. Thus, the sound absorption efficiency at low frequencies is improved but can be worsened in some higher frequency bands.

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Section: A Microstructurementioning

confidence: 99%

“…8(c) (see crosses, calculated here for struts having triangular concave cross-section shape). Note that the viscous characteristic length K may also be derived from the analytical study of the sound propagation in a pore channel 17 and given by…”

Section: Viscous Length Kmentioning

confidence: 99%

Effect of the microstructure closed pore content on the acoustic behavior of polyurethane foams

Doutres¹,

Atalla²,

Dong³

2011

Journal of Applied Physics

124

134

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“…R is the inverse of the second rank intrinsic permeability tensor K and it represents dissipation phenomena due to viscous losses at low frequencies of fluid motion. The conception of K was extended to take into account the change in fluid flow regime occurring between low and high frequencies of wave propagation (Johnson et al, 1987) K ij ðxÞ ¼ j 0 1 À 2 J 1 ðdvÞ dvJ 0 ðdvÞ…”

Section: Fabric Dependence Of Tensors Appearing In the Poroelastmentioning

confidence: 99%

Fabric dependence of quasi-waves in anisotropic porous media

Cardoso

Cowin

2011

The Journal of the Acoustical Society of America

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Assessment of bone loss and osteoporosis by ultrasound systems is based on the speed of sound and broadband ultrasound attenuation of a single wave. However, the existence of a second wave in cancellous bone has been reported and its existence is an unequivocal signature of poroelastic media. To account for the fact that ultrasound is sensitive to microarchitecture as well as bone mineral density (BMD), a fabric-dependent anisotropic poroelastic wave propagation theory was recently developed for pure wave modes propagating along a plane of symmetry in an anisotropic medium. Key to this development was the inclusion of the fabric tensor-a quantitative stereological measure of the degree of structural anisotropy of bone-into the linear poroelasticity theory. In the present study, this framework is extended to the propagation of mixed wave modes along an arbitrary direction in anisotropic porous media called quasi-waves. It was found that differences between phase and group velocities are due to the anisotropy of the bone microarchitecture, and that the experimental wave velocities are more accurately predicted by the poroelastic model when the fabric tensor variable is taken into account. This poroelastic wave propagation theory represents an alternative for bone quality assessment beyond BMD.

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“…G is the frame shear modulus and K U is the undrained bulk modulus. ρ is the bulk density, ρ f is the fluid modulus, and the parameter ρ % is defined via fluid viscosity η f and the frequency-dependent permeability k(ω) (e.g., Johnson et al, 1987). Definitions of C and M and their relationships to other parameters can be found in standard poroelasticity literature (e.g., Pride, 2003).…”

Section: Theorymentioning

confidence: 99%

Poroelastic modeling of seismic boundary conditions across a fracture

Schoenberg

Nakagawa

2006

SEG Technical Program Expanded Abstracts 2006

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SummaryA fracture within a porous background is modeled as a thin porous layer with increased compliance and finite permeability. For small layer thickness, a set of boundary conditions can be derived that relate particle velocity and stress across a fracture, induced by incident poroelastic waves. These boundary conditions are given via phenomenological parameters that can be used to examine and characterize the seismic response of a fracture. One of these parameters, here it is called membrane permeability, is shown through several examples to control the scattering amplitude of the slow P waves for very low-permeability fractures, which in turn controls the intrinsic attenuation of the waves.

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Theory of dynamic permeability and tortuosity in fluid-saturated porous media

Cited by 1,820 publications

References 34 publications

Effect of the microstructure closed pore content on the acoustic behavior of polyurethane foams

Effect of the microstructure closed pore content on the acoustic behavior of polyurethane foams

Fabric dependence of quasi-waves in anisotropic porous media

Poroelastic modeling of seismic boundary conditions across a fracture

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