Generalized theory of acoustic propagation in porous dissipative media

Generalized theory of acoustic propagation in porous dissipative media

1962 | Maurice A. Biot
Maurice A. Biot's 1962 paper presents a generalized theory of acoustic propagation in porous dissipative media, extending previous work to include anisotropy, viscoelasticity, and solid dissipation. The theory introduces a "visco-dynamic operator" to describe the dynamic properties of the fluid in motion relative to the solid. This operator incorporates fluid inertia, viscosity, and pore geometry, and is evaluated using variational and Lagrangian methods. The paper discusses various dissipative models, including intergranular effects, small fluid-filled cracks, and microscopic air bubbles, and shows how these can be translated into specific operators within the general thermodynamic framework. The theory is applied to both low- and high-frequency ranges. In the low-frequency range, the visco-dynamic operator is derived using the Poiseuille flow model, and its form is validated against exact solutions. In the high-frequency range, a complex correction factor is introduced to account for the effects of fluid viscosity and inertia. The paper also discusses the use of scaled-model tests to evaluate the visco-dynamic operator, and shows how the operator can be derived using Lagrangian methods and normal coordinates. The paper also addresses the effects of anisotropy, solid dissipation, and thermoelastic dissipation. It shows how the visco-dynamic operator can be generalized to anisotropic media and how the theory can be extended to include the effects of surface tension and interfacial phenomena. The paper concludes with a discussion of various viscoelastic models, including those involving intergranular contact areas and fluid-filled cracks, and shows how these can be represented using operators derived from the general thermodynamic theory. The paper also discusses the effects of fluid compressibility and the importance of considering the relaxation times of different components in the porous medium.Maurice A. Biot's 1962 paper presents a generalized theory of acoustic propagation in porous dissipative media, extending previous work to include anisotropy, viscoelasticity, and solid dissipation. The theory introduces a "visco-dynamic operator" to describe the dynamic properties of the fluid in motion relative to the solid. This operator incorporates fluid inertia, viscosity, and pore geometry, and is evaluated using variational and Lagrangian methods. The paper discusses various dissipative models, including intergranular effects, small fluid-filled cracks, and microscopic air bubbles, and shows how these can be translated into specific operators within the general thermodynamic framework. The theory is applied to both low- and high-frequency ranges. In the low-frequency range, the visco-dynamic operator is derived using the Poiseuille flow model, and its form is validated against exact solutions. In the high-frequency range, a complex correction factor is introduced to account for the effects of fluid viscosity and inertia. The paper also discusses the use of scaled-model tests to evaluate the visco-dynamic operator, and shows how the operator can be derived using Lagrangian methods and normal coordinates. The paper also addresses the effects of anisotropy, solid dissipation, and thermoelastic dissipation. It shows how the visco-dynamic operator can be generalized to anisotropic media and how the theory can be extended to include the effects of surface tension and interfacial phenomena. The paper concludes with a discussion of various viscoelastic models, including those involving intergranular contact areas and fluid-filled cracks, and shows how these can be represented using operators derived from the general thermodynamic theory. The paper also discusses the effects of fluid compressibility and the importance of considering the relaxation times of different components in the porous medium.
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