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Expansion of a high‐pressure gas sphere in a porous medium II: Fluid compressible

 

作者: David Epstein,  

 

期刊: The Journal of the Acoustical Society of America  (AIP Available online 1976)
卷期: Volume 59, issue 1  

页码: 40-45

 

ISSN:0001-4966

 

年代: 1976

 

DOI:10.1121/1.380823

 

出版商: Acoustical Society of America

 

关键词: 3060;2560

 

数据来源: AIP

 

摘要:

The work presented in an earlier paper [D. Epstein, J. Geophyos. Res. 72, 3701–3710 (1967)] on the expansion of a high‐pressure gas bubble in a fluid‐saturated porous medium, with the fluid treated as incompressible, is extended by treating the fluid as slightly compressible. Two limiting cases are considered: If the particulate matter is carried along with the fluid, the porous medium acts as a dense liquid, with parameters determined by simple functions of the density and compressibility of the fluid and solid particles, and the usual equations of motion apply. However, if the relative velocity of the fluid with respect to the solid is essentially equal to the fluid velocity, the motion is assumed to be governed by a compressible, generalized Darcy equation. From this equation a pair of integrodifferential equations for the bubble radius as a function of time are derived. The form of the radius‐time curve depends on a nondimensional resistance factorm? = (1/2) β?/c, a combination of quantities characteristic of the fluid, the porous medium, and the gas bubble. The transition regime between ideal and Darcy flow is determined as a function of this parameter. For very small values, the bubble pulsates about the equilibrium raius ?. With increasingm?, the ratio of radiated acoustic energy to energy dissipated decreases, until the Darcy limit is reached, where bubble pulsation no longer occurs, and the expansion radius approaches ? monotonically.Subject Classification: [43]30.60; [43]25.60.

 

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