Similarity of sharp-edged porous media

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Abstract

The dynamic interaction between a rigid porous structure (porosity f) and its saturating fluid is studied. From the microscopic conservation laws and constitutive relations, macroscopic equations are derived. An averaging technique proposed and discussed by authors like Lévy, Auriault and Burridge and Keller is used. The macroscopic equations are studied in the high-frequency limit. The high-frequency behaviour is characterized by the tortuosity parameter a¿ and by an effective pore radius ¿, denned previously by Johnson et al. The low frequency behaviour is characterized by the ratio of the steady-state permeability K0 and the porosity f. A similarity parameter M = 8a¿K0/f¿2 (in the two-dimensional case M = 12a¿K0/f¿2) is defined, which is approximately equal to 1 for configurations that have smooth microscopic geometries. For sharp-edged pore geometries, however, M is no longer found equal to one. Numerical computations are performed using a Schwartz-Christoffel transformation.
LanguageEnglish
Pages979-990
Number of pages12
JournalInternational Journal of Engineering Science
Volume32
Issue number6
DOIs
StatePublished - 1994

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Porous materials
Porosity
Geometry
Conservation
Fluids

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@article{0ff6ec9811144eabbf0bd60fbb9fe34f,
title = "Similarity of sharp-edged porous media",
abstract = "The dynamic interaction between a rigid porous structure (porosity f) and its saturating fluid is studied. From the microscopic conservation laws and constitutive relations, macroscopic equations are derived. An averaging technique proposed and discussed by authors like L{\'e}vy, Auriault and Burridge and Keller is used. The macroscopic equations are studied in the high-frequency limit. The high-frequency behaviour is characterized by the tortuosity parameter a¿ and by an effective pore radius ¿, denned previously by Johnson et al. The low frequency behaviour is characterized by the ratio of the steady-state permeability K0 and the porosity f. A similarity parameter M = 8a¿K0/f¿2 (in the two-dimensional case M = 12a¿K0/f¿2) is defined, which is approximately equal to 1 for configurations that have smooth microscopic geometries. For sharp-edged pore geometries, however, M is no longer found equal to one. Numerical computations are performed using a Schwartz-Christoffel transformation.",
author = "D.M.J. Smeulders and {Hassel, van}, R.R. and {Dongen, van}, M.E.H. and J.K.M. Jansen",
year = "1994",
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pages = "979--990",
journal = "International Journal of Engineering Science",
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Similarity of sharp-edged porous media. / Smeulders, D.M.J.; Hassel, van, R.R.; Dongen, van, M.E.H.; Jansen, J.K.M.

In: International Journal of Engineering Science, Vol. 32, No. 6, 1994, p. 979-990.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Similarity of sharp-edged porous media

AU - Smeulders,D.M.J.

AU - Hassel, van,R.R.

AU - Dongen, van,M.E.H.

AU - Jansen,J.K.M.

PY - 1994

Y1 - 1994

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AB - The dynamic interaction between a rigid porous structure (porosity f) and its saturating fluid is studied. From the microscopic conservation laws and constitutive relations, macroscopic equations are derived. An averaging technique proposed and discussed by authors like Lévy, Auriault and Burridge and Keller is used. The macroscopic equations are studied in the high-frequency limit. The high-frequency behaviour is characterized by the tortuosity parameter a¿ and by an effective pore radius ¿, denned previously by Johnson et al. The low frequency behaviour is characterized by the ratio of the steady-state permeability K0 and the porosity f. A similarity parameter M = 8a¿K0/f¿2 (in the two-dimensional case M = 12a¿K0/f¿2) is defined, which is approximately equal to 1 for configurations that have smooth microscopic geometries. For sharp-edged pore geometries, however, M is no longer found equal to one. Numerical computations are performed using a Schwartz-Christoffel transformation.

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ER -