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Article: Flows through porous media: A theoretical development at macroscale

TitleFlows through porous media: A theoretical development at macroscale
Authors
KeywordsConvective inertia
First principles
Generalized Darcy's law
Issue Date2000
PublisherSpringer Verlag Dordrecht. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0169-3913
Citation
Transport In Porous Media, 2000, v. 39 n. 1, p. 1-24 How to Cite?
AbstractGood separation of microscale with macroscale leads to the existence of a macroscale description of flows through porous media. Such a macroscale description is developed in a systematic and rigorous way through exploiting necessary and sufficient condition for three fundamental principles regarding physical relations: principle of frame-indifference, principle of observer trans-formation and second law of thermodynamics. This leads to a generalized Darcy's law, an algebraic nublap - v - L relation at macroscale with effects of G and M reflected in three material coefficients. Here nublap is piezometric pressure gradient. G denotes macroscale geometric properties of the medium. M stands for thermophysical (material) properties of the medium and fluids. v is the fluid velocity vector relative to the solid. L is the velocity gradient tensor of the fluid velocity u. Such a generalized relation can be used for both low and high flow rates. Also developed in the present work is a linear theory to simplify the works of determining effects of G and M. It is found that nublap cannot depend on fluid velocity u itself. L affects nublap only through its symmetric part (velocity strain tensor D). The symmetry and positive-definiteness of H, the inverse of permeability tensor, follow logically from the three fundamental principles. Eigenvectors of H are the same as those of D with corresponding eigenvalues related to those of D through a quadratic relation. Six scalars formed by v and D (rather than the Reynolds number) are found to be scalars characterizing convective inertia effects. The incompressibility is found to be responsible for the vanishing of the first correction term to the classical Darcy's law as the Reynolds number tends to zero. The vanishing of D forms the applicability condition of classical Darcy's law. This requires u to be vanished, uniform, or in rigid body rotation. | Good separation of microscale with macroscale leads to the existence of a macroscale description of flows through porous media. Such a macroscale description is developed in a systematic and rigorous way through exploiting necessary and sufficient condition for three fundamental principles regarding physical relations: principle of frame-indifference, principle of observer transformation and second law of thermodynamics. This leads to a generalized Darcy's law, an algebraic ▽ p - v - L relation at macroscale with effects of G and M reflected in three material coefficients. Here ▽p is piezometric pressure gradient. G denotes macroscale geometric properties of the medium. M stands for thermophysical (material) properties of the medium and fluids. v is the fluid velocity vector relative to the solid. L is the velocity gradient tensor of the fluid velocity u. Such a generalized relation can be used for both low and high flow rates. Also developed in the present work is a linear theory to simplify the works of determining effects of G and M. It is found that ▽p cannot depend on fluid velocity u itself. L affects ▽p only through its symmetric part (velocity strain tensor D). The symmetry and positive-definiteness of H, the inverse of permeability tensor, follow logically from the three fundamental principles. Eigenvectors of H are the same as those of D with corresponding eigenvalues related to those of D through a quadratic relation. Six scalars formed by v and D (rather than the Reynolds number) are found to be scalars characterizing convective inertia effects. The incompressibility is found to be responsible for the vanishing of the first correction term to the classical Darcy's law as the Reynolds number tends to zero. The vanishing of D forms the applicability condition of classical Darcy's law. This requires u to be vanished, uniform, or in rigid body rotation.
Persistent Identifierhttp://hdl.handle.net/10722/75582
ISSN
2015 Impact Factor: 1.653
2015 SCImago Journal Rankings: 0.759
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorWang, Len_HK
dc.date.accessioned2010-09-06T07:12:35Z-
dc.date.available2010-09-06T07:12:35Z-
dc.date.issued2000en_HK
dc.identifier.citationTransport In Porous Media, 2000, v. 39 n. 1, p. 1-24en_HK
dc.identifier.issn0169-3913en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75582-
dc.description.abstractGood separation of microscale with macroscale leads to the existence of a macroscale description of flows through porous media. Such a macroscale description is developed in a systematic and rigorous way through exploiting necessary and sufficient condition for three fundamental principles regarding physical relations: principle of frame-indifference, principle of observer trans-formation and second law of thermodynamics. This leads to a generalized Darcy's law, an algebraic nublap - v - L relation at macroscale with effects of G and M reflected in three material coefficients. Here nublap is piezometric pressure gradient. G denotes macroscale geometric properties of the medium. M stands for thermophysical (material) properties of the medium and fluids. v is the fluid velocity vector relative to the solid. L is the velocity gradient tensor of the fluid velocity u. Such a generalized relation can be used for both low and high flow rates. Also developed in the present work is a linear theory to simplify the works of determining effects of G and M. It is found that nublap cannot depend on fluid velocity u itself. L affects nublap only through its symmetric part (velocity strain tensor D). The symmetry and positive-definiteness of H, the inverse of permeability tensor, follow logically from the three fundamental principles. Eigenvectors of H are the same as those of D with corresponding eigenvalues related to those of D through a quadratic relation. Six scalars formed by v and D (rather than the Reynolds number) are found to be scalars characterizing convective inertia effects. The incompressibility is found to be responsible for the vanishing of the first correction term to the classical Darcy's law as the Reynolds number tends to zero. The vanishing of D forms the applicability condition of classical Darcy's law. This requires u to be vanished, uniform, or in rigid body rotation. | Good separation of microscale with macroscale leads to the existence of a macroscale description of flows through porous media. Such a macroscale description is developed in a systematic and rigorous way through exploiting necessary and sufficient condition for three fundamental principles regarding physical relations: principle of frame-indifference, principle of observer transformation and second law of thermodynamics. This leads to a generalized Darcy's law, an algebraic ▽ p - v - L relation at macroscale with effects of G and M reflected in three material coefficients. Here ▽p is piezometric pressure gradient. G denotes macroscale geometric properties of the medium. M stands for thermophysical (material) properties of the medium and fluids. v is the fluid velocity vector relative to the solid. L is the velocity gradient tensor of the fluid velocity u. Such a generalized relation can be used for both low and high flow rates. Also developed in the present work is a linear theory to simplify the works of determining effects of G and M. It is found that ▽p cannot depend on fluid velocity u itself. L affects ▽p only through its symmetric part (velocity strain tensor D). The symmetry and positive-definiteness of H, the inverse of permeability tensor, follow logically from the three fundamental principles. Eigenvectors of H are the same as those of D with corresponding eigenvalues related to those of D through a quadratic relation. Six scalars formed by v and D (rather than the Reynolds number) are found to be scalars characterizing convective inertia effects. The incompressibility is found to be responsible for the vanishing of the first correction term to the classical Darcy's law as the Reynolds number tends to zero. The vanishing of D forms the applicability condition of classical Darcy's law. This requires u to be vanished, uniform, or in rigid body rotation.en_HK
dc.languageengen_HK
dc.publisherSpringer Verlag Dordrecht. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0169-3913en_HK
dc.relation.ispartofTransport in Porous Mediaen_HK
dc.subjectConvective inertiaen_HK
dc.subjectFirst principlesen_HK
dc.subjectGeneralized Darcy's lawen_HK
dc.titleFlows through porous media: A theoretical development at macroscaleen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0169-3913&volume=39&spage=1&epage=24&date=2000&atitle=Flows+through+porous+media:+a+theoretical+development+at+macroscaleen_HK
dc.identifier.emailWang, L:lqwang@hkucc.hku.hken_HK
dc.identifier.authorityWang, L=rp00184en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1023/A:1006647505709en_HK
dc.identifier.scopuseid_2-s2.0-0034003899en_HK
dc.identifier.hkuros62961en_HK
dc.identifier.hkuros49085-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0034003899&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume39en_HK
dc.identifier.issue1en_HK
dc.identifier.spage1en_HK
dc.identifier.epage24en_HK
dc.identifier.isiWOS:000085449500001-
dc.publisher.placeNetherlandsen_HK
dc.identifier.scopusauthoridWang, L=35235288500en_HK

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