Rigorous link between fluid permeability, electrical conductivity, and relaxation times for transport in porous media

Marco Avellaneda, S. Torquato

Research output: Contribution to journalArticle

Abstract

A rigorous expression is derived that relates exactly the static fluid permeability k for flow through porous media to the electrical formation factor F (inverse of the dimensionless effective conductivity) and an effective length parameter L, i.e., k = L2/8F. This length parameter involves a certain average of the eigenvalues of the Stokes operator and reflects information about electrical and momentum transport. From the exact relation for k, a rigorous upper bound follows in terms of the principal viscous relation time Θ1 (proportional to the inverse of the smallest eigenvalue): k≤vΘ1/F, where v is the kinematic viscosity. It is also demonstrated that vΘ1≤DT1, where T 1 is the diffusion relaxation time for the analogous scalar diffusion problem and D is the diffusion coefficient. Therefore, one also has the alternative bound k≤DT1/F. The latter expression relates the fluid permeability on the one hand to purely diffusional parameters on the other. Finally, using the exact relation for the permeability, a derivation of the approximate relation k≃Λ2/8F postulated by Johnson et al. [Phys. Rev. Lett. 57, 2564 (1986)] is given.

Original languageEnglish (US)
Pages (from-to)2529-2540
Number of pages12
JournalPhysics of Fluids A
Volume3
Issue number11
StatePublished - 1991

Fingerprint

Relaxation time
Porous materials
permeability
relaxation time
electrical resistivity
Fluids
fluids
eigenvalues
Momentum
kinematics
derivation
diffusion coefficient
Viscosity
viscosity
scalars
momentum
operators
conductivity
Electric Conductivity

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

Rigorous link between fluid permeability, electrical conductivity, and relaxation times for transport in porous media. / Avellaneda, Marco; Torquato, S.

In: Physics of Fluids A, Vol. 3, No. 11, 1991, p. 2529-2540.

Research output: Contribution to journalArticle

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