### 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 = L^{2}/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 Θ_{1} (proportional to the inverse of the smallest eigenvalue): k≤vΘ_{1}/F, where v is the kinematic viscosity. It is also demonstrated that vΘ_{1}≤DT_{1}, 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≤DT_{1}/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≃Λ^{2}/8F postulated by Johnson et al. [Phys. Rev. Lett. 57, 2564 (1986)] is given.

Original language | English (US) |
---|---|

Pages (from-to) | 2529-2540 |

Number of pages | 12 |

Journal | Physics of Fluids A |

Volume | 3 |

Issue number | 11 |

State | Published - 1991 |

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### ASJC Scopus subject areas

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

### Cite this

*Physics of Fluids A*,

*3*(11), 2529-2540.

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

Research output: Contribution to journal › Article

*Physics of Fluids A*, vol. 3, no. 11, pp. 2529-2540.

}

TY - JOUR

T1 - Rigorous link between fluid permeability, electrical conductivity, and relaxation times for transport in porous media

AU - Avellaneda, Marco

AU - Torquato, S.

PY - 1991

Y1 - 1991

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=0000070953&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0000070953

VL - 3

SP - 2529

EP - 2540

JO - Physics of fluids. A, Fluid dynamics

JF - Physics of fluids. A, Fluid dynamics

SN - 0899-8213

IS - 11

ER -