### 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) |
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Pages (from-to) | 2529-2540 |

Number of pages | 12 |

Journal | Physics of Fluids A |

Volume | 3 |

Issue number | 11 |

DOIs | |

State | Published - 1991 |

### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

*Physics of Fluids A*,

*3*(11), 2529-2540. https://doi.org/10.1063/1.858194