Flow, conduction, and a characteristic length in periodic bicontinuous porous media

The Stokes equation system and Ohm’s law were solved within periodic bicontinuous porous media of simple-cubic (sc) symmetry. The results were used to test the permeability scaling law proposed by Johnson, Koplik, and Schwartz [Phys. Rev. Lett. 57, 2564 (1986)], which uses a length parameter Λ to relate the Darcy permeability k and formation factor F. We found that the scaling law M==8Fk/${\mathrm{\Lambda }}^2$≊1 was obeyed by many bicontinuous porous media within the sc crystallographic family. However, this is not valid when the constrictions in the porous media approach an orificelike aspect: The scaling law is not universal.