Diffusion in anisotropic porous media

An experimental system was constructed in order to measure the two distinct components of the effective diffusivity tensor in transversely isotropic, unconsolidated porous media. Measurements were made for porous media consisting of glass spheres, mica particles, and disks made from mylar sheets. Both the particle geometry and the void fraction of the porous media were determined experimentally, and theoretical calculations for the two components of the effective diffusivity tensor were carried out. The comparison between theory and experiment clearly indicates that the void fraction and particle geometry are insufficient to characterize the process of diffusion in anisotropic porous media.Roman Letters A interfacial area between - and -phases for the macroscopic system, m² - A_e area of entrances and exits of the -phase for the macroscopic system, m² - A interfacial area contained within the averaging volume, m² - a characteristic length of a particle, m - b average thickness of a particle, m - c_A concentration of species A, moles/m³ - c_o reference concentration of species A, moles/m³ - c_A intrinsic phase average concentration of species A, moles/m³ - c_a c_A–c_A, spatial deviation concentration of species A, moles/m³ - C c_A/c₀, dimensionless concentration of species A - binary molecular diffusion coefficient, m²/s - D_eff effective diffusivity tensor, m²/s - D_xx component of the effective diffusivity tensor associated with diffusion parallel to the bedding plane, m²/s - D_yy component of the effective diffusivity tensor associated with diffusion perpendicular to the bedding plane, m²/s - D_eff effective diffusivity for isotropic systems, m₂/s - f vector field that maps c_A on to c_a, m - h depth of the mixing chamber, m